Most ways a complex system could be run do not work.
The ones that do occupy small, bounded regions of the settings available, from atomic nuclei and planetary orbits to ecosystems, companies and AI agents. Staying inside a region costs continuous effort, and whatever pays that cost becomes the weak point.
Persistence proves nothing. Only the response to a push shows a system is stable.
The theory is also written up as a paper, Islands of Stability, a draft preprint at bitandbeing.com/research.
The idea
a diagramthe logo
The site's logo: two settings of a system, the point where it holds, and rings of depth out to the shore. Proposition 1: most settings do not work. Proposition 2: only a push shows how deep an island is. Proposition 3: for islands of the same depth, age says nothing about the time left.
Rules for a technology whose frontier moves every few months: how long a compute record lasts, against the years the EU's AI Act took to make. Proposition 6's ratio, with real numbers.
The asteroid belt from 895,910 real orbits: gaps and islands at Jupiter's resonances, and a test of where proposition 3 stops applying, which ran twice: the first run was invalid, and the corrected run was void because its own control failed.
The ice-age flips in Greenland's ice: did the cold spells end at random or on a clock? Two tests on the real record, run once. The cold spells look memoryless, and there was no clock.
23,191 marine genera from the Paleobiology Database: Van Valen's law of constant extinction, the mass extinctions, and a re-run of published work, under rules fixed in advance, that kills proposition 3 here.
US business cycles since 1854, the calm before 2008, a currency peg you can run to its end, and the incomes of 141 countries since 1950. A test of expansions in 42 countries, run once. Its verdict is unresolved.
The US death rate by age, the glucose tolerance test as a push that finds what watching misses, and herd immunity as an island paid for by every birth cohort. A test of the measles runway, country by country, run once. Its verdict is unresolved.
Supercooled water and diamond: states that persist without being stable. Real droplets freezing in a wind tunnel, and a tray of droplets to freeze in your browser, where frailty imitates memory.
Each domain's figure is drawn, simplified, from its page's data. All 12 domains →
This site states that idea precisely enough to be wrong, and runs one experiment that could show it is. It is named for the island of long-lived superheavy nuclei that physics predicted decades before anyone measured its shore. The principle is meant to hold across the sciences. The first instrument measures AI agents only, and its results say nothing on their own about the other domains.
State of the evidenceLast change 2026-10-08 · specification v3.0: the fossil-record re-run entered
Propositions
6
2 measured, 1 tested in three sciences, 1 tested in one, 2 framing
Measurements
1 snapshot
18,720 runs on three local models, plus 18,000 noise-floor runs
Forecasts
4 open
With probabilities, 0 resolved, 3 more listed, unscored
Cases
5 drafts
1 control candidate, 2 controls required
Next resolution day
2027-09
Annual
The idea in plain words
Six propositions, and where each one stands.
The Theory page states each one precisely, names what would kill it, and defines three technical senses of ‘island’. Every use on this site says which sense it means.
If stability is local, ‘it works’ is incomplete information.
Adding a dependency, scaling up, changing the environment, or reorganizing can move a system across a boundary even when each step looks reasonable. The useful questions become where a system works, what keeps it there, and how far it sits from an edge.
One framing proposition sharpens this for the present moment: AI is shortening how long each business regime lasts, while review, compliance and hiring move at the old speed. That is the motivation for the research, not a result of it.
The idea did not start with companies or computers.
Wherever a system can be set many ways, stable behavior tends to hold only in bounded regions, with instability between them, and the regions can shift. A few places where science has mapped them:
01real datareference case
Nuclear physics
The name’s origin. Superheavy nuclei are predicted to live far longer inside a small region of proton and neutron numbers, an island beyond the sea of fast decay. The chart of every known nucleus, from the published table.
Trojan asteroids share Jupiter’s orbit around two stable points, and resonances clear the Kirkwood gaps. Measured from 895,910 real orbits. On the same chart, stars that burn to stay stable beside ones that cost nothing.
Diamond is metastable at the surface of the Earth: it persists only because the barrier to becoming graphite is high. Supercooled water does the same, until a speck of ice arrives. Real droplets freezing in a wind tunnel show the wait.
A shallow lake can stay clear or turn turbid under the same nutrient load, and switch abruptly when pushed past a threshold. The standard lake model runs in your browser. Push it and watch.
Van Valen’s 1973 law says a genus’s age tells you nothing about its chance of dying out: proposition 3, fifty years early. 23,191 fossil genera test it. Published work finds it fails where depth is measured, and a re-run of that work under fixed rules kills it here.
A slope holds until rain pushes it past a threshold. In the last ice age, Greenland’s climate flipped between two states again and again. Two tests asked whether the cold spells ended at random or on a clock, and found no clock.
Companies pass through temporary equilibria. What holds one in place becomes, in time, the thing that fails. Census data show young firms dying far more often than old ones, and why that alone cannot say whether firms grow safer.
Booms end, currency pegs break, and a few countries cross from poor to rich. US business cycles since 1854, a peg you can run to its end, and a test of expansions in 42 countries, run once.
A life is not memoryless: the death rate by age is a bathtub. A glucose drink finds diabetes that fasting tests miss, and herd immunity is an island paid for by every birth cohort. A test of the measles runway, country by country, ran once, and its verdict is unresolved.
Rules for a technology whose frontier moves every few months. How long a compute record lasts, against the years the EU's AI Act took to make: proposition 6's ratio, with real numbers.
Each domain needs its own instrument. A result in one says nothing on its own about another. The site keeps the domains apart and names the one each claim is about. Where each proposition stands in each domain →
What is here
01
The Theory
Six propositions, each with its prior owners, its strongest objection, and the observation that would kill it. Two of the six are framing propositions with no test yet, and say so. Versioned. The changelog records survivals as well as revisions.
Sweep an AI agent across two dials, inject faults, and see whether its working region is a band with an edge or a continent with a slope. Snapshot 1, on three local models: a continent with a slope.
Five draft cases: systems that were called stable and were not, each with the evidence that existed before the failure. Plus four open forecasts with probabilities and named resolvers.
Noise floor measured: 18,000 runs, every identical rerun reproduced exactly
27–29 Sep 2026Snapshot · done
Snapshot 1 swept and analyzed: 18,720 runs on three local models
30 Sep 2026Deposit · done
Four more pre-registrations and snapshot 1's results bundle deposited on Zenodo
30 Sep 2026Tests · done
The lake, orbits, ice-age and expansions tests run once, after their deposits
30 Sep 2026Tests · done
The corrected orbits test (void, its control failed) and the measles test of proposition 4 (unresolved), each deposited and run once. Specification v2.0
The evolution re-run of Finnegan, Payne and Wang (2008), run once: killed. Specification v3.0
Oct 2026Publication · planned
Newsletter issue 1: snapshot 1 and the four tests
Dec 2026Case · planned
Case 1 coded, with two controls
Sep 2027Forecast resolution · planned
Resolution day 1
Budget. Snapshot 1 ran on a local workstation GPU, about two GPU days for the sweep and the noise floor, at no API cost. An exploratory trial of five larger models through OpenRouter, outside the snapshot, cost about 2 dollars.
Launch conditions
5 / 7
The draft banner at the top of every page stays until all seven hold.
✓
The noise floor and rerun jitter measured and published.
met · measured 26–27 Sep 2026, published 30 Sep 2026 in the results bundle
✓
The pre-registration deposited with a DOI.
met · 10.5281/zenodo.22982434, 26 Sep 2026
✓
The objection intake live, as GitHub issues, so the version rule has an input.
One case fully sourced, and two controls coded blind to outcome by two independent coders, with an agreement statistic published.
not met · case 1 due Dec 2026
✓
The harness repository public, before snapshot 1.
met late · public since 30 Sep 2026, after snapshot 1, not before it. The lock deposited before the runs identifies the exact code that ran, and the code on the main branch still matches it
Two named human reviewers from outside AI have filed objections, accepted or not.
not met
✓
The changelog RSS feed live, and full citations with DOIs for every prior owner.
Not a blog, not a score for your company, not a certification, not a tracker that needs weekly updates, and not a promise that islands exist. Snapshot 1 found a continent for all three models it measured, with no upper tool edge between two and six tools, and says so on the Map page.
The newsletter
A new snapshot, a new case, or a resolved forecast. Nothing else.
Robert Encarnação. Twenty-five years in technology, AI transformation programs at the executive level. Essays live at bitandbeing.com and consulting at encarnacao.net. What lives here is the part that can lose.
Objections and corrections are welcome. Accepted ones move the version number and are attributed.
Draft site. Snapshot 1 of the AI-agent map is measured, and tests in five other sciences have verdicts.5 of 7 launch conditions met →
Six propositions about stability, each with its prior owners, its strongest objection, and the observation that would kill it.
v3.0, 8 October 20261 measurement: snapshot 1, agent domain0 accepted external objections4 propositions with an instrument or a deposited test
In brief
Most ways a complex system could be run do not work. The ones that do sit in small, bounded regions of the settings available: islands of stability. Staying on one often takes continuous effort, and whatever pays for it becomes the weak point. This page states the idea as six propositions, each precise enough to be shown wrong, and records every change to them.
The six propositions, in plain words
Sparsity. Working configurations are rare and bounded. Most of the space around them does not work. snapshot 1 measured
The evidence rule. Looking stable is not evidence. Only recovery from a push shows an island is there. snapshot 1 measured
Exit statistics. For islands of the same depth, age says nothing about how long they have left. tests run
Cost. Where stability is held by a flow, it is paid for continuously, and whatever pays for it becomes the weak point. test run
Transit. Survival is decided in the crossing, not on either island. framing, not testable yet
The era ratio. If the world changes faster than you can reconfigure, no map helps: get faster, park on the widest island, or hibernate. framing, not testable yet
Where the evidence stands
Measured once, in AI agents. Snapshot 1 of the Map found no edge between two and six tools where an agent starts to fail. Its working region is a slope along the failure rate, not a band with an edge: proposition 1's test came out restricted for two models and below resolution for the third. Proposition 2's test survived for all three.
Killed in one domain. The re-run of published work on fossil genera, under rules fixed in advance, killed proposition 3 in the fossil record: with geographic range and species richness held fixed, a genus's chance of extinction still fell with its age, as the evolution page shows. What this means for the proposition's wording is the author's decision, pending. No other registered test has killed a proposition.
Not yet testable. Propositions 5 and 6 frame the others. They are not counted until they have an instrument.
How this page is organized
Index: the six propositions in one table, with their instruments and status.
Six propositions. Propositions 1 and 2 have been measured once, in the agent domain. Propositions 2 and 3 also have tests in ecology, astronomy, climate and economics, deposited and run on 30 September 2026. Their verdicts are on those pages, except in astronomy, where neither of two runs counts: the first was invalid, and the corrected run's control failed. Proposition 4's first test, on measles, ran on 30 September 2026 and came out unresolved. It is illustrated in some sciences and broken in others. Propositions 5 and 6 are framing propositions and do not count toward the tally. Proposition 6's candidate instrument is built and demonstrated, with its series still to be named.
Number
Proposition
Plain meaning
Sense
Instrument
Status
Anchor
P1
Sparsity
Working configurations are rare and bounded. Most of the space around them does not work.
For islands of the same depth, age says nothing about how long they have left.
Basin-island
Tests run on 30 September 2026: the lake's E3 (memory survives, depth unresolved, warning survives), the ice-age cold spells (C1 survives, C2 no clock) and expansions in 42 countries (X1 unresolved). On 8 October 2026, the fossil-record re-run of Finnegan, Payne and Wang (2008): killed. The orbits' stickiness test ran twice, and neither run counts: r1 invalid, r2 void. A long-horizon harness variant is planned
Seaborg's sense. A region on a chart whose occupants outlast their neighbors. A convention about relative lifetime, not a dynamical regime.
Basin-island
An attractor with a sticky boundary in a dissipative system. The KAM picture transfers only as chaotic saddles and long transients.
Grid-island
A subsystem that keeps running when its connection to the whole is cut. The power engineer's islanding.
Every object on this site uses exactly one sense and says which.
Admissibility rule. An island claim that states no cost line and no fragility line is a claim about a ghost, and is not admitted.
Cross-domain rule. A proposition moves between domains, from nuclear physics, astronomy and chemistry to ecology, climate, organizations, agent systems and infrastructure, only when the mathematical or causal structure transfers, not merely the vocabulary. Each proposition below names the domain it is currently stated for, and the ledger on the Sciences page records where each one stands in each domain.
Economics. Economics holds prior owners for five of the six propositions, from Milgrom and Roberts on complementarities to Minsky on stability that destabilizes, and one candidate instrument, Hamilton’s Markov-switching estimate of regime duration. They are listed under each proposition, under Sources and objections. Lucas’s 1972 islands model is a name collision, not a precedent: it is about information frictions.
The six propositions
Each block gives the domain the proposition is stated for, the form in which it can be tested, the observation that would kill it, the instrument, the instrument's status, and one row on what follows if it holds, labeled as the implication of an unmeasured claim. The sense of island it uses, its prior owners, its economics precedents, and the strongest objection on record sit under "Sources and objections" in each block, collapsed by default and opened for print or when the address ends in ?expand. The plain-language line for each proposition is in the index above. Each block has a versioned anchor, for example theory.html#v0.2-p3, so that essays and decks can cite the exact wording they read. Where each proposition carries over, only resembles, or breaks in other sciences is recorded in the ledger on the Sciences page, not here. This page changes when an instrument or a test's status changes.
snapshot 1 measured the instrument has run under deposited rules, and the result bears on the proposition in one domainpre-registration drafted, deposit pending instrument written and dated, protocol frozen locally, not yet runno instrument yet nothing to runframing, not testable yet no instrument, and not counted toward the tallyThe measurement count is one snapshot, in one domain. Tests in four more domains were deposited and run on 30 September 2026.
Among the configurations organizations actually attempt, the viable region is a small fraction, and it shrinks as size, coupling density and coupling strength grow. The remainder is sea, not a neighboring basin. In configuration space, sea means no viable regime exists at that setting. Scale bought without decoupling moves a program from island to sea.
Stated for
Organizations in the statement. The principle is meant to hold across the sciences. The Map tests one reading in one domain, AI agents.
Testable form
In the agent domain, the Map's test 1: a logistic regression of success on tools, tools squared and failure rate, deposited in pre-registration r4. It survives if the curve bends down, the peak lies inside two to six tools, and success falls from the peak to six tools by more than chance. It is restricted if that drop is shown to be under 15 points. The test is narrower than the proposition, and the organizational reading is not tested by it.
Killed by
Most attempted configurations viable. A tools-squared term that is not negative, a peak outside the tested range, or a drop at the upper edge that stays inside the per-cell intervals.
Instrument
The Map (pre-registration r4, deposited, snapshot 1 measured).
Status
snapshot 1 measured
Snapshot 1
No upper tool edge for any of the three local models between two and six tools: test 1 is restricted for gpt-oss-20b and Qwen3-14B and below resolution for Qwen3-4B, whose success was still rising at six tools. In this domain and range the working region is a slope along the failure axis, not a band on the tool axis. Which tool was added mattered more than how many. See the Map.
If this holds
partly measured Do not add tools or coupling without decoupling. In snapshot 1, adding tools did not by itself lower success between two and six, but one tool, the spreadsheet, lowered it in both orders. Question: which of your recent additions moved you toward an edge, and would you know?
Sources and objections
Sense used
Basin-island, reduced to enclosure on a stateless system.
Milgrom and Roberts 1990 on complementarities, where practices form mutually reinforcing clusters, mixed configurations underperform both pure ones, and no incremental path runs between clusters. Multiple-equilibrium and poverty-trap models at the macro scale.
Strongest objection
Definitional until state variables are named. In dissipative systems basins tile state space, so "sea" needs its configuration-space reading.
Persistence is not evidence of an island. A system can sit near a vanished attractor or a sticky boundary for years and look stable on every passive measure, and only a measured restoring response to a perturbation of its state shows that an island is there. Once an island is known to be there, watching its fluctuations can locate its edge as well as pushing it, unless the push is large against those fluctuations. Boundaries are observed before interiors, and every located island is a revisable estimate.
Stated for
Any system with a state that can be perturbed. The instrument tests agent systems, within a run.
Testable form
In the agent domain, the Map's test 2: runs that recovered from a fault injected mid-run, against the same document without faults. It survives when they take more turns by more than chance (pre-registration r4). It is narrower than the proposition: it shows that recovery costs something, not that persistence fails as evidence. The organizational reading is not tested by it.
Killed by
Persistence reliably predicting recovery. Passive statistics telling a system near a vanished attractor from one inside a live island as well as a perturbation does. For an island known to be there, a push that is small against the system's fluctuations locating its edge better than watching does.
Instrument
The Map, fault-injection arm (pre-registration r4, deposited, snapshot 1 measured). The lake's tests E1 and E2 (deposited and run): E1 restricted, E2 survives.
Status
snapshot 1 measured
Snapshot 1
Test 2 survives for all three models: a fault costs 0.3 to 0.8 extra turns, all of it the retry itself. The push showed what success without faults hid: after a fault the small Qwen gave up in 61 percent of runs, gpt-oss-20b in 33 and the larger Qwen in 15.
If this holds
implication of an unmeasured claim Judge stability by fault-injection recovery, not by uptime. Question: has your stability ever been tested by a push, or only observed?
Minsky 1986, whose financial instability hypothesis says stability is destabilizing, with the Great Moderation as the canonical false island. Schelling 1971 on tipping, where a stable-looking mix sits one nudge from a threshold.
Strongest objection
Stateless inference has no trajectory in configuration space, so "return" is defined only within a run, as recovery after an injected fault.
An island's lifetime is a first-passage time. Under a stationary disturbance process, exit from an island of given depth is memoryless, so once its depth is known a configuration's age is no evidence of its remaining life. Islands that differ in depth show a hazard falling with age without any memory, and islands that end by exhausting a reserve rather than by disturbance age on schedule. Neither is a counterexample. Some exits are noise-induced with no precursor, which bounds any early-warning instrument's recall below one. Sudden per island, progressive across the archipelago.
Stated for
Agent systems, since v0.1. The organizational reading was withdrawn after the objection recorded below.
Changed in v0.2
Conditions stated: islands of given depth, with differences in depth and exhaustion named as ways a hazard can change with age without memory. The falsifier is unchanged. The frozen tests were written against the v0.1 wording, kept under Earlier wording, and their verdicts will be entered against it.
Testable form
On agent systems, long-horizon runs under a stationary fault process yield the first-passage distribution directly.
Killed by
Hazard falling with age conditional on depth. Dwell linear in depth. Every exit showing precursors.
Instrument
Tests in four domains, deposited and run on 30 September 2026: the lake's E3 (a model: memory survives, depth unresolved, warning survives), the ice-age cold spells, C1 and C2 (real data: C1 survives, C2 finds no clock), and expansions in 42 countries, X1 (real data, the first test written against this version's wording: unresolved). A fifth domain followed on 8 October 2026: the fossil record, a re-run of Finnegan, Payne and Wang (2008) on real data, deposited and run once: killed. The orbits' stickiness test (a model) ran twice, and neither run counts: the first did not measure what it was built to measure, and the corrected run's positive control failed, which makes it void. For agent systems, a long-horizon variant of the harness remains planned, not built.
Status
killed in one domain
If this holds
implication of an unmeasured claim Do not read a long run of calm as safety. Question: what is your exit hazard, independent of age?
Young 1993 and Kandori, Mailath and Rob 1993 on stochastic stability, where the equilibrium that survives persistent small shocks is the one with the largest basin and expected escape times grow exponentially with its depth.
Strongest objection
The organizational result may be frailty rather than memory, and the two cannot be separated without a depth measure independent of dwell, which no public record supplies.
In a system held by a throughput, depth is a flow, not a stock. It is purchased by continuous station-keeping against drift and decays when the expenditure stops. The expenditure concentrates fragility in the stabilizer, and exits from engineered islands run through the stabilizer more often than through outside shock. The second half is credited, not claimed. Its owners are listed under Sources and objections below. What nobody codes is the first half: what the stabilizer costs in margin, and how vulnerable a system decides to run.
Stated for
Systems held by a throughput: islands kept by something flowing through them, such as energy, money or managed inputs. Infrastructure, through the Cases page. Stars, firms and managed ecosystems as illustrations. No agent-system or organizational instrument yet.
Scope, defined
A system is held by a throughput when its stored reserve would run out, at its net outflow, in less than its typical dwell on the island. That is a runway shorter than the stay, and it can be measured before and apart from whether the island ends.
Changed in v0.2
Scope stated, and the falsifier restricted to it. The v0.1 wording is kept under Earlier wording.
Testable form
A margin ledger per island: what is spent to hold position, and where the fragility went.
Killed by
Depth persisting without expenditure in a system held by a throughput.
Instrument
The measles runway test, deposited as 10.5281/zenodo.23071574 and run once on 30 September 2026: does a country's outbreak-free spell end sooner when more children are born unvaccinated? Unresolved: the chance of an outbreak rose with the unvaccinated inflow, short of the effect the rules required. The Cases page illustrates the proposition with CrowdStrike, July 2024.
Status
test run: unresolved
If this holds
implication of an unmeasured claim Budget for the stabilizer and audit it as your largest risk. Question: what does your stabilizer cost, and where did the fragility go?
Sources and objections
Sense used
All three. The cost line is required whichever sense is used.
Minsky 1986 again, and the moral-hazard literature, where a lender of last resort or deposit insurance relocates fragility into too-big-to-fail rather than removing it. Capital buffers under Basel are a priced station-keeping cost.
Strongest objection
The location half is settled literature, and the flow half has no instrument.
Framing propositions, not yet testable
These keep their numbers and falsifiers, carry no instrument, and do not count toward the instrument tally. They are here because without them the theory is agent benchmarking.
Survival is decided in the passage. A transit has a duration, a reserve burn rate, and a minimum invariant set that must be carried across for the arriving system to count as the same system. None of the three follows from the properties of the two islands. The word "hopping" is retired. Nothing hops in the physics this site cites.
Stated for
Organizations and infrastructure. No instrument in any domain.
Testable form
Transit cost under scripted reconfiguration mid-run, recorded as performance lost and time to recover. For example, an agent in the middle of a task has its tool set swapped or its orchestrator topology changed, and the run continues. The transit cost is the performance lost and the time to recover.
None. A reconfiguration arm of the harness is the likely route. It is not scoped.
Status
framing, not testable yet
If this holds
implication of an unmeasured claim Plan the crossing, not only the destination: its duration, its reserve burn, and what must be carried across. Question: what is the minimum you must carry across a migration for it to still be you?
Dixit 1989 on entry and exit under uncertainty, and Dixit and Pindyck 1994 on real options, where sunk costs create bands of inaction with hysteresis and the value of waiting prices the decision not to cross.
Whether navigation is possible at all is set by the environment's regime dwell time divided by the organization's reconfiguration time. Above one, island choice and transit design matter. Near one, timing dominates. Below one, no navigation strategy works and three moves remain: shorten reconfiguration time, park on the widest reachable island, or hibernate. The bet that is this site's own: AI shrinks the numerator in AI-exposed sectors while review, compliance and hiring hold the denominator.
Stated for
Organizations, at the scale of eras. No instrument in any domain.
Testable form
Transition outcomes against the ratio, with regime dwell time estimated by a Markov-switching model on a named public series. The series is not yet named.
Killed by
Outcomes independent of the ratio. Era proxies stable or lengthening.
Instrument
Built and demonstrated on the Economy page: Hamilton's (1989) regime-switching model, which on US output recovers the NBER's recessions without seeing them. On that series the high-growth regime's expected length rose several times over after 1984, which would count against this proposition were US output its series, which it is not. The series for the numerator is not named, and it must be frozen together with the model's specification, since Hamilton's original form settles elsewhere on today's revised data. One forecast is placed on the Cases page.
Status
framing, not testable yet
If this holds
implication of an unmeasured claim Measure your reconfiguration time before debating strategy. Question: how long does a real reconfiguration take you, end to end?
Hamilton 1989, whose Markov-switching model estimates expected regime durations from data. McGrath 2013 on transient advantage and D’Aveni 1994 on hypercompetition, on the shortening of advantage eras.
Strongest objection
The sign of AI’s effect on era length is a bet. Regime durations can be estimated with Markov-switching models on public series, but no series yet isolates AI’s effect on them.
Open objections
Every objection that changed the text is listed with its source, and every objection still standing is listed as open. Four accepted rows came out of the author's own review round and are folded into v0.1. Two came out of an outside review of this draft site that the author commissioned, and are folded into pre-registration draft r2. Two more came out of a second outside review, also commissioned, and are folded into pre-registration draft r3. All eight are attributed so they can be checked, and none counts as an external objection. Two more were raised internally with v0.2 and stand open. That counter starts at zero and moves only when an objection from outside the author's review rounds changes a proposition's text.
Date
Objection
Source
Status
2026-09-24
Stateless inference has no trajectory, so basin vocabulary must be reduced to enclosure and within-run recovery.
Refutation round
Accepted into v0.1.
2026-09-24
Organizational hazard falls with time since last change.
Success is monotone in fault rate, so an island cannot be enclosed on the fault axis. The shape written into the pre-registration must be a band with an upper tool edge and a fault cap.
Outside review, September 2026
Accepted into pre-registration draft r2.
2026-09-24
Boundary width must be judged against sampling error at 50 to 100 runs per cell, not against rerun jitter.
Outside review, September 2026
Accepted into pre-registration draft r2.
2026-09-25
The upper tool edge depends on which tools are added. The tool mix must be pre-registered, with a second mix as a replicate.
Second outside review, September 2026
Accepted into pre-registration draft r3.
2026-09-25
The fault cap is near-certain, so it tests nothing. The shape of the boundary along the fault axis, a cliff or a slope, is reported descriptively, and pairwise cell comparisons are replaced by a single pre-registered model.
Second outside review, September 2026
Accepted into pre-registration draft r3.
2026-09-24
Can proposition 1 be stated for organizations without a declared state space? Candidate state variables, not yet declared: coupling density (shared dependencies per function), decision latency, and reconfiguration time.
The author
Open.
2026-09-29
Narrowing proposition 4 to systems held by a throughput, after meeting nuclei, orbits and supercooled water, looks like a retreat.
Raised internally with v0.2
Open. Answer given: those systems were outside the stated domain, none was a test, and the runway definition keeps the scope independent of outcomes.
2026-09-29
Naming differences in depth and exhaustion as exceptions to proposition 3 could excuse any hazard that changes with age.
Raised internally with v0.2
Open. Answer given: each exception must be shown, not assumed. Differences in depth need a depth measure that separates the islands, and exhaustion needs a reserve that runs down. Where neither is shown, a falling hazard counts against the proposition.
To object, use the objection form on GitHub. Every objection gets a public answer there, and one that still stands is listed here. Two named human reviewers from outside AI filing objections is launch condition 6, because every objection so far came from commissioned model reviews.
Versions
v0.0 was five claims distilled from the April 2025 essay, which argues them rather than listing them. v0.1 replaced them with six propositions after two rounds of hostile review. v0.1.1 was an editorial patch after an outside review of this draft site. v0.1.2, dated 25 September 2026, is an editorial patch after a second outside review: the thesis is stated first on the home page, each proposition carries a plain-language line and an "if this holds" row, a glossary and reading paths were added, and the instrument versions were renamed to an r-numbered scheme. The method is described in the footnote at the end of the page. Nobody is asked to believe the review was independent. v0.1.3, dated 29 September 2026, is an editorial patch that brings each proposition's status up to date with the pages on other sciences. No proposition's wording changed. v0.2, the same day, is the first minor version: it states proposition 4's scope, systems held by a throughput, and proposition 3's conditions, islands of given depth, with frailty and exhaustion named. Both changes come from the pages on other sciences, not from an outside objection, and are labeled internal. The v0.1 wording of both is kept under Earlier wording. v0.2.1, also that day, is an editorial patch: statuses brought up to date with the Economy page and its frozen test X1, and proposition 6's candidate instrument marked as built. No wording changed, and the anchors stay those of v0.2. v0.2.2, the same day, moves the cross-domain illustrations to the ledger on the Sciences page, so that this page keeps only what bears on testing: each proposition's instrument and status. v0.2.3, dated 30 September 2026, replaces the semicolons in the specification's wording with periods, commas and colons, as across the site. No proposition's meaning changed. v1.0, dated 30 September 2026, is the first major version. A measurement moves the major version, and v1.0 enters them together: snapshot 1 of the Map and the tests run in ecology, climate and economics. It also refines proposition 2 as the lake's pre-registration said a restricted E1 would, a change from the site's own evidence. Proposition 2's earlier wording is kept under Earlier wording, and every v0.2 anchor still resolves. v2.0, the same day, enters the first test of proposition 4, the measles runway, which came out unresolved. A measurement moves the major version whatever its verdict. No proposition's wording changed, and every v1.0 anchor still resolves. The corrected orbits test, run the same day, was void and moves nothing. v2.0.1, the same evening, is an editorial patch: this page opens with a summary in plain words, its sections are regrouped so the history follows the theory, and its spelling is American throughout. No proposition's wording changed, and every anchor still resolves. v3.0, on 8 October 2026, enters the re-run of Finnegan, Payne and Wang (2008), a test of proposition 3 in the fossil record, which came out killed. A measurement moves the major version whatever its verdict. No proposition's wording changed, and every v2.0 anchor still resolves.
Earlier wording
Earlier wording of the propositions whose text changed, kept so that links and frozen tests citing it still resolve: proposition 2 as it stood from v0.1 to v0.2.3, and propositions 3 and 4 as they stood in v0.1.
Proposition 2, v0.1 to v0.2.3
The evidence rule
Persistence is not evidence of an island. A system can sit near a vanished attractor or a sticky boundary for years and look stable on every passive measure. An island is established only by a measured restoring response to a perturbation of the system's state. Boundaries are observed before interiors, and every located island is a revisable estimate.
Stated for any system with a state that can be perturbed. Killed by: persistence reliably predicting recovery, or passive early-warning statistics locating islands as well as perturbation does.
Proposition 3, v0.1
Exit statistics
An island's lifetime is a first-passage time. Under a stationary disturbance process, exit is memoryless, so a configuration's age is no evidence of its remaining life. Some exits are noise-induced with no precursor, which bounds any early-warning instrument's recall below one. Sudden per island, progressive across the archipelago.
Stated for agent systems. Killed by: hazard falling with age conditional on depth, dwell linear in depth, or every exit showing precursors.
Proposition 4, v0.1
Cost
Depth is a flow, not a stock. It is purchased by continuous station-keeping against drift and decays when the expenditure stops. The expenditure concentrates fragility in the stabilizer, and exits from engineered islands run through the stabilizer more often than through outside shock. The second half is credited, not claimed. Its owners are listed under Sources and objections below. What nobody codes is the first half: what the stabilizer costs in margin, and how vulnerable a system decides to run.
Stated for infrastructure, through the Cases page. Killed by: depth persisting without expenditure.
Dropped from v0.0
Wording and objects that appeared in the essay or the first draft and do not survive into v0.1.
"Never continents." Global attractors exist. L4 and L5 are stable under Routh's condition.
"Not size."May 1972. Configuration decides whether size is survivable.
"Fails suddenly when nudged." It conflated four kinds of physics. The boundary's shape, not the drop's height, is the claim.
"Before you arrive." The nuclear island was predicted in 1966. In 2025 experiments located part of its shoreline at rutherfordium. Its peak, height and extent are still unknown.
"Hopping." Retired. See proposition 5.
AI inside the ontology. AI is no longer an object of the theory. It enters once, as the bet in proposition 6.
The self as a standalone thread. The continuity criterion enters once, as the invariant list in proposition 5, and nowhere else.
The digital immune system as an example of stability. It is now the case for proposition 4.
Changelog
Four channels move the version, and a fifth kind of entry records what did not move it. Every entry is also in the changelog feed, for any RSS reader, where each item links back to its row.
A measurement moves the major version.
An accepted external objection moves the minor version.
A scope change drawn from the site's own evidence moves the minor version and is labeled internal.
An editorial change moves the patch version.
A run that fails to kill a proposition is entered as a dated survival. Confirmation is an entry, not silence.
A Map test is narrower than the proposition it bears on: its verdict is entered against the test, with the proposition named.
Snapshots at most twice a year.
Version
Date
Entry
Channel
v3.0
2026-10-08
The third major version. The re-run of Finnegan, Payne and Wang (2008), a test of proposition 3 in the fossil record, ran once after its deposit and came out killed. It is a measurement, so the major version moves, as the rule says, whatever the verdict. What the kill means for the proposition's wording is the author's decision, pending. No proposition's wording changed. Every proposition gets a v3.0 anchor, and the v2.0 anchors still resolve. The glossary now defines the verdict words.
Major version, from a measurement.
v2.0.1
2026-09-30
Editorial: the page opens with In brief, the idea and the six propositions in plain words, where the evidence stands, and a guide to the page. Sections regrouped so the history follows the theory: open objections now come after the propositions, and the versions, earlier wording, what was dropped and this changelog come last. Spelling made American throughout. No proposition's wording changed, and every anchor still resolves.
Patch version.
v2.0
2026-09-30
The second major version. The measles runway test, proposition 4's first test, ran once after its deposit and came out unresolved. It is a measurement, so the major version moves, as the rule says, whatever the verdict. No proposition's wording changed. The corrected orbits test, run the same day, was void and moves nothing. Every proposition gets a v2.0 anchor, and the v1.0 anchors still resolve.
Major version, from a measurement.
Orbits test r2
2026-09-30
Run once, after its deposit. Void: its control, the undisturbed arm, did not show the stickiness theory predicts, so under the rules no verdict on proposition 3 is entered. The ages the rules compare fell among quick passes through the neighborhood, before any sticking shows. The disturbed arm's stays were memoryless.
Void run. Counts neither for nor against proposition 3, and moves nothing.
Measles runway test
2026-09-30
Run once, after its deposit. Unresolved: the chance that a country's outbreak-free spell ends rose with the share of its people born unvaccinated since the spell began, but the interval reached below the smallest effect the rules required.
Measurement. Neither a survival nor a kill. Entered in v2.0.
Pre-registrations: orbits r2, measles runway r1
2026-09-30
Frozen with every file hashed and deposited on Zenodo before they ran: orbits r2 (10.5281/zenodo.23071492) and the measles runway r1 (10.5281/zenodo.23071574). Orbits r2 corrects r1's design: its neighborhood is measured from the island's full edge, its undisturbed arm is a positive control, and every disturbed stay starts at the island's center. The measles runway is proposition 4's first test: does a country's outbreak-free spell end sooner when more children are born unvaccinated?
Instrument. Does not move the specification version.
Harness public
2026-09-30
The harness repository is public at github.com/delimiterbob/islands-harness, after snapshot 1 rather than before it. Objections are filed there as issues, with the objection form. The code on its main branch still matches the lock deposited before the runs.
Instrument. Does not move the specification version.
v1.0
2026-09-30
The first major version. Measurements move the major version, and v1.0 enters them together: snapshot 1 of the Map, and the tests deposited and run on 30 September 2026 in ecology, climate and economics. The orbits test's invalid run moves nothing. Proposition 2 takes the refinement its lake pre-registration named in advance for a restricted E1: only a push shows that an island is there, but once it is, watching can locate its edge as well as a push that is small against the system's fluctuations. Its killed-by line changes with it, and its earlier wording is kept under Earlier wording. Every proposition gets a v1.0 anchor, and the v0.2 anchors still resolve. The page also lists every prior owner's work in full, with DOIs checked against Crossref, and publishes this changelog as a feed.
Major version, from measurements. Proposition 2's refinement is internal, from the site's own evidence, and counts as no external objection.
v0.2.3
2026-09-30
Editorial: semicolons removed from the specification's wording, as across the site, in favor of periods, commas and colons. Proposition 1's plain line now reads "Working configurations are rare and bounded. Most of the space around them does not work." Proposition 3 is killed by "hazard falling with age conditional on depth, dwell linear in depth, or every exit showing precursors." No proposition's meaning changed, and the anchors are unchanged.
Patch version.
Expansions X1
2026-09-30
Run once, after its deposit. Unresolved: within each country and decade, expansions grew more likely to end with age, short of the bar the rules set for a departure.
Measurement. Neither a survival nor a kill.
Ice-age tests
2026-09-30
Computed once, after their deposit. C1, whether the cold spells were memoryless, survives. C2, a 1,470-year clock, finds no clock.
Measurement. Dated survivals of proposition 3 in this record.
Orbits test
2026-09-30
Run once, after its deposit. The registered verdict is a kill of proposition 3 in this model: memory under a steady disturbance. After the run, the test's neighborhood turned out not to contain the island, so what it counted were fragments of laps, not stays near the island. The result and the flaw are on the orbits page. Recorded as invalid, the author's decision on 30 September 2026. A corrected test, r2, is drafted, to be deposited before it runs.
Invalid run. Counts neither for nor against proposition 3, and moves nothing.
Lake tests
2026-09-30
Run once, after their deposit. E1, watching or pushing, restricted: pushing was never clearly better than watching. E2, the ghost, survives. E3a, memory, survives. E3b, depth, unresolved. E3c, warning, survives.
Measurement. Dated survivals of propositions 2 and 3 for E2, E3a and E3c. The pre-registration reads a restricted E1 as a refinement of proposition 2, adopted in v1.0.
Instrument. Does not move the specification version.
v0.2.2
2026-09-29
Editorial: the "across the sciences" rows of propositions 1 to 5 removed. Where each proposition stands in each domain is kept in one place, the ledger on the Sciences page, so the two pages cannot drift apart. This page keeps each proposition's instrument and status and changes when those change. No proposition's wording changed, and the anchors are unchanged.
Patch version.
v0.2.1
2026-09-29
Editorial: statuses brought up to date with the Economy page. Proposition 6's candidate instrument, Hamilton's regime-switching model, marked as built and demonstrated on US output, with its series not named. Test X1 listed under proposition 3. Economics added to the "across the sciences" rows of propositions 1 to 5. No proposition's wording changed, and the anchors are unchanged.
Patch version.
Pre-registration: expansions X1 r1
2026-09-29
Frozen locally with every file hashed and the OECD data file included, to be deposited on Zenodo with the other bundles and run only after: the permission to compute comes from the deposit's DOI. The first test written against version 0.2's wording. Before the freeze only the data file's structure was read, and the sample was then limited to measured quarters, since most countries' early decades are OECD estimates.
Instrument. Does not move the specification version.
v0.2
2026-09-29
Proposition 4's scope stated: systems held by a throughput, with a runway definition measured apart from outcomes, and its falsifier restricted to that scope. Proposition 3's conditions stated: exits memoryless for islands of given depth, with differences in depth and exhaustion named as ways a hazard can change with age without memory. Both drawn from the pages on other sciences. The skeptic's reading of each is entered as an open objection. The v0.1 wording is kept under its anchors.
Minor version, internal: from the site's own evidence, not an outside objection. The count of accepted external objections stays at zero.
v0.1.3
2026-09-29
Editorial: each proposition's status brought up to date with the pages on other sciences (nuclear physics, ecology, orbits, stars, climate, organizations, chemistry) and the Sciences ledger. Frozen tests listed under propositions 2 and 3. An "across the sciences" row added to propositions 1 to 4. The cross-domain rule's list of domains extended. No proposition's wording changed.
Patch version.
Pre-registrations: lake r1, orbits r1, ice-age r1
2026-09-29
Frozen locally with every file hashed, to be deposited on Zenodo before the site goes live and run only after: the random seeds, or for the ice-age tests the permission to compute, come from each deposit's DOI. The lake's E3c alarm was revised before its freeze after a disclosed pilot of its positive control. The ice-age tests were re-frozen after a loader fix, before anything was computed.
Instrument. Does not move the specification version.
Snapshot 1
2026-09-29
Measured on three local models, 18,720 runs. Map test 1 (upper tool edge) restricted for gpt-oss-20b and Qwen3-14B, below resolution for Qwen3-4B. Map test 2 (recovery cost) survives for all three, the cost being the retry itself. Bearing on proposition 1: in the agent domain, between two and six tools, a slope along the fault axis rather than a band with an upper tool edge.
Measurement. Entered in v1.0.
Pre-registration r4
2026-09-26
Rules confirmed decision by decision, frozen with every fixed input hashed, and deposited on Zenodo before any run (DOI 10.5281/zenodo.22982434). Tau and task difficulty set by calibration. Calibration band widened to [0.15, 0.95] on simulation evidence. Three local models. Both tool orders run, order B descriptive.
Instrument. Does not move the specification version.
v0.1.2
2026-09-25
Editorial: thesis stated first on the home page. Plain-language line and "if this holds" row per proposition. Glossary. Reading paths. Construct mapping and threats to validity on the Map. Author named. Instrument versions renamed to an r-numbered scheme (draft v0.2 is now draft r2).
Patch version.
Pre-registration draft r3
2026-09-25
Tool mix fixed, with a replicate mix. Single regression model as the P1 test. Fault cap demoted to a consistency check. Fault-axis boundary shape added as a descriptive comparison. Viable fraction descriptive at 50 percent. One-tool cells out of scope. Not yet deposited.
Instrument. Does not move the specification version.
v0.1.1
2026-09-24
Editorial: hero restated to what exists. Propositions 5 and 6 grouped as framing. Cross-domain rule added. Method note moved to a footnote. Economics prior owners added under each proposition and Markov-switching named as a candidate instrument for proposition 6.
Patch version, per the three-channel rule.
Pre-registration draft r2 (formerly draft v0.2)
2026-09-24
Axis logic corrected (band with an upper edge and a fault cap). Decision rules split per proposition. Sampling error added as the boundary criterion. Rerun jitter reported separately. Not yet deposited.
Instrument. Does not move the specification version.
v0.1
2026-09-24
Six propositions, method note, instrument status column, open-objections list.
Baseline. The counted changelog starts here.
v0.0
2025-04-14
Five claims distilled from the essay.
Origin. Not counted.
Next entries: the first accepted outside objection, and the next test deposited.
Versioned permalinks. Each proposition carries an anchor of the form v3.0-p3, so a link such as theory.html#v3.0-p3 keeps pointing at the wording it cited after the version moves. Anchors carry the minor version: a patch edits wording under the same anchor and records the edit in the changelog, while a minor or major move creates new anchors and keeps the older wording reachable at its own. Links to earlier anchors still resolve: each proposition also carries the anchors of the earlier versions whose wording it kept, and wording that changed is kept under Earlier wording.
Glossary
Terms used on this site, one sentence each. Where a term has a technical meaning elsewhere, the sentence gives the meaning used here.
Basin
The set of starting states from which a system settles into the same attractor.
Sea
A setting in configuration space at which no viable regime exists.
Enclosure
The reduced form of a basin for a stateless system: a bounded region of settings where the task succeeds, judged on a sweep rather than on a trajectory.
Boundary width
How far a setting can move before success drops, judged against sampling error rather than rerun jitter.
Sticky boundary
A basin edge where trajectories linger for a long time before leaving, so the system looks stable while it is not inside the basin.
Ghost attractor
The remnant of an attractor that no longer exists, near which a system slows down and looks stable for a long time.
Chaotic saddle
An unstable set that traps trajectories for a long but finite time before they escape.
First-passage time
The time a system takes to leave a region for the first time. An island's lifetime is one.
Stabilizer
Whatever a system spends to hold its position against drift, and the place its fragility collects.
Station-keeping
The continuous expenditure that keeps a system on its island. Depth decays when it stops.
Transit
The passage between islands, with a duration, a reserve burn rate, and a minimum that must be carried across.
Regime dwell time
How long the environment stays in one regime before it switches.
Framing proposition
A proposition that keeps its number and its falsifier but has no instrument and does not count toward the instrument tally.
Viable fraction
The share of tested cells whose success rate is at or above 50 percent, reported descriptively and used as no criterion.
Brier score
The mean squared difference between a forecast probability and the outcome, with lower being better.
KAM
Kolmogorov, Arnold and Moser, whose theorem says some regular motions survive small perturbations in conservative systems. It transfers to this site only as chaotic saddles and long transients.
Survives
A test's verdict when its result falls where the proposition predicts, by the margin its rules fixed before the run, which counts for the proposition in that domain without proving it.
Killed
A test's verdict when it finds what the proposition says cannot happen, by the margin its rules fixed before the run, so the proposition fails in the domain tested.
Unresolved
A test's verdict when its result falls between the margins for survival and for a kill, so it counts neither for nor against the proposition.
Restricted
A test's verdict when the effect the proposition predicts is shown to be smaller than the smallest size its rules count.
Below resolution
A test's verdict when the measurement could not decide either way, the word snapshot 1's rules use for unresolved.
Void
A run that does not count because a check built into it failed, such as a control that should have shown the effect and did not.
Invalid
A run that does not count because it was found, after the run, not to measure what it was built to measure.
References
Every work named above as a prior owner or an economics precedent, in full. 26 of the 35 have a DOI, and each was checked against its Crossref record on 30 September 2026. A work without a DOI says so, and links a stable address where one exists.
Amburgey, T. L., Kelly, D., and Barnett, W. P. 1993. Resetting the clock: the dynamics of organizational change and failure. Administrative Science Quarterly 38(1): 51–73. https://doi.org/10.2307/2393254
Beyer, B., Jones, C., Petoff, J., and Murphy, N. R., editors. 2016. Site Reliability Engineering: How Google Runs Production Systems. O’Reilly Media. No DOI. Free to read at sre.google.
Boettiger, C., and Hastings, A. 2012. Quantifying limits to detection of early warning for critical transitions. Journal of the Royal Society Interface 9(75): 2527–2539. https://doi.org/10.1098/rsif.2012.0125
Bronson, N., Aghayev, A., Charapko, A., and Zhu, T. 2021. Metastable failures in distributed systems. In Proceedings of the Workshop on Hot Topics in Operating Systems (HotOS ’21), 221–227. ACM. https://doi.org/10.1145/3458336.3465286
Carlson, J. M., and Doyle, J. 2002. Complexity and robustness. Proceedings of the National Academy of Sciences 99(suppl. 1): 2538–2545. https://doi.org/10.1073/pnas.012582499
D’Aveni, R. A., with Gunther, R. 1994. Hypercompetition: Managing the Dynamics of Strategic Maneuvering. Free Press. No DOI.
Dixit, A. K. 1989. Entry and exit decisions under uncertainty. Journal of Political Economy 97(3): 620–638. https://doi.org/10.1086/261619
Encarnação, R. 2026. The Preservation of the Continuity of the Self: Causal Processes, Descriptive Bottlenecks, and Survival in Copyable Minds. Preprint, August 2026, bit&being. No DOI. bitandbeing.com/research.
Gardner, M. R., and Ashby, W. R. 1970. Connectance of large dynamic (cybernetic) systems: critical values for stability. Nature 228: 784. https://doi.org/10.1038/228784a0
Hamilton, J. D. 1989. A new approach to the economic analysis of nonstationary time series and the business cycle. Econometrica 57(2): 357–384. https://doi.org/10.2307/1912559
Henrard, J. 1982. Capture into resonance: an extension of the use of adiabatic invariants. Celestial Mechanics 27: 3–22. https://doi.org/10.1007/BF01228946
Huang, L., et al. 2022. Metastable failures in the wild. In Proceedings of the 16th USENIX Symposium on Operating Systems Design and Implementation (OSDI ’22). USENIX Association. No DOI. usenix.org.
Kandori, M., Mailath, G. J., and Rob, R. 1993. Learning, mutation, and long run equilibria in games. Econometrica 61(1): 29–56. https://doi.org/10.2307/2951777
Keppel, G., et al. 2012. Refugia: identifying and understanding safe havens for biodiversity under climate change. Global Ecology and Biogeography 21(4): 393–404. https://doi.org/10.1111/j.1466-8238.2011.00686.x
Kussell, E., and Leibler, S. 2005. Phenotypic diversity, population growth, and information in fluctuating environments. Science 309(5743): 2075–2078. https://doi.org/10.1126/science.1114383
Levins, R. 1968. Evolution in Changing Environments: Some Theoretical Explorations. Princeton University Press. https://doi.org/10.1515/9780691209418
Levins, R. 1969. Some demographic and genetic consequences of environmental heterogeneity for biological control. Bulletin of the Entomological Society of America 15(3): 237–240. https://doi.org/10.1093/besa/15.3.237
Lewontin, R. C. 1969. The meaning of stability. In Diversity and Stability in Ecological Systems, Brookhaven Symposia in Biology 22: 13–24. No DOI.
Lucas, R. E., Jr. 1972. Expectations and the neutrality of money. Journal of Economic Theory 4(2): 103–124. Named above as a name collision, not a precedent. https://doi.org/10.1016/0022-0531(72)90142-1
Martin, S. 2004. The cost of restoration as a way of defining resilience: a viability approach applied to a model of lake eutrophication. Ecology and Society 9(2): 8. https://doi.org/10.5751/ES-00659-090208
McGrath, R. G. 2013. The End of Competitive Advantage: How to Keep Your Strategy Moving as Fast as Your Business. Harvard Business Review Press. No DOI.
Menck, P. J., Heitzig, J., Marwan, N., and Kurths, J. 2013. How basin stability complements the linear-stability paradigm. Nature Physics 9: 89–92. https://doi.org/10.1038/nphys2516
Milgrom, P., and Roberts, J. 1990. The economics of modern manufacturing: technology, strategy, and organization. American Economic Review 80(3): 511–528. No DOI.
Minsky, H. P. 1986. Stabilizing an Unstable Economy. Yale University Press. No DOI.
Neishtadt, A. I. 1975. Passage through a separatrix in a resonance problem with a slowly-varying parameter. Journal of Applied Mathematics and Mechanics 39(4): 594–605. https://doi.org/10.1016/0021-8928(75)90060-X
Proposition 5 names refugia and metapopulation ecology as prior owners without naming a work. Three representative works, chosen for this list, stand for them: Levins 1969, Hanski 1998 and Keppel et al. 2012.
How to cite
The specification: Encarnação, R. 2026. Islands of Stability, specification v3.0. https://islandsofstability.com/theory. To cite one proposition, link its permanent anchor, such as theory#v3.0-p3, which keeps pointing at the wording you read after the version moves.
Every test was deposited on Zenodo before it ran, and snapshot 1's results after it:
The harness that ran snapshot 1 is tag v1.0.0, confirmed at commit 79b627f. The lock in the first deposit holds the hash of every file the freeze covered.
Method footnote
The review that produced v0.1: the five claims were sent to five outside models. Their responses and the essay were then read by about 130 reviewing agents with ten fact checks and a refutation round. Version 0.1.1 followed a first outside review of this draft site by five models on 24 September 2026. A second outside review of the draft site by five models on 25 September 2026 produced v0.1.2 and draft r3. All objections that were accepted are attributed in the open-objections table.
Draft site. Snapshot 1's numbers are real measurements. The two grids marked illustrative are not.
Where does an AI agent keep doing its job as it is given more tools and its tools start failing?
Snapshot 1: measured 27 to 29 September 2026Pre-registration r4: deposited 26 September 2026, DOI 10.5281/zenodo.22982434Noise floor: measured3 local models, 18,720 runsCadence: at most two snapshots a year
Snapshot 1 swept three open-weight models, run on a local workstation, across the number of tools the agent is given (1 to 6) and the share of its tool calls that fail (0 to 50 percent): 100 runs per cell, in two tool orders, 18,720 runs in all. The rules were deposited before the first run.
The answer, for all three models, is a continent with a slope, not a band with an edge. Adding tools between two and six did not by itself lower success. Every step up in the failure rate did. gpt-oss-20b held 92 percent success with no failures and 50 percent when half its tool calls failed. The two Qwen models held far smaller islands and never produced a fully correct record, because they never computed the invoice total right.
Scope. The principle this site studies is meant to hold across the sciences. This instrument measures one domain, AI agents, on one task. Its two tests are narrower than the theory's propositions 1 and 2, and they say nothing on their own about organizations or any other domain.
Snapshot 1
The grid shows one model at a time. Each cell is the share of runs that succeeded, with its 95 percent interval underneath. The one-tool column is out of scope: the task needs two tools.
Loading the snapshot data.
Snapshot 1. The cells fill from the snapshot data when the page loads.
Viable fraction
pending
Share of cells above 50 percent success. Reported, not a criterion.
Upper tool edge
pending
Negative curvature with an interior peak in the draft r3 model. Proposition 1.
Boundary width
pending
Rungs from 90 to 10 percent success. Claimed only where adjacent cells differ by more than their intervals. Proposition 2.
Recovery time
pending
After a fault injected mid-run, against unperturbed controls. Proposition 2.
Fault-axis shape
pending
Sigmoid versus linear fit. Descriptive, feeds no proposition yet.
Values from the snapshot file. Tiles marked descriptive decide nothing. The two verdicts follow the pre-registered rules.
The verdicts, as pre-registered
Two tests, each scored on its own, on tool order A. The deposit calls them P1 and P2. This page calls them tests 1 and 2 so they are not mistaken for the theory's propositions, which they bear on but do not decide.
Model
Test 1: upper tool edge
Test 2: recovery cost
In plain words
gpt-oss-20b
restricted drop 0 points [-7, 7]
survives +0.8 turns [0.6, 1.1]
No upper tool edge: a drop of 15 points or more at six tools is ruled out. A failure costs +0.8 extra turns, but net of re-asking for the failed data it costs nothing.
Qwen3-14B
restricted drop 0 points [-13, 13]
survives +0.8 turns [0.6, 1.0]
No upper tool edge: a drop of 15 points or more at six tools is ruled out. A failure costs +0.8 extra turns, but net of re-asking for the failed data it costs nothing.
Qwen3-4B
below resolution peak 5.7 tools [4.5, ∞]
survives +0.3 turns [0.1, 0.5]
No edge found: success was still rising at six tools, so there was no peak to fall from. A failure costs +0.3 extra turns, but net of re-asking for the failed data it costs nothing.
Verdict words: survives means the prediction held, restricted means the prediction failed by more than the smallest effect worth reporting, and below resolution means the data cannot tell. The full rules are in the pre-registration.
What else the data show
These reports were committed in writing on 27 September 2026, while the sweep was running and before any of its results were looked at. They are descriptive: none changes a verdict.
Model
Success, no failures → half the calls failing
Fully correct
Total right
Gave up after a failure
Recovery cost beyond the retry
gpt-oss-20b
92% → 50% 92 · 84 · 77 · 64 · 56 · 50
60%
60%
33%
-0.8 turns [-1.1, -0.6]
Qwen3-14B
38% → 21% 38 · 35 · 31 · 28 · 25 · 21
0%
0%
15%
-0.5 turns [-0.7, -0.4]
Qwen3-4B
29% → 18% 29 · 27 · 24 · 22 · 19 · 18
0%
0%
61%
-0.9 turns [-1.0, -0.8]
What "success" means. A run succeeds when its weighted field score reaches 0.8. The total is worth 2 of 10, so a run whose only error is the total still counts as a success. The Qwen models never got a total right, so every Qwen success is a record correct in everything except the total.
Giving up. After an injected failure, the small Qwen stopped without submitting in most runs. The larger Qwen rarely did. Grit differs more between models than tool count does.
Recovery. A failure costs extra turns only because the agent asks again for what failed. Beyond that retry, faulted runs took fewer turns than their controls, because some gave up early.
Which tool, not how many
The tools arrive in a fixed order, so a change at one step could be the tool, not the count. Tool order B adds the same tools in a different order to tell the two apart. For gpt-oss-20b, the model that could compute the total, the same tool moved success in both orders:
Tool added
Mix A: position
Mix A: change in success
Mix B: position
Mix B: change in success
web search
tool 3
−4 points [−9, +1]
tool 4
+4 points [−1, +10]
calculator
tool 4
+5 points [0, +10]
tool 5
0 points [−5, +5]
spreadsheet
tool 5
−6 points [−11, −1]
tool 3
−10 points [−15, −5]
email
tool 6
+3 points [−2, +8]
tool 6
+1 points [−4, +6]
Change in success when the tool is added, pooled over failure rates, with its 95 percent interval. Bold: the interval excludes zero. For the two Qwen models no step moved success beyond chance in either order. The spreadsheet holds each line's amount and should help, but it hurt in both orders.
Why the spreadsheet hurts. Its numbers are right: all 452 line amounts match the answer key. The trouble is when the model reaches for it. In all 453 runs where gpt-oss-20b opened the spreadsheet, it did so right after the invoice had failed to load. Instead of asking for the invoice again, it switched to the spreadsheet, which has the line items but not the invoice number, date, vendor or currency. In 184 of those runs it never saw the invoice at all, and only 16 percent of the runs that opened the spreadsheet succeeded, against 75 percent of those that did not. So the damage grows with the failure rate: in tool order A, 3 points with no failures and 12 when half the calls fail.
In plain words: a plausible shortcut pulled the agent away from simply trying again. A partial substitute did more harm than the failure it was reaching around. With no failures the model never opened the spreadsheet, and the few points lost there are arithmetic slips of the kind any change to the prompt can shift.
The instrument, checked first
Before the sweep, the noise floor measured how much the instrument itself varies. Each model reran one cell (3 tools, 20 percent failures): 50 times with identical inputs on 20 documents, and 50 times with a new random seed on all 100 documents.
Model
Identical reruns reproduced
Outcome changes, fixed seeds
Cell success across 50 seeds
phi
Documents whose outcome depends on the seed
gpt-oss-20b
100%
0 of 20
71–84%
0.69
70 of 100
Qwen3-14B
100%
0 of 20
30–33%
0.16
7 of 100
Qwen3-4B
100%
0 of 20
23–27%
0.20
4 of 100
Every identical rerun reproduced its transcript byte for byte, so the setup is exactly repeatable. With new seeds the cell's success moved far less than chance alone would move it (phi below 1), so each cell's interval is wider than it needs to be: the intervals err on the safe side. The Qwen models give nearly the same answer on a document whatever the seed, but gpt-oss-20b does not. The noise floor is reported beside the intervals, never inside them.
How it was run
Task
Invoices
Extract an invoice's fields and submit the record. The invoices are synthetic, and no amounts are printed: each line, the tax and the total must be computed from stated rules.
Axes
2
Tool count, 1 to 6, against the share of tool calls made to fail, 0 to 50 percent in six steps. One-tool cells are out of scope.
Models
3 local
gpt-oss-20b, Qwen3-14B and Qwen3-4B on llama.cpp, one request at a time. No hosted model in snapshot 1.
Runs
18,720
100 per cell per tool order, two orders, three models. Plus 18,000 noise-floor runs.
Intervals
95%
Wilson per cell, Newcombe between cells. The verdicts come from one pre-registered model per test.
Reproducible
Exactly
Every stack passed a three-regime determinism gate, and every identical noise-floor rerun matched byte for byte.
The tool mix
The task needs two tools: fetch_document and submit_record. Each step above two adds one tool in a fixed order. Tool order A, the one the verdicts use:
Tool 3: search_web, a plausible alternative route to the document.
Tool 4: calculator. At this task's difficulty it can do the arithmetic the reader otherwise does in its head.
Tool 5: read_spreadsheet, which holds each line's amount, so it too can help.
Tool 6: send_email, plausible but the wrong action.
Tool order B adds the spreadsheet third, then web search, the calculator and email. Both orders ran in snapshot 1. Only order A moves the verdicts, and order B is reported as descriptive, as the pre-registration says. An earlier version of this page called the calculator irrelevant and the spreadsheet a near-duplicate. At the difficulty chosen by calibration neither is true.
What each dial stands for
Experimental variable
Represents here
Does not claim to measure
Tool count
The number of external systems an agent can reach
Organizational size
Tool-failure rate
How reliable those systems are
Market or environmental volatility
Recovery cost
The extra turns an agent spends after a failure
Organizational recovery
Success rate
Getting the job done under this fixed harness
General agent capability
The mapping from these dials to the theory's terms is an assumption, not a finding.
The two shapes the map could return
Before the sweep, this page showed the two answers the instrument could give. Both grids are illustrative, not data. Snapshot 1 returned the second shape for all three models: a continent with a slope.
Illustrative shape, not data: a band. High success sits at two to four tools and falls off at five and six, an upper edge with an interior peak, and decays as faults rise. The one-tool column is out of scope, not a finding.Table view
Figure A, illustrative values, percent success. Not data. The one-tool column is out of scope: the task is defined at two tools.
Fault rate
1 tool (out of scope)
2 tools
3 tools
4 tools
5 tools
6 tools
0 percent
-
88
93
90
61
33
10 percent
-
85
90
86
56
30
20 percent
-
74
81
75
47
25
30 percent
-
52
58
53
35
20
40 percent
-
30
33
31
24
15
50 percent
-
18
19
18
15
11
Illustrative shape, not data: a continent. Success at six tools stays within sampling error of the peak, so there is no interior peak and no upper edge, and it decays smoothly with faults. This is the shape that restricts test 1, and the one snapshot 1 found. The one-tool column is out of scope, not a finding.Table view
Figure B, illustrative values, percent success. Not data. The one-tool column is out of scope: the task is defined at two tools.
Fault rate
1 tool (out of scope)
2 tools
3 tools
4 tools
5 tools
6 tools
0 percent
-
90
92
91
89
88
10 percent
-
84
86
85
83
82
20 percent
-
72
74
73
71
70
30 percent
-
55
57
56
54
53
40 percent
-
36
37
36
35
34
50 percent
-
21
22
21
20
20
Pre-registration
The rules, revision r4, were confirmed by the author decision by decision, frozen with every fixed input hashed, and deposited on Zenodo on 26 September 2026 before any snapshot run: doi.org/10.5281/zenodo.22982434. The deposit holds the rules, their prose version, the configuration and its lock, the method note and the calibration and determinism records.
Test 1, upper tool edge (P1 in the deposit). One logistic regression per model on tool order A: success against tools, tools squared and failure rate, clustered by document.
Survives: the curve bends down, its peak lies inside two to six tools, and success at the peak is above success at six tools by more than chance, with no failures.
Restricted: no downward bend, a peak outside the range, or a drop at six tools shown to be smaller than 15 points, the smallest effect worth reporting.
Below resolution: the data cannot tell.
Test 2, recovery cost (P2 in the deposit). Runs that recovered from an injected failure against the same document without failures: survives when they took more turns by more than chance, restricted when any extra cost is shown to be below one turn, and below resolution otherwise.
Decided before the sweep, 27 September 2026. Every run the server rejected as unparseable model output is recorded with its cause and reported both ways. The verdicts keep the deposited rule. The descriptive reports above were committed before any result was looked at.
The full rules, the smallest effects, the bootstrap and the order in which verdicts are assigned are in the deposit and in the method note inside it.
Threats to validity
One task. Snapshot 1 speaks about invoice extraction under this harness, not agents in general.
Three small local models. A replicate, not a population. An exploratory trial of larger models through OpenRouter, outside the snapshot, found far bigger islands.
What success means. The 0.8 threshold admits a record whose total is wrong. The fully correct rate is reported beside it.
Tool identity. The order of tools decides what a step measures. Tool order B separates the two, descriptively.
An instruction conflict. The prompt asks for one submission. A failure on the submit tool forces a second. The failure axis partly measures whether a model breaks that instruction to retry.
Unparseable replies. gpt-oss-20b produced 24 replies the server could not parse. Counting them as failures changes neither verdict.
Construct mapping. The dials above stand in for the theory's terms by assumption.
The harness is a pinned Python package: a fixed executable grader, a fault injector, a runner that resumes after any interruption, the statistics and a reviewer's command that recomputes every number from the raw runs. The results bundle, 38,475 files, is deposited as 10.5281/zenodo.23066893 and passes that check exactly. The repository is public at github.com/delimiterbob/islands-harness. The deposited lock identifies the exact code that ran.
The same instrument can map your own agent on your own task before production. That is a service, and it lives at encarnacao.net.
Credited instruments
The Map does not replace any of these. It borrows from most of them.
METR's task-horizon measurements. How long a task an agent can complete at a given success rate, tracked across model releases.
Chroma's context rot study. Performance degrading as input length grows, even on simple tasks.
NoLiMa. Long-context retrieval when the answer shares no words with the question.
tau-bench pass^k. The chance an agent succeeds on all k attempts at the same task, not just once.
FormatSpread. How far accuracy moves when only the prompt format changes.
PromptBench. Robustness to adversarial edits of the prompt.
HAL's scaffold-by-model grids. The same agent scaffolds run across many models, with cost beside accuracy.
Sinha et al. on self-conditioning. Models becoming more likely to err after seeing their own earlier errors in context.
What none of them publishes is a two-axis viability grid with its tests deposited before the sweep, and within-run recovery with sampling error and a measured noise floor beside it.
What was cut
Hysteresis and ghost rate as grid quantities. Stateless inference has no path through the grid, so there is nothing to lag. They may return as within-run quantities.
Per-release cadence. At most two snapshots a year, each dated, with the models pinned. Tracking the same map across model versions is the plan for islands that move.
Model size as an axis. In snapshot 1 it is a replicate: the same grid on three local models.
A hosted headline model and a deposited cliff forecast. Snapshot 1 ran on local models only, at no API cost, so the spend forecast and the cliff forecast built on it were not made.
A ring-shaped island enclosed on the failure axis. No mechanism, corrected in draft r2.
Draft site. Each domain page states whether its numbers are real data, a model or an illustration.
The site's propositions, carried into physics, astronomy, ecology, climate, chemistry, economics and law, each on its own terms.
Each page below names the sense of island it uses, says whether its numbers are real data, a model or an illustration, and says where each proposition stands in that domain: tested, frozen for a test, illustrated, only resembled, or broken. The cross-domain rule on the theory page decides which: a proposition moves into a domain only when its mathematical or causal structure does. A result in one domain says nothing on its own about another.
The domains
Each domain has two labels. The first says what its numbers are. The second says how far its testing has got: no test, test drafted, test frozen, test deposited, or tests run. Two domains have no test by design: nuclear decay is the reference the others are measured against, and stars leave their island on schedule, by running out of fuel, so they cannot test what the propositions claim. The verdicts are in the ledger, one row per proposition.
real data2 tests run
AI agents
The first instrument: where an agent keeps doing its job as it gets more tools and its tools start failing. Snapshot 1, three models, 18,720 runs.
Rules for a technology whose frontier moves every few months: how long a compute record lasts, against the years the EU's AI Act took to make. Proposition 6's ratio, with real numbers.
The asteroid belt from 895,910 real orbits: gaps and islands at Jupiter's resonances, and a test of where proposition 3 stops applying, which ran twice: the first run was invalid, and the corrected run was void because its own control failed.
The ice-age flips in Greenland's ice: did the cold spells end at random or on a clock? Two tests on the real record, run once. The cold spells look memoryless, and there was no clock.
23,191 marine genera from the Paleobiology Database: Van Valen's law of constant extinction, the mass extinctions, and a re-run of published work, under rules fixed in advance, that kills proposition 3 here.
US business cycles since 1854, the calm before 2008, a currency peg you can run to its end, and the incomes of 141 countries since 1950. A test of expansions in 42 countries, run once. Its verdict is unresolved.
The US death rate by age, the glucose tolerance test as a push that finds what watching misses, and herd immunity as an island paid for by every birth cohort. A test of the measles runway, country by country, run once. Its verdict is unresolved.
Supercooled water and diamond: states that persist without being stable. Real droplets freezing in a wind tunnel, and a tray of droplets to freeze in your browser, where frailty imitates memory.
One row per proposition, one column per domain, in the words each domain page uses. Framing propositions 5 and 6 are applied in one domain so far, the economy.
Proposition
AI agents
AI governance
Nuclei
Lake
Orbits
Stars
Ice ages
Evolution
Firms
Economy
Health
Water
P1 Sparsity
measured: restricted or below resolution
not applied
resemblance of form
not applied
not applied
not applied
not applied
not applied
resemblance
resemblance
not applied
not applied
P2 The evidence rule
measured: survives
illustration
illustration
E1 restricted, E2 survives
illustration
not applied
description only
not applied
not applied
illustration
illustration, real data
illustration
P3 Exit statistics
no instrument yet
not applied
reference case
E3a survives, E3b unresolved, E3c survives
scope test: r1 invalid, r2 void
condition not met
C1 survives, C2 no clock
killed
objection shown
described, X1 unresolved
condition not met
illustration, real data
P4 Cost
no instrument yet
not applied
does not transfer
illustration
does not transfer
carries over (illustration)
hypothesis
illustration (the Red Queen)
illustration
illustration, real runways
measles runway: unresolved
does not transfer
P5 Transit
no instrument yet
illustration
not applied
not applied
not applied
not applied
not applied
not applied
not applied
illustration
not applied
not applied
P6 The era ratio
not applied
illustration, real data
not applied
not applied
not applied
not applied
not applied
not applied
not applied
instrument built, series not named
not applied
not applied
What the pattern suggests
Proposition 4 splits the domains in two. It carries over where an island is held up by something flowing through it: a star by the fuel it burns, a firm by the money it spends, a currency peg by the reserves its central bank sells, a clear lake by the nutrients someone keeps out of it, and, if the leading explanation is right, the ice age's warm state by the ocean's heat transport. It breaks where an island is held by a barrier or by a conservation law: a nucleus, an orbit, a supercooled droplet, a diamond. Those keep their depth for free, which is exactly proposition 4's own falsifier. Version 0.2 of the theory now states that scope: in a system held by a throughput, depth is a flow, with the scope defined by a runway measured apart from outcomes.
Proposition 3 needs two conditions the domains keep testing. Exits are memoryless only when the disturbance is steady and the islands being counted are alike. Stars leave their island by exhaustion, on schedule. Orbits without friction stick, so the orbits test expected memory there. Neither of its two runs counts: the first did not measure what it was built to measure, and the corrected run's control failed. And firms and mixed droplets show how differences between islands produce a falling hazard with no memory at all. The fossil record goes further: a published analysis of marine genera (Finnegan, Payne and Wang, 2008) found the fall with age remains after geographic range and species richness are accounted for, which by version 0.2's terms counts against the proposition there. Its re-run on today's database, under rules fixed in advance, killed proposition 3 in the fossil record. The proposition's falsifier already said "conditional on depth". Version 0.2 spells out what that condition carries. The answer recorded to the obvious objection is that each exception must be shown, not assumed.
Both changes were adopted by the author in v0.2, labeled internal because they come from the site's own evidence rather than an outside objection. The skeptic's reading of each is entered as an open objection on the theory page.
Proposition 6 has its first real numbers. On the AI governance page, the compute record changes hands every few months, while the EU's AI Act took years to make: a ratio well below one, where proposition 6 says navigation fails. It is an illustration, not a test, because the proposition's series is not named.
Draft site. The chart and every number on this page come from NUBASE2020, the published evaluation of nuclear data.
Islands across the sciences · nuclear physics · reference case
The chart of nuclides
The island this site is named after, drawn from the standard table of every known nucleus.
Sense of island: chart-islandData: NUBASE2020, published 2021Tests no proposition
Every atom has a nucleus made of protons and neutrons, and each combination is called a nuclide. Of the 3,340 nuclides ever observed, 253 have never been seen to decay. The rest fall apart, some within a billionth of a trillionth of a second, others over billions of years. Drawn with neutrons across and protons up, the survivors make a thin band through a wide sea of decay, and past its far end physicists have predicted, since the 1960s, a second island that nobody has reached.
Which sense of island. This page uses the chart-island, Seaborg's sense: a region on a chart whose occupants outlast their neighbors. That is a convention about relative lifetime, not a claim about dynamics, and the theory page keeps it apart from the other two senses. The table near the end says, proposition by proposition, where the site's claims carry over to nuclei, where the resemblance is only one of form, and where it breaks.
The chart
Each square is one nuclide, placed by its number of neutrons (across) and protons (up). Hover over a square or tap it to read it. With a keyboard, focus the chart and use the arrow keys.
Loading the table.
Source: NUBASE2020 (Kondev, Wang, Huang, Naimi and Audi, 2021). Squares with the page's ink color have never been seen to decay. In the half-life view, paler squares decay faster (in dark mode, dimmer ones do), and faded squares have half-lives the evaluators estimated rather than measured. Thin lines mark the magic numbers of protons and neutrons (2, 8, 20, 28, 50, 82, 126), where nuclei hold together unusually well. The dashed outline is where theory puts the island of stability: 184 neutrons and, depending on the model, 114, 120 or 126 protons. Nuclides reported after the evaluation, such as rutherfordium-252 in 2025, are not on the chart.
What the chart shows
Every number in this section is counted from the table by a script and written into the page by another. None is typed by hand. The method is at the end of the page.
Rare
Of the 3,340 nuclides ever observed, 253 (7.6 percent) have never been seen to decay. The evaluators list 218 more that the trends of the chart say should exist, but nobody has made them. 288 have a measured abundance in nature: the 253 stable ones, 32 that decay so slowly that some survive from before the Earth formed, and three that are topped up by the decay of uranium. Others occur only in traces, made by cosmic rays or by the decay of uranium and thorium, and most of the chart exists only when made in a laboratory, a reactor or a star.
Bounded, and narrower as nuclei grow
No stable nucleus is heavier than lead-208 (82 protons, 126 neutrons). The share of observed nuclides that are stable falls as nuclei grow, from 14 percent among the lightest to about 8 percent among the heaviest that have any, and is zero above 208 nucleons.
Nucleons (mass number)
Observed
Stable
Share stable
1 to 40
283
40
14 percent
41 to 80
494
49
10 percent
81 to 120
595
54
9 percent
121 to 160
673
53
8 percent
161 to 208
696
57
8 percent
209 to 295
599
0
0 percent
The band also bends. Light stable nuclei carry about one neutron per proton (1.07 on average up to calcium), heavy ones about one and a half (1.47 on average from promethium to lead, and lead-208 carries 1.54). And it has holes: technetium (43) and promethium (61) have no stable isotope, and no stable nucleus has 5, 8, 147 or 151 nucleons. Tin, with the magic number of 50 protons, has the most stable isotopes: 10.
The reason is known. The strong force that binds a nucleus reaches only to its nearest neighbors, while the electric repulsion between protons reaches across the whole nucleus, so every proton pushes on every other. As a nucleus grows, the repulsion grows faster than the binding. Extra neutrons add binding without adding charge, which is why the band bends toward them, but past lead no arrangement is stable at all.
Persistence is not depth
In 246 of the 1,662 cases where both half-lives are measured (15 percent), a nucleus holding extra energy, in an excited state, outlives the same nucleus in its lowest-energy state. The extreme is tantalum-180. In its ground state it decays with a half-life of 8.2 hours. With 75.3 keV more energy it has never been seen to decay (half-life above 4.5 × 1016 years), and it is the only excited nuclear state found in nature.
Nuclide
Extra energy
Half-life, excited
Half-life, ground state
tantalum-180
75.3 keV
never seen to decay (> 4.5 × 1016 years)
8.2 hours
bismuth-210
271 keV
3 million years
5 days
polonium-212
2,923 keV
45 seconds
294 nanoseconds
silver-108
109 keV
439 years
2.4 minutes
silver-110
118 keV
250 days
25 seconds
holmium-166
5.97 keV
1,133 years
1.1 days
americium-242
48.6 keV
141 years
16 hours
indium-114
190 keV
50 days
1.2 minutes
What holds such states is a blocked exit, not a deeper well. To decay, the nucleus would have to change its spin by a large step, and transitions that need a large step are extremely slow. The newest superheavy nucleus shows the same thing: rutherfordium-252, reported in 2025 after this table was published, lives 60 nanoseconds in its ground state and about 13 microseconds in an excited one, some 200 times longer.
"Stable" means "not yet seen to decay"
For 55 of the 253 stable nuclides, experiments have looked for a decay and set only a lower limit on the half-life (calcium-40: more than 9.9 × 1021 years), and for 68 the table lists a decay that is allowed on energy grounds but has never been seen. Bismuth-209 was counted as stable until 2003, when its alpha decay was measured. Its half-life is 2.01 × 1019 years, about 1.5 billion times the age of the universe. On this chart, stable means not yet seen to decay.
The shore of the superheavy island
124 nuclides with 104 or more protons have been made, most of them a few atoms at a time. In all 13 of the elements with at least three measured half-lives, half-life rises with the number of neutrons: within an element, each added neutron multiplies it by about 2.1 on average. The most neutron-rich reached have 177 neutrons (nihonium-290, livermorium-293, tennessine-294 and oganesson-295), seven short of the 184 at which every model places the island. The longest-lived superheavy nucleus known is dubnium-268, at 1.2 days.
Measured half-lives of the elements with 104 to 118 protons, one line per element, against the number of neutrons, on a logarithmic scale. The dotted line at 162 neutrons marks a gap in the energy levels of deformed nuclei that lengthens the lives of its neighbors. The dashed line at 184 marks the island's predicted center, which no experiment has reached.
Charted from the inside out
The chart was filled in from the inside out. The stable nuclides were identified first (median year 1930), the radioactive ones up to bismuth later (median 1973), and the superheavy shore last (median 2004). The count of known nuclides passed 1,000 in 1954, 2,000 in 1977 and 3,000 in 2009. Press Play above the chart to watch it fill.
That order runs against a clause of proposition 2, that boundaries are observed before interiors, and the reason is instructive. Proposition 2 is about islands found by pushing a system until it fails to recover. The mainland of this chart was found by waiting: nature had already kept the stable nuclei for billions of years, and the unstable ones had to be made. For the superheavy island the clause does describe what happened: its shore is charted, and its interior is not.
Cost line and fragility line
The site admits an island claim only if it states what the island costs and where it breaks. For the nuclear island:
Cost line. Nothing is spent to keep a nucleus on the island: binding energy is released when a nucleus forms, not paid to hold it together. The cost on this chart is the cost of getting there. The heaviest elements have been made only a few atoms at a time, over months of continuous beam.
Fragility line. As nuclei grow, alpha decay and fission take over, which is where the band ends. Nuclei with 104 or more protons exist only because of the extra binding that closed shells give. Without it they would split apart almost at once. The predicted island is made entirely of that extra binding.
How the propositions meet the chart
The cross-domain rule lets a proposition move to a new domain only when its mathematical or causal structure transfers, not merely its vocabulary. Nuclear physics is a domain where the answers are known, which makes it a place to check the site's words rather than to test its claims.
The stable region is rare and bounded, and it narrows as nuclei grow. The cause has the same form as proposition 1's clause on coupling: a repulsion that couples every proton to every other grows faster with size than the binding, and past a size no arrangement holds. A shared form, not a test.
On a chart-island, persistence is the definition of the island, so proposition 2 cannot be tested here. Two of its clauses still show. Excited states that outlive their ground state persist because the exit is blocked, not because the well is deeper. And every located island is a revisable estimate: bismuth-209 was stable until 2003, and the models still disagree on the proton number at the island's center.
Radioactive decay is the textbook memoryless exit: a nucleus that has lasted a billion years is exactly as likely to decay in the next second as one made a second ago. Proposition 3 borrows this structure (Kramers's 1940 escape rate is among its prior owners). Here it holds by physics, which makes decay the reference that a hazard estimate for agent systems should reproduce.
Does not carry over. A nucleus keeps its binding without spending anything: here depth is a stock, not a flow. That is proposition 4's own falsifier, depth persisting without expenditure, and it holds because a nucleus faces no drift: nothing wears it down while it waits. Charts like this one led version 0.2 of the theory to write that scope into the wording: proposition 4 is now stated for systems held by a throughput, which a nucleus is not.
Nothing on this page tests a proposition. The physics is settled and the table was published in 2021, before this page existed, so there was nothing to pre-register. The page does three things. It shows the object the site is named after, measured rather than drawn. It checks the site's vocabulary against a system whose answers are known. And it marks where the resemblance ends. Instruments that can test propositions in other sciences will be listed under Islands across the sciences as they are built.
Source and method
Table: NUBASE2020, F.G. Kondev, M. Wang, W.J. Huang, S. Naimi and G. Audi, The NUBASE2020 evaluation of nuclear physics properties, Chinese Physics C 45, 030001 (2021), doi:10.1088/1674-1137/abddae. License: CC BY 3.0. File nubase_4.mas20.txt from the IAEA mirror of the Atomic Mass Data Center, retrieved 2026-09-29, 761,906 bytes, SHA-256 1585a5eea86c5e17e90307c7e6e786d060049c4039e392a261ff6db977df9859.
Errors in the table. A script checks the whole table for errors a reader can find without another source: impossible discovery years, stable nuclides listed with an observed decay, decay codes the format does not define, decay branches that add up to more than 100 percent, and natural abundances that do not add up to 100 percent. It found seven candidates. Five are errors. The published file is left as it is, and each correction is applied before anything is counted:
227Ac, discovery year: 1851 in the table, 1902 here. 1851 is before radioactivity was discovered in 1896. Fry and Thoennessen's survey of nuclide discoveries credits Giesel's 1902 paper. Source: C. Fry and M. Thoennessen, Discovery of the actinium, thorium, protactinium, and uranium isotopes, arXiv:1203.1194.
151Ho, beta-plus branch: B+=88 3 in the table, B+=78 3 here. The ground state's branches add up to 110 percent (beta-plus 88, alpha 22). The evaluated structure data give electron capture and beta-plus 78(3) percent, alpha 22(3). Source: IAEA LiveChart of Nuclides, ground state of holmium-151 (ENSDF evaluation by B. Singh), queried 2026-09-29.
126Pdp, decay-mode code: B=72 8 in the table, B-=72 8 here. The code 'B' has no sign. Palladium-126 has 80 neutrons, far more than any stable palladium isotope, so only beta-minus decay is possible. Source: the table's own format, and beta-plus is energetically impossible for this nucleus.
123Te, decay mode of a stable nuclide: EC=100 in the table, EC ? here. Tellurium-123 is listed as stable, with only a lower limit on its half-life, but its decay mode is written as an observed one. The table writes an allowed but unobserved decay with '?', as it does for every other stable nuclide. Source: the table's own format.
204Tl, decay-mode code: EC+B+=2.92 7 in the table, EC=2.92 7 here. 'EC+B+' is not a code the format defines. The decay energy of thallium-204 is too small for beta-plus emission, so the branch is electron capture, which the format writes EC. Source: the table's own format and the decay energy in the same evaluation.
The other two were checked and are right:
4He: Correct. Rutherford and Royds identified the alpha particle as helium-4 in 1908, before isotopes were named. The rule's 1913 threshold is for identifications by mass.
127Agn: Correct. This excited state of silver-127 was reported in Physics Letters B in 2021, and the evaluators included it.
Counting rules. A nuclide counts as observed when the table gives its year of discovery. The others are the evaluators' expectations from trends. Stable means listed as stable. A half-life counts as measured when it is not derived from trends, not a limit and not approximate. An excited state is compared with its ground state only when both half-lives are measured, or when the excited state is listed as stable. The predicted island's position is from the literature, not the table: Myers and Swiatecki (Nuclear Physics 81, 1966) and Sobiczewski, Gareev and Kalinkin (Physics Letters 22, 1966) put it at 114 protons and 184 neutrons. Self-consistent models put the proton number at 120 or 126 (Bender, Nazarewicz and Reinhard, Physics Letters B 515, 2001). Bismuth-209's decay: de Marcillac and colleagues, Nature 422, 2003. Rutherfordium-252: Khuyagbaatar and colleagues, arXiv:2501.08955, 2025.
Code. The code that reads the table refuses any file whose SHA-256 differs from the one above, and every number on this page is counted from the table, not typed by hand.
Draft site. The lake below is a model running in your browser. Its tests ran once, on 30 September 2026.
A shallow lake can stay clear or turn murky under the same nutrient load. Where is the edge of the clear state, and how would you find it: by watching, or by pushing?
Sense of island: basin-islandModel: Carpenter, Ludwig and Brock, 1999Tests run once, 30 September 2026
Phosphorus washes into a lake from the land around it. Some settles into the mud, and the mud releases it again, faster when the water is already rich in it. That feedback gives a lake two ways to be: clear, with little phosphorus in the water, or murky, with a lot, and in a middle range of loadings both are possible. A clear lake in that range stays clear until something pushes it far enough, and then it turns murky and stays murky even after the push is gone. Ecologists have seen this in real lakes, and they model it with one equation. This page runs that equation.
A model, not a lake. Everything here happens in the standard lake model, run in your browser. The model is the object the site's propositions 2 and 3 are stated for, a basin-island: an attractor with a boundary. Tests of those propositions in this model were frozen with their decision rules, deposited with a date, and then run once. What a model test can show, and what it cannot, is at the end of the page.
Push the lake
The lake starts clear. Raise the loading and watch the clear state's valley grow shallow. Push the lake and see whether it comes back. The left panel is the phosphorus in the water over time. The right panel is the landscape the lake rolls on: each valley is a stable state, and the hill between them is the edge.
The lake above, drawn from the model's phosphorus level. Clear water lets light reach the plants on the bottom. As phosphorus rises the water turns green with algae and hides them. The disk hanging from the boat is a Secchi disk, which limnologists lower into a lake until it vanishes. It is drawn at the depth where it would still be seen. An illustration: the colors and depths follow the phosphorus level but are not computed from optics.
Phosphorus over the last 60 time units. Blue: the clear state. Red dashes: the edge. Orange: the murky state.
The landscape at this loading. The dot is the lake.
The map of the lake
In this model the clear state exists only while the loading is below 0.660, and the murky state only above 0.389. Between those two loadings both exist, and which one a lake is in depends on its history. The two ends are called folds: at each, a stable state meets the edge and both vanish.
Where the lake can rest, for each loading. The blue line is the clear state and the orange line the murky one. In the shaded band both exist, and the dashed red line between them is the edge. The dot is the lake in the panel above. Raising the loading slowly carries a clear lake along the blue line until it ends, and then the lake falls to the orange line. To get it back, the loading has to come down to where the orange line ends, much lower. That gap is called hysteresis.
How the island shrinks
Two numbers describe the clear state's island at each loading. The recovery rate is how fast the lake pulls a small disturbance back. The depth is how high the hill is between the clear valley and the edge. Both come from the model's equation, and neither needs noise to compute.
Loading
Clear state
Edge
Room before the edge
Recovery rate
Depth
0.450
0.452
1.054
0.603
0.97
0.077
0.500
0.504
1.000
0.496
0.93
0.050
0.550
0.560
0.951
0.392
0.87
0.028
0.600
0.622
0.899
0.277
0.72
0.011
0.640
0.688
0.843
0.155
0.47
0.0021
0.655
0.728
0.805
0.077
0.25
0.00026
The recovery rate stays high over most of the range and then collapses near the edge. That collapse is critical slowing down: just before a lake tips, it takes longer and longer to recover from anything. It is also why watching might work: a lake that recovers slowly also wanders further and remembers its recent past longer, and those passive signs are the early warnings ecologists look for. Whether they find the edge as well as a push does is the first question below.
What the tests asked
Three tests were frozen with their decision rules and the smallest effects that would count, then deposited with a date, as the Map's were, and run once. Their random seeds come from that deposit's identifier. The results follow the three questions.
restricted
E1. Watching or pushing: which finds the edge?
Six lakes approach the edge. One observer only watches each lake's natural fluctuations. Another pushes it ten times and times its recovery. Both take the same 101 measurements and use the same method to estimate where the edge is. Bears on proposition 2, which is killed if watching locates the edge as well as pushing does.
survives
E2. The ghost: a doomed lake that looks safe
One lake is just inside the edge and will stay clear. Another is just past it: its clear state has vanished, but it lingers where the state used to be and will tip in a few dozen time units. Over the observation window it drifts no more than its natural fluctuation. Can watching tell them apart? Can a push? Bears on proposition 2's central clause, that persistence is not evidence of an island.
E3a survives · E3b unresolved · E3c survives
E3. Exits: memory, depth and warning
With steady weather, clear lakes eventually tip by chance. Does the chance of tipping fall as a lake ages? Does the average stay grow in a straight line with the island's depth, or exponentially? And does every tip give a warning? Bears on proposition 3, which says exits are memoryless and some come without warning. Here theory predicts the answer, so this test checks that the proposition's structure carries over to lakes rather than discovering anything.
Results
The three tests ran once, on 30 September 2026, after the frozen document was deposited as 10.5281/zenodo.23065462. Their random seeds come from that identifier, and every verdict follows the deposited rules. An earlier draft of the deposit was abandoned unpublished before any run, and nothing was run with its number.
Watching was as good as pushing in 3 of the 4 settings. In the setting that favored pushing most, a push of 0.03 at noise 0.005, pushing's error was 0.85 times watching's (0.75 to 0.99), where 0.8 or less was needed. Every setting is in the table below.
Pushing told doomed lakes from safe ones better than watching by 14.7 points of balanced accuracy (12.3 to 17.0), where 10 were needed. Pushing called 96.8 percent of the doomed lakes doomed and 41.9 percent of the safe ones, watching 57.2 and 31.8 percent. No safe lake was tipped by a push.
The Weibull shape of 2,000 lakes' exit times was 1.014 (0.980 to 1.049), inside the band of 0.9 to 1.1 that counts as memoryless. Every lake had tipped before the run ended.
At depth ratios 3, 4, 5, 6 and 7 the mean stays were 245, 575, 1,492, 3,623 and 9,579 time units. A straight line misses them by up to 607 percent and an exponential by up to 13 percent. The rules needed one of the two within 10 percent and the other outside it.
At a false-alarm rate of 10 percent, the alarm caught 20.1 percent of 1,286 exits (18.0 to 22.3), where 50 percent or less was needed. Its positive control caught 88.6 percent (85.5 to 91.1), above the 80 percent it had to reach for the test to count.
Noise
Push
Pushing's error over watching's, with its interval
Surveys where pushing found no edge
Call
0.005
0.01
1.68 (1.42 to 2.04)
24.2 percent
watching as good
0.005
0.03
0.85 (0.75 to 0.99)
0.6 percent
unresolved
0.01
0.01
4.93 (3.28 to 7.28)
39.2 percent
watching as good
0.01
0.03
1.23 (1.09 to 1.45)
11.7 percent
watching as good
Each verdict is on a test in a model of a lake, narrower than the proposition it bears on. The tests say what propositions 2 and 3 imply in this model, and nothing on their own about real lakes, organizations or AI agents. The pre-registration read a restricted E1 as a refinement of proposition 2: pushing is evidence only when the push is large against the lake's own fluctuations. Proposition 2 took that refinement in v1.0.
Cost line and fragility line
Cost line. A clear lake in the bistable range stays clear for free only while the loading stays where it is. Keeping the loading low is continuous work in the catchment, such as buffer strips, fertilizer rules and sewage treatment, and the island's depth is bought by it. When the work stops and the loading creeps up, the island shrinks.
Fragility line. The clear state ends at the upper fold. Before that, a storm's worth of phosphorus larger than the distance to the edge tips it, and near the fold that distance goes to zero. Once murky, the lake does not come back until the loading falls below the lower fold.
Illustrated, not tested: the clear island's depth is set by a loading that someone has to keep low. The model takes the loading as given, so it cannot measure the cost.
A model test shows what the propositions imply in the system the model describes, under the model's assumptions: one variable, weather as white noise, pushes that act instantly. If a proposition fails in the standard model of a bistable lake, that is a real strike against its general form. If it holds, it has held in the easiest case, which is necessary but far from sufficient. The next step for this domain is real data, such as the whole-lake experiment in which Carpenter and colleagues pushed Peter Lake toward a regime shift and watched for early warnings (Science 332, 2011).
Source and method
Model: dx/dt = a − b x + r xq/(hq + xq), from Carpenter, Ludwig and Brock, Ecological Applications 9, 1999, with b = 1, r = 1, h = 1 and q = 8, where x is phosphorus in the water and a the loading, both in the model's units. The numbers on this page are computed from the model's equation, and the design numbers for the tests from its equations alone. The browser runs the same equation with Euler steps of 0.01 time units and Gaussian noise. The frozen pre-registration (r1) is deposited, with its code, as 10.5281/zenodo.23065462.
Draft site. The belt is measured from NASA/JPL data. The map is a model running in your browser. Its test ran twice, on 30 September 2026, and neither of its two runs counts: the first did not measure what it was built to measure, and the corrected run's own control failed.
Islands across the sciences · astronomy · real data and a model
Orbits
Around the Sun, stable orbits sit in islands. Jupiter clears some lanes of the asteroid belt and shelters crowds in others, and the same cause does both.
The belt: chart-island, real dataThe map: islands of regular motionTwo runs, neither counts
An asteroid's year depends on its distance from the Sun. Where that year is a simple fraction of Jupiter's, say one third of it, the asteroid meets Jupiter at the same points of its orbit over and over, and the repeated pulls add up instead of averaging out. These places are called resonances. Some of them empty the belt. Others hold asteroids in place for billions of years. In the physics of orbits, the stable regions have been called islands of stability for decades: islands of regular motion in a chaotic sea.
Which sense of island. The belt below is a chart-island, as on the nuclear page: regions of a chart whose occupants have outlasted their neighbors. The map further down shows the original dynamical islands, regions of regular motion in a system without friction. The theory page says this second picture carries over to its own islands only as chaotic saddles and long transients. The test on this page was built to check where one proposition stops applying because of that. It ran twice, and neither of its two runs counts: the first did not measure what it was built to measure, and the corrected run's own control failed.
The belt, measured
Every numbered asteroid, counted by its distance from the Sun. The scale is logarithmic, so that the small groups beyond the main belt show. Dashed lines mark Jupiter's resonances: red where the belt is emptier than just beside it, green where it is fuller.
Asteroids per 0.005 au of distance from the Sun (1 au is the Earth's distance). Data: NASA/JPL Small-Body Database, all numbered asteroids, retrieved 29 September 2026. The distances are the orbits' semi-major axes.
Resonance
Distance (au)
Within 0.01 au
Same width beside
Ratio
Reading
4:1
2.06
52
374.5
0.14
gap
3:1
2.50
583
16,829.0
0.03
gap
5:2
2.82
2,512
15,003.0
0.17
gap
7:3
2.96
5,509
10,409.0
0.53
gap
2:1 (the Hecuba gap)
3.28
158
3,495.0
0.05
gap
3:2 (the Hildas)
3.97
1,210
201.0
6.0
cluster
4:3 (the Thule group)
4.29
7
1.5
4.7
cluster
1:1 (the Trojans)
5.20
1,506
1,026.0
1.5
cluster
Of 895,910 numbered asteroids, the deepest gap is at the 3:1 resonance: 583 asteroids within 0.01 au of it, against 16,829 in the same width beside it. The Trojans spread over about 0.3 au around Jupiter's own distance: 10,590 asteroids there, against 14.5 on average in equal widths either side. The database classes 10,633 of them as Jupiter Trojans, and 3,821 asteroids sit in the Hilda group at the 3:2 resonance.
Why the same cause cuts both ways: in a gap, the repeated pulls make the orbit chaotic, its elongation wanders until it crosses the orbit of Mars, and the asteroid is eventually removed. Wisdom showed this for the 3:1 gap in 1982 and 1983. In the islands, the resonance keeps the repeated meetings away from Jupiter: the Hildas are at the far point of their orbits whenever Jupiter passes, and the Trojans stay sixty degrees ahead of it or behind it.
Islands in a chaotic sea
The standard map is the textbook model of motion near a resonance: at each step a kick of strength K changes a momentum, and the momentum moves an angle. Click anywhere in the square to start an orbit and watch where it goes. Near the middle, orbits trace closed curves: that is the island. Elsewhere they scatter through the chaotic sea. Raise K and the sea floods the islands. Lower it and the islands grow and merge.
Click in the square to start an orbit.
Chaotic orbits that come close to an island tend to stick to it: its edge is layered with smaller islands, and an orbit can linger among them for a very long time before it drifts off. In the asteroid belt that shows up as asteroids that sit near a resonance's edge far longer than chance would suggest.
What the test asked
no verdict
Does a long stay near an island predict a long remaining stay?
Proposition 3 says that under a steady stream of disturbances, a stay's age is no evidence of how long it has left. Orbits without friction are the case where that should fail: a stay near an island that has already lasted a long time tends to last much longer, because the orbit is stuck in the island's layered edge. The test followed 10,000 orbits of the map for a million steps, once undisturbed and once with a small random kick at every step. Only the disturbed arm meets proposition 3's condition, so only it can count for or against the proposition. The undisturbed arm shows whether the condition is needed. Theory predicted both answers, so this was a check of the proposition's scope rather than a discovery.
Result of the corrected test, r2
The corrected test ran once, on 30 September 2026, after its rules were deposited as 10.5281/zenodo.23071492. Its random seed comes from that identifier.
Arm
Role
R, with its interval
Stays counted
Call under the rules
Undisturbed, stays counted from entry
the control
0.31 (0.31 to 0.31)
157,412,984
unresolved
Disturbed, a kick of 0.1 at every step, each stay from the center
the test
0.99 (0.98 to 0.99)
28,417,946
memoryless
The control did not show the memory theory predicts, so the instrument failed its own check. In the undisturbed arm half of all stays ended within 2 steps, and all but one in a hundred within 30: the two ages the rules compare fall among quick passes through the neighborhood, before any sticking shows. The disturbed arm's stays were memoryless, but a test whose control fails counts neither way. Verdict on proposition 3: void. Under the rules the test is void, and no verdict on proposition 3 is entered.
The first run, r1, recorded as invalid
The test ran once, on 30 September 2026, after its rules were deposited as 10.5281/zenodo.23066015. Its random seed comes from that identifier.
Arm
R, with its interval
Stays counted
Call under the rules
Undisturbed
0.67 (0.66 to 0.68)
1,240,547,674
unresolved
Disturbed, a kick of 0.1 at every step
81.42 (81.29 to 81.54)
1,120,798,688
memory
R compares the time a stay has left once it reaches an age only one stay in a hundred reaches with the time left at the median age. Memoryless stays give 1, and stays that stick give much more. Under the deposited rules, memory in the disturbed arm kills proposition 3 in this model, and that is the registered verdict.
Recorded as invalid. After the run, the test turned out not to measure what it was built to measure. Its neighborhood, a square drawn around the island, does not contain the island: the island's own orbits swing outside the square on every lap. So the stays it counted are fragments of laps, not stays near the island. In the undisturbed arm, none of 1,240,547,674 stays lasted more than 4 steps, where theory expects stays of thousands of steps at an island's edge. The author has recorded the run as invalid: its verdict counts neither for nor against proposition 3, and its numbers stay here as they came out. A corrected test, r2, followed. Its neighborhood is measured from the island's full edge, its undisturbed arm must first show the stickiness theory predicts before any verdict counts, and every disturbed stay starts at the island's center, so that all have the same depth. It was deposited and run once. Its result is above.
Cost line and fragility line
Cost line. Nothing is spent to keep an asteroid in a resonance: orbits without friction keep their energy. As with nuclei, the island is paid for once, by where the asteroid ended up.
Fragility line. The Trojan islands exist only because Jupiter is light compared with the Sun: Jupiter's share of their combined mass would have to be below about 0.0385 for the points they circle to be stable, and it is about 0.001. The islands also leak slowly: pulls from the other planets let some Trojans drift out over the age of the Solar System.
Illustrated. An orbit stuck to an island's edge looks regular for a long time before it leaves: proposition 2's sticky boundary, in the system where the phrase comes from.
Tested for its scope: whether a stay's age predicts its remaining length, with and without a steady disturbance. It ran twice: the first run was invalid and the corrected run void, so neither counts.
Data: NASA/JPL Small-Body Database (SBDB) Query API, query https://ssd-api.jpl.nasa.gov/sbdb_query.api?fields=spkid,a,e,i,class&sb-kind=a&sb-ns=n, retrieved 2026-09-29, 36,954,812 bytes, SHA-256 1de4bfccccfb39a32895f353bb404c69021c42cf3f7b6273b4443af6f8ba1536. Data: NASA/JPL Small-Body Database, Solar System Dynamics Group, Jet Propulsion Laboratory. The elements are osculating (the orbit at the database's epoch), not proper elements, which blurs the gaps and groups slightly.
Resonances: an asteroid that makes p orbits while Jupiter makes q sits at Jupiter's distance times (q/p)2/3, by Kepler's third law, with Jupiter's mean distance 5.2029 au (Standish, JPL). At each resonance the count within 0.01 au is compared with the mean of two windows of the same width, 0.05 au either side. The Trojans spread wider, so their island is also measured over 0.3 au against equal widths 0.6 au either side. The map: p′ = p + K sin θ, θ′ = θ + p′, both modulo 2π (Chirikov, Physics Reports 52, 1979). On the 3:1 gap: Wisdom, Astronomical Journal 87, 1982, and Icarus 56, 1983. The frozen test (r1) is deposited, with its code, as 10.5281/zenodo.23066015.
Draft site. The chart and every number on this page come from ESA's Gaia mission, Data Release 3.
Islands across the sciences · astronomy · reference case
Stars
A chart of where stars spend their lives, from every well-measured star within 100 parsecs of the Sun.
Sense of island: chart-islandData: Gaia Data Release 3Tests no proposition
Every star has a color, set mostly by its surface temperature, and a true brightness. Gaia has measured both, with the precision this chart needs, for 228,623 stars within 100 parsecs (about 326 light-years) of the Sun. Put on one chart, they do not spread out: most crowd into a single narrow band, the main sequence, and the rest gather in a few other places.
Why this chart is about islands. In a steady population, the number of stars in each part of the chart is proportional to how long stars stay there. Where the chart is crowded, stars linger. Where it is empty, they pass through quickly or never go. That is the chart-island sense exactly: regions whose occupants outlast their neighbors. And this chart holds both kinds of island the site distinguishes: one paid for continuously, and one that costs nothing.
The chart
Each star is placed by its color (across: blue on the left, red on the right) and its true brightness (up: brighter stars higher). Darker shading means more stars. The dashed band is the main sequence as fitted to these stars. The dashed line below it separates the white dwarfs. The ring marks where the Sun would sit.
Color: Gaia's BP minus RP. Brightness: absolute G magnitude, the brightness a star would have at 10 parsecs (smaller is brighter). Data: ESA Gaia DR3. The query and its filters are listed at the end of the page.
What the chart shows
Of the 228,623 stars, 198,056 (86.6 percent) lie within one magnitude of the main sequence's ridge. 4,150 (1.8 percent) are evolved stars, subgiants and giants, brighter than the band on its red side. 17,613 (7.7 percent) are white dwarfs, and the remaining 8,804 (3.9 percent) fall between these regions.
Stars spend most of their lives on the main sequence, which is why it holds most of them, and only a short time as giants, which is why the giants are few: a star like the Sun is a subgiant and giant for roughly a tenth as long as it burns hydrogen on the main sequence. The white dwarfs pile up because nothing ends them. They only cool and fade.
Two kinds of island on one chart
The main sequence is paid for. A star on the main sequence holds its size by burning hydrogen in its core: the energy streaming out holds the star up against its own gravity. The Sun turns about 4.3 million tonnes of its mass into energy every second to stay where it is. When the hydrogen in the core runs out, the balance fails and the star leaves the main sequence, swelling into a subgiant and then a giant. The Sun will spend about ten billion years on the main sequence, and it is a little under halfway through.
A white dwarf costs nothing. What is left when a star like the Sun has spent its fuel is a white dwarf: a core the size of the Earth, held up not by burning anything but by the resistance of its electrons to being squeezed. It has no fuel and needs none. It simply cools, over billions of years. The white dwarfs on this chart are an island of the kind the nuclear and orbits pages found: a stock, not a flow.
Cost line and fragility line
Cost line. For the main sequence, the fuel burned every second, about 4.3 million tonnes of mass turned into energy for the Sun, and far more for heavier stars, which burn faster and leave sooner. For white dwarfs, nothing.
Fragility line. For the main sequence, the fuel in the core: when it is spent, the star leaves, whatever else happens around it. For white dwarfs, a mass limit: above about 1.4 times the Sun's mass, electrons cannot hold a white dwarf up.
Does not apply, and shows why. Proposition 3's condition is a stationary stream of disturbances. Stars leave the main sequence by using up their fuel, so a star's age does predict its remaining life there. Islands that run out of fuel end on schedule, not by chance.
Carries over, for the main sequence: its stability is bought by continuous burning, it ends when the burning stops, and the exit runs through the stabilizer, the core's fuel, rather than through outside shocks. White dwarfs, on the same chart, are the stock-held counterexample, like nuclei. An illustration in a domain where the causal structure transfers, not a test.
Nothing on this page tests a proposition: the physics of stars is settled, and the data were public before this page existed. The page measures the chart, shows where the site's words fit it, and names the one proposition whose structure it shares, P4, as an illustration.
Source and method
Data: ESA Gaia Archive, Gaia Data Release 3 (gaiadr3.gaia_source), retrieved 2026-09-29 through its query service, 228,623 rows, 13,317,543 bytes, SHA-256 c4d25979befe4906d98762bd13e259af01228e7bcceacbdc0f95f4cfd80c1af3. The query: SELECT source_id, phot_g_mean_mag, bp_rp, parallax FROM gaiadr3.gaia_source WHERE parallax > 10 AND parallax_over_error > 10 AND phot_g_mean_mag IS NOT NULL AND bp_rp IS NOT NULL AND phot_bp_mean_flux_over_error > 10 AND phot_rp_mean_flux_over_error > 10 AND ruwe < 1.4. This work has made use of data from the European Space Agency (ESA) mission Gaia, processed by the Gaia Data Processing and Analysis Consortium (DPAC). Gaia Collaboration, Vallenari et al., Astronomy and Astrophysics 674, A1 (2023).
Absolute magnitude is G + 5 log10(parallax in milliarcseconds) − 10. Within 100 parsecs dust dims stars too little to matter here and is ignored. Regions: white dwarfs lie below the line MG = 3.25 (BP−RP) + 9.625. The main sequence is the stars within 1 magnitude of a cubic fitted to the median brightness in color bins of 0.05 between 0.4 and 3.5. Evolved stars are brighter than that band by more than 1 magnitude and redder than 0.7. The Sun's place, color 0.82 and absolute magnitude 4.67, is from Casagrande and VandenBerg (Monthly Notices of the Royal Astronomical Society 479, 2018).
Draft site. The record is real ice-core data. Its two tests were computed once, on 30 September 2026.
During the last ice age, Greenland's climate jumped between a cold state and a warm one again and again, each warming taking only decades. Did those states end at random, or on a clock?
Sense of island: basin-islandData: NGRIP ice core, GICC05 timescaleTests computed once, 30 September 2026
Snow that fell on Greenland over the last hundred thousand years is still there, pressed into ice layer by layer. The ratio of heavy to light oxygen in each layer records how cold it was when the snow fell: the lower the number, the colder. Read down the ice, and the last ice age turns out not to have been steadily cold. The climate kept jumping into warm spells, within a few decades each time, stayed for centuries or millennia, slid back, and waited in the cold again. These are the Dansgaard-Oeschger events, named for the two scientists who found them.
Which sense of island. Each state, cold and warm, is a basin-island: a state the climate stayed in until something moved it out. That is the sense proposition 3 is stated in, and this is the first page on the site where it meets real measurements rather than a model.
The record
The record holds 6,113 measurements, one for every 20 years from 30 to 122,270 years before 2000. The frozen event rule finds 35 warmings and 34 coolings in the published list of events, counting the start of the present warm period and the separately numbered spells that some interstadials are split into.
The NGRIP oxygen-isotope ratio (per mil, higher is warmer) in 20-year means, oldest on the left. Green ticks mark each warming as defined by the frozen event rule, numbered as the Greenland interstadials are. Shaded bands are the cold periods between a cooling and the next warming. The last warming on the right is the start of the present warm period, the Holocene.
What the tests asked
Both tests were frozen before any age, duration or isotope value had been computed from these files, then deposited with a date and computed once. They replicate a known question under rules fixed in advance: the published readings disagree, and the author and Claude know them.
survives
C1. Are the cold spells memoryless?
If the warmings came at random, a cold spell that had already lasted a long time was no closer to ending than a fresh one. The test fits how the chance of ending changes with a cold spell's age. With about 30 cold spells it can see a strong pattern, not a mild one, and its thresholds say so.
no clock
C2. A 1,470-year clock?
One well-known reading found the warmings keeping time with a 1,470-year beat. If they did, their ages cluster at one phase of that cycle. The test checks exactly that period, declared in advance, with a strict threshold.
Warning signs before each warming, rising variability or memory in the last 400 years of each cold spell, are reported as a table without a verdict: with one measurement every 20 years there are too few points before each warming for a fair test, and finer data have been read both ways.
Results
The two tests were computed once, on 30 September 2026, after the frozen rules were deposited as 10.5281/zenodo.23066235. They draw no random numbers, and both verdicts follow the deposited rules.
The Weibull shape of the 34 cold spells' lengths was 0.97 (0.74 to 1.22), where memoryless is 1. Survival needed an interval that holds 1 and lies within 0.6 to 1.6.
At the period declared in advance, the phases of the 35 warmings did not cluster: Rayleigh p = 0.71, where a clock needed less than 0.01.
Reported without a verdict, as the rules require:
Warm spells: the same fit gives a shape of 0.75 (0.58 to 0.94) over 34 spells. Their chance of ending falls with age, the pattern proposition 3 rules out for islands of the same depth. These warm spells lasted from 100 to 13,900 years, and without a measure of depth a mix of shallow and deep warm states cannot be told apart from real aging. That is why it carries no verdict.
Drift: the correlation between a cold spell's length and its starting age is -0.22 (p = 0.22).
Other periods: none of 101 trial periods from 1,000 to 2,000 years reached p below 0.01. The lowest was 0.016, at 1,590 years.
Warning signs: before the 24 warmings with enough measurements, variance rose before 11, autocorrelation before 11, and both before 5.
Every trial period
Period, years
Rayleigh r
p
1,000
0.078
0.809
1,010
0.135
0.534
1,020
0.153
0.442
1,030
0.200
0.246
1,040
0.141
0.501
1,050
0.068
0.852
1,060
0.269
0.078
1,070
0.071
0.838
1,080
0.111
0.653
1,090
0.023
0.982
1,100
0.035
0.959
1,110
0.145
0.485
1,120
0.208
0.222
1,130
0.276
0.069
1,140
0.273
0.072
1,150
0.082
0.794
1,160
0.131
0.550
1,170
0.186
0.301
1,180
0.072
0.837
1,190
0.069
0.850
1,200
0.155
0.434
1,210
0.141
0.504
1,220
0.257
0.099
1,230
0.140
0.505
1,240
0.077
0.815
1,250
0.157
0.426
1,260
0.070
0.846
1,270
0.214
0.201
1,280
0.318
0.028
1,290
0.174
0.351
1,300
0.056
0.897
1,310
0.052
0.912
1,320
0.084
0.783
1,330
0.123
0.591
1,340
0.099
0.714
1,350
0.037
0.955
1,360
0.034
0.960
1,370
0.160
0.411
1,380
0.217
0.194
1,390
0.188
0.292
1,400
0.277
0.067
1,410
0.127
0.571
1,420
0.116
0.630
1,430
0.170
0.366
1,440
0.259
0.095
1,450
0.102
0.700
1,460
0.159
0.416
1,470
0.100
0.707
1,480
0.171
0.362
1,490
0.243
0.127
1,500
0.208
0.223
1,510
0.248
0.117
1,520
0.218
0.189
1,530
0.149
0.462
1,540
0.170
0.368
1,550
0.221
0.181
1,560
0.235
0.144
1,570
0.207
0.224
1,580
0.248
0.115
1,590
0.342
0.016
1,600
0.321
0.026
1,610
0.191
0.279
1,620
0.069
0.847
1,630
0.017
0.990
1,640
0.048
0.922
1,650
0.037
0.954
1,660
0.102
0.699
1,670
0.150
0.460
1,680
0.106
0.680
1,690
0.137
0.521
1,700
0.222
0.179
1,710
0.208
0.222
1,720
0.125
0.580
1,730
0.068
0.851
1,740
0.089
0.759
1,750
0.156
0.431
1,760
0.171
0.360
1,770
0.082
0.793
1,780
0.083
0.788
1,790
0.238
0.138
1,800
0.305
0.037
1,810
0.261
0.091
1,820
0.141
0.500
1,830
0.093
0.741
1,840
0.193
0.274
1,850
0.239
0.136
1,860
0.200
0.248
1,870
0.118
0.619
1,880
0.101
0.704
1,890
0.130
0.557
1,900
0.109
0.665
1,910
0.051
0.916
1,920
0.065
0.866
1,930
0.098
0.719
1,940
0.082
0.791
1,950
0.035
0.958
1,960
0.058
0.890
1,970
0.102
0.699
1,980
0.108
0.669
1,990
0.071
0.839
2,000
0.022
0.983
Warning signs, warming by warming
Warming
Measurements
Log variance ratio
Change in autocorrelation
GI-24.2
118
1.62
0.58
GI-23.2
46
-0.16
0.32
GI-21.2
127
0.06
0.71
GI-20c
66
-0.26
0.79
GI-19.2
88
-0.28
-0.48
GI-19.1
38
0.33
0.22
GI-18
265
0.30
0.53
GI-17.2
220
0.04
-0.05
GI-15.2
35
1.21
-0.75
GI-14e
34
-0.20
-0.43
GI-12c
74
-0.06
-1.02
GI-11
47
0.75
-0.08
GI-10
39
-0.17
-0.65
GI-9
32
0.23
-0.11
GI-8c
84
-1.27
-0.15
GI-7c
55
0.69
-0.27
GI-6
50
-0.06
-0.33
GI-5.2
43
0.00
-0.63
GI-5.1
60
-0.05
0.22
GI-4
85
-0.57
0.52
GI-3
41
-0.16
-0.04
GI-2.2
210
-0.18
0.42
GI-1e
410
-0.50
0.70
Holocene
60
0.05
0.19
Cost line and fragility line
Cost line. The warm state is thought to be held by the Atlantic's overturning circulation, which carries heat north continuously. If that is right, the warm island is paid for by a flow, as proposition 4 describes. This is the leading explanation, not a settled one.
Fragility line. Fresh water from melting ice can weaken that circulation, and the cold states that followed large releases of icebergs were among the longest. What pushed the climate back into the warm state is less clear.
Tested by C1 (memory) and C2 (a clock). The background climate also changed over the period, so proposition 3's condition of a steady disturbance may not hold. The analysis reports whether the cold spells' lengths drift with age.
Isotopes: the NGRIP record in 20-year means on the GICC05modelext timescale, from Seierstad and colleagues (Quaternary Science Reviews 106, 2014), with the measurements of the North Greenland Ice Core Project members (Nature 431, 2004). Events: Table 2 of Rasmussen and colleagues (Quaternary Science Reviews 106, 2014). Both distributed by the Centre for Ice and Climate, University of Copenhagen. Their checksums are in the deposited bundle, and the code refuses any other file. The event rule, the tests and their thresholds are in the pre-registration (r1, 10.5281/zenodo.23066235), frozen with the code in lock.json. The chart is drawn from the same record by code that computes none of the tests' statistics. The two readings the tests weigh: Rahmstorf, Geophysical Research Letters 30, 2003 (a 1,470-year clock), and Ditlevsen, Andersen and Svensson, Climate of the Past 3, 2007 (noise-driven). On warning signs, Ditlevsen and Johnsen, Geophysical Research Letters 37, 2010, and Boers, Nature Communications 9, 2018.
Draft site. The genera and their ages are real data from the Paleobiology Database.
Islands across the sciences · paleobiology · real data
Evolution
How long do kinds of animals last? A law stated in 1973 says their age tells you nothing, which is proposition 3, fifty years early.
Sense of island: basin-islandData: The Paleobiology DatabasePublished evidence against P3
A genus is a group of closely related species, such as the oysters or the trilobite Paradoxides. It appears in the fossil record, lasts a while and disappears, and the record keeps the dates. The Paleobiology Database, built by hundreds of paleontologists, lists every genus they have entered with the rocks where it was found. This page takes the marine animals that left the richest records, eight groups and 23,191 genera over more than 500 million years, and asks the question proposition 3 asks: does a genus's age say anything about how long it has left?
In 1973 the paleontologist Leigh Van Valen plotted, for group after group, the share of its genera that had lasted at least so many million years, on a scale where a constant chance of dying out draws a straight line. The lines came out nearly straight. Within a group, he concluded, a taxon's chance of extinction does not depend on how long it has already lasted, and he called this the law of constant extinction. It is proposition 3, stated for taxa: exit is memoryless, and age is no evidence of remaining life.
Van Valen's survivorship curves: the share of each group's genera that lasted at least so long, on a log scale, counted from one million years, with genera alive today treated as still running. Highlighted: the group chosen below. Red dashed: a straight line of constant extinction with the same median. Other groups in gray. Data: The Paleobiology Database.
The database gives both appearances for 23,191 valid genera of the eight groups. Of these, 6,982 (30 percent) were found in a single interval only, too briefly for the timescale to resolve, and are left out of the fits. Another 3,287 are alive today and count as still running. Half of a group's genera were gone within 9 million years for cephalopods and within 58 for snails. The Weibull shape sums up how the chance of dying out changes with age, 1 for Van Valen's constant chance and below 1 for a chance that falls with age, with 95 percent intervals: trilobites 1.01 (0.98 to 1.05), corals 0.92 (0.88 to 0.96), brachiopods 0.89 (0.86 to 0.91), bryozoans 0.87 (0.82 to 0.93), snails 0.84 (0.81 to 0.87), cephalopods 0.81 (0.79 to 0.84), bivalves 0.76 (0.73 to 0.79) and echinoderms 0.75 (0.72 to 0.78).
Trilobites follow the law. The other groups bend the same way: young genera die out faster than old ones. There are three explanations, and the first two are proposition 3's own alternatives.
Frailty. Genera differ in depth, and the shallow ones go first, so the survivors of any age are the deep ones. Version 0.2 of the theory names this as no counterexample, provided it is shown.
Memory. A genus becomes safer as it ages: more species, a wider range, more ways to survive a bad spell.
The record. A short-lived genus is less likely to be found in more than one layer of rock, so short lives are counted less reliably than long ones.
Telling frailty from memory needs a measure of depth that does not depend on survival. Geographic range is the obvious one, since widespread lineages have long been known to survive better (Jablonski, Science, 1986), and the number of species in a genus is another. That test has been done, on this same database. Finnegan, Payne and Wang (Paleobiology, 2008) found that in most intervals of the marine record young genera were more likely to die out, and that range and species richness did not explain it away: a link between age and extinction risk remained after both were accounted for.
What this means for proposition 3. Version 0.2 says a falling hazard is no counterexample only where differences in depth are shown to produce it, and that otherwise it counts against the proposition. Here depth was measured, by range and richness, and the fall with age remained. In this domain, then, the published evidence counts against proposition 3, as far as range and richness capture depth. A defender could name other kinds of depth. The rule is that they must be measured, not assumed. A replication on today's larger database, with rules fixed in advance, has now run. It could not be blind to this result. Its verdict is below.
The re-run, with rules fixed in advance
Proposition 3 is killed by a hazard falling with age conditional on depth. A test deposited before it ran re-ran Finnegan and colleagues' analysis on today's database: does a genus's chance of extinction still fall with its age once its geographic range and species richness are held fixed? If it does, the proposition is killed here. If the fall disappears, it was a difference in depth, the exception the proposition names, and it survives.
The test ran once, on 8 October 2026, after its rules were deposited as 10.5281/zenodo.23248063. Its bootstrap seed comes from that identifier.
Test
Bears on
Verdict
What was found
Does a genus's chance of extinction fall with its age once its geographic range and richness are held fixed?
Across 10,368 genera found in more than one bin of 10 million years, 7,918 of which went extinct, each doubling of a genus's age multiplied its odds of extinction by 0.63 (0.61 to 0.66), with range and richness held fixed. A kill needed the interval's upper end below 0.90, and survival the whole interval within 0.90 to 1.11. All 1,000 resamples converged.
Reported without a verdict, as the rules require:
Without range and richness, the study's first finding: 0.63 (0.61 to 0.66).
Without the five mass-extinction bins: 0.62 (0.60 to 0.65).
With bins of 5 million years: 0.69 (0.67 to 0.71), over 11,854 genera.
Class by class, for the 16 classes with at least 30 extinctions: Anthozoa 0.70, Asteroidea 0.75, Bivalvia 0.59, Cephalopoda 0.34, Crinoidea 0.61, Echinoidea 0.78, Gastropoda 0.78, Gymnolaemata 0.65, Holothuroidea 0.72, Lingulata 0.80, Ophiuroidea 0.72, Rhynchonellata 0.68, Stenolaemata 0.66, Strophomenata 0.48 and Trilobita 0.85. The 54 genera with no class given: 0.10.
Of 707,897 occurrences, 616,431 were used, and 91,466 with an age range over 10 million years were left out. Of the genera, 10,558 were found in a single bin and left out, and 2,450 of those kept were censored, being alive today or last found in the youngest two bins.
Two deviations from the deposited document, neither of which can change the verdict. The database marks some occurrences with the class NO_CLASS_SPECIFIED, which the code counted as a class of its own instead of as missing. It is the most common class of 54 genera, 93 of the 44,185 rows at risk. And the run took 2 hours 27 minutes, not the hour the document estimated.
The interval lies far below 0.90. With range and richness held fixed, each doubling of a genus's age cut its odds of extinction by more than a third, as Finnegan and colleagues found in 2008. Holding range and richness fixed hardly moved the ratio, 0.63 either way, so as measured here they explain none of the fall. The fall holds without the mass-extinction bins and with bins of 5 million years, and its point estimate is below 1 in every class with enough extinctions to count. Under the deposited rules, proposition 3 is killed in the fossil record. Of the three readings of a falling hazard above, the test rules out frailty as range and richness measure it, and leaves memory and the record. What the kill means for the proposition's wording is the author's decision, pending.
When everything ends at once
Proposition 3's memoryless exit needs a steady disturbance. The fossil record has five times when the disturbance was anything but steady: the mass extinctions, when a large share of all genera disappeared together, whatever their age.
Extinct genera of the eight groups, counted by when they were last seen (the end of the last interval they are found in), in five-million-year bins, oldest on the left. Red: the bins holding the five mass extinctions. Data: The Paleobiology Database.
In a typical five-million-year bin, 172 extinct genera of these groups were last seen. In the bin holding the end-Permian extinction (251.9 million years ago), 1,071, the end-Ordovician extinction (445.2 million years ago), 707, the end-Cretaceous extinction (66 million years ago), 619, the Late Devonian extinction (372.2 million years ago), 304 and the end-Triassic extinction (201.4 million years ago), 252. The Late Devonian crisis was spread over several million years, and shows in more than one bin.
At these moments no age protects a genus. They are the paleontological version of the pandemic's quarter in the economy's record, and of the jumps a lake makes when pushed past its edge: exits imposed from outside, arriving for everyone at once. Any test of proposition 3 here has to allow for them, as Finnegan and colleagues did, by comparing genera only with others alive in the same interval.
The Red Queen
Van Valen explained his law with a line from Lewis Carroll. In Through the Looking-Glass the Red Queen tells Alice that here "it takes all the running you can do, to keep in the same place." Every species lives among others that are also evolving, competitors, predators and parasites, so its environment keeps getting worse unless it keeps changing too. If each group's fitness keeps being eroded at a steady rate, its chance of extinction stays the same at every age.
That is proposition 4 in biology's own words: depth held by continuous station-keeping against drift, lost when the running stops. The same 1973 paper holds a prior claim on propositions 3 and 4 together.
Cost line and fragility line
Cost line. A lineage pays continuously, generation after generation, in the selection that keeps it fitted to a world of other evolving species: the Red Queen's running.
Fragility line. A narrow range. In ordinary times, genera whose species were widespread, numerous or good at dispersing survived better. In the end-Cretaceous extinction those advantages stopped counting, and what helped was a lineage spread over a wide area (Jablonski, 1986).
Van Valen's law of constant extinction is proposition 3 stated for taxa in 1973. Trilobites follow it. Seven groups of eight bend toward a hazard falling with age, which may be frailty, memory or the record. Mass extinctions break the stationarity condition. A published analysis of this database (Finnegan, Payne and Wang, 2008) found the fall with age remains when range and richness are accounted for, which by version 0.2's terms counts against the proposition here. Its re-run on today's database, with rules fixed in advance, came out killed.
The Red Queen: a lineage keeps its place only by evolving continuously against a world that also evolves. Station-keeping against drift, in Van Valen's own explanation of his law. Illustration.
Data: every genus the Paleobiology Database lists under Brachiopoda, Bivalvia, Gastropoda, Trilobita, Anthozoa, Echinodermata, Bryozoa and Cephalopoda, with first and last appearances, from its data service, retrieved 2026-09-29, SHA-256 0fa5b6f7d75cabdd57b7a394b2dcc62e26691e8d733c99fd4a5bad6935eca735, CC BY 4.0, credit to the Paleobiology Database and its contributors. The file's checksum is recorded, and the code refuses any other file.
Method. Valid genus names only, with both appearances recorded. A genus's first and last appearance are the midpoints of the intervals it is first and last found in. Its duration is the difference. Genera alive today are censored. Genera found in one interval only are left out, and the fits count from 1 million years. Survivorship is Kaplan-Meier. The Weibull shape is a maximum-likelihood fit with right censoring and a profile-likelihood interval. Extinct genera are counted by the end of the last interval they are found in, in bins of 5 million years. Description only.
Draft site. The death rates are real Census data. The red curve is a model you can change.
Islands across the sciences · organizations · real data
Firm survival
Young firms die far more often than old ones. Does a firm become safer as it ages, or do the fragile ones simply die first?
Sense of island: basin-islandData: US Census Business Dynamics StatisticsTests no proposition
The founding essay of this site is about organizations: firms that find a way of working, hold it for a while, and have to cross to another when the world changes. Proposition 3 once had an organizational reading, that a firm's age says nothing about how long it has left. It was withdrawn after an objection that this page makes visible with real data.
How often firms die, by age
Averaged over 2004 to 2023, 18.7 percent of American firms in their first year of age died within the year, against 5.0 percent of firms aged 26 or more: 3.7 times as often. Most of the fall comes in the first five years, and at the average rates only about 51 percent of new firms would reach their fifth year.
Bars: the share of US firms of each age that died within a year, averaged over 2004 to 2023, with the lowest and highest year marked. Red curve: a model population in which every firm's yearly chance of dying is constant, set with the sliders below.
Memory or frailty?
The falling bars look like firms growing safer with age: learning, building customers, gathering reserves. But the same shape appears without any firm changing at all. Suppose some firms are fragile and some are sturdy, and each keeps the same chance of dying every year, forever. The fragile ones die first, so the older the group, the more of it is sturdy, and the group's death rate falls. The red curve is exactly such a population: every firm in it is memoryless. Move the sliders and see how close it comes.
The best fit has 35 percent of new firms fragile, each with a 40 percent chance of dying every year, and the rest sturdy, each with a 5.8 percent chance, and it comes within 1.2 percentage points of every real average. Make all firms alike and the curve goes flat: without differences between firms, memoryless firms produce no liability of newness.
This is the objection recorded against proposition 3's organizational reading: a death rate that falls with age may be frailty, the weak leaving first, rather than memory, each firm growing safer. The two cannot be told apart from counts like these without a measure of each firm's depth that does not depend on how long it has survived, and no public record supplies one. The same trap waits in any domain where islands differ in depth: supercooled water droplets, lakes, and agent systems.
Cost line and fragility line
Cost line. A firm stays in business only by paying for it continuously: wages, rent, suppliers, interest. Its island is a flow, as proposition 4 describes, and it ends when the money to keep paying runs out.
Fragility line. Cash: most firms that die run out of it, whatever else went wrong first. Young firms have the least of it, which is one of the reasons offered for the liability of newness, alongside frailty.
The death rate falls with age. That would meet the proposition's falsifier only among firms of the same depth, and the data cannot say whether it is memory or frailty. Version 0.2 names frailty in the proposition's wording. This is why the organizational reading was withdrawn. The page shows the objection, not a test.
Not applied here. Proposition 6's era ratio needs data on how fast firms reconfigure, which these counts do not hold.
not applied
Source and method
Data: US Census Bureau, Business Dynamics Statistics, 2023 release, firm age (bds2023_fa.csv), from the Census Bureau, retrieved 2026-09-29, 86,502 bytes, SHA-256 52a36e61791aacfaedc0466a4d9b8c1c94a8b0dfbe05e967840119bf6d5695a1. A class's yearly death rate is its firm deaths over its firms counted that year plus its deaths, since the firms counted are the survivors. Rates are averaged over 2004 to 2023, when every age class exists. The two-kind model is fitted by least squares at each class's nominal age (26 and over at 30). It describes what the data cannot rule out and tests nothing.
Draft site. The business-cycle dates, output, reserves and incomes are real data. The currency peg is a model you can change.
Islands across the sciences · economics · real data and a model
Economy
Booms, pegs and growth: which economic states last, what holds them up, and how they end.
Sense of island: basin-island, chart-island for incomesData: NBER, BEA, World Bank, Maddison ProjectTest X1 run once, 30 September 2026
Economics has studied islands of stability for longer than most sciences, under other names: regimes, equilibria, pegs, traps. The theory page lists economists as prior owners of five of its six propositions. This page takes four economic islands in turn, each with public data: the business cycle, the calm before 2008, the currency peg, and the long-run spread of incomes across countries. It mostly describes. One test has run: X1, on expansions in 42 countries, deposited and run on 30 September 2026. Its verdict is unresolved.
Since the middle of the nineteenth century, the National Bureau of Economic Research has dated every turn of the American economy: the month an expansion peaked and the month the contraction that followed hit bottom. If an expansion is an island in the sense of proposition 3, an expansion's age should say nothing about how long it has left.
Each bar is one phase of the US business cycle, placed at the year it began: expansions upward, contractions downward, in months. Dashed lines are each era's averages. The open bar is the expansion that began in April 2020, still running when the dates were retrieved. Data: NBER.
The NBER has dated 35 expansions since December 1854. They have grown longer: from 1854 to 1919 they averaged 26.6 months, from 1919 to 1945 35.0, and since 1945 64.2, the longest 128 months, from June 2009 to February 2020. Contractions shrank, from 21.6 months to 18.2 and then 10.3. The expansion that began in April 2020 had not been declared over when the dates were retrieved. It counts here as lasting at least 65 months, to September 2025, since the committee has announced every peak since 1980 within a year of it.
A Weibull fit sums up in one number, its shape, how the chance of ending changes with age: 1 for a chance that stays the same, above 1 for one that rises. Measured from the fifth month, expansions before 1919 have a shape of 2.47 (95 percent interval 1.63 to 3.48) and contractions since 1945 1.70 (95 percent interval 1.01 to 2.60), leaving out the two-month contraction of 2020: both grew more likely to end as they aged. Expansions since 1945 come out at 1.64 (95 percent interval 0.98 to 2.49), an interval that just includes 1, and contractions before 1919 at 1.32 (95 percent interval 0.88 to 1.83). Measured from month zero every shape is higher: postwar expansions, for instance, come out at 1.84 (95 percent interval 1.11 to 2.79).
A shape above 1 means the chance of ending rises with age. Part of that is built into the dating: the committee does not call phases much shorter than half a year, so no phase can end in its first months, and a curve fitted from month zero rises by construction. The fits above start each phase's clock at the fifth month, the minimum of the rule written to reproduce the committee's choices (Bry and Boschan, 1971), as the economists who first asked this question did. Daniel Sichel reported in 1991 significant evidence that expansions before the Second World War and contractions after it grow more likely to end as they age. The data since then tell the same story.
For proposition 3 this is description, not a test. The dates are public and well studied, and nothing separates one expansion's depth from another's, so a rising rate could be exhaustion, something used up as the expansion runs, and a falling one could be frailty. Version 0.2 counts neither as evidence until the reserve or the depth is shown. Test X1 asked the same question of expansions in 42 countries, comparing each country's expansions only with each other and allowing for each decade. Its data were downloaded and only their structure read before the freeze, and it ran once after its deposit.
Test X1: the result
Test X1 ran once, on 30 September 2026, after its frozen rules were deposited as 10.5281/zenodo.23066598. It draws no random numbers, and the verdict follows the deposited rules.
Within each country and decade, an expansion's chance of ending rose with its age: the shape was 1.38 (1.15 to 1.63), where memoryless is 1, over the 142 expansions that ended, of 169, in the 40 of 42 countries that had one. Memoryless is ruled out (p = 0.001), but a departure needed the interval's lower end above 1.25, and survival needed an interval that holds 1.
Reported without a verdict, as the rules require:
Without decade effects: 1.23 (1.02 to 1.45).
Without country effects: 0.94 (0.76 to 1.12). Pooling countries whose expansions run long with ones whose expansions run short hides the aging, which is why the test compares each country only with itself.
Contractions: 1.54 (1.18 to 1.92).
Through the latest quarter, pandemic included: 1.48 (1.28 to 1.69). The pandemic ended expansions everywhere at once, whatever their age, which is why it was kept out of the test.
The sample as first drafted, estimated quarters included: 1.23 (1.07 to 1.40).
The quiet years
From the mid-1980s, American output grew more steadily than ever before. Economists called it the Great Moderation, and in a 2004 speech of that name Ben Bernanke, then a Federal Reserve governor, weighed how much of it better policy had earned. Proposition 2 says that looking stable is not evidence of an island. Only recovery from a push is. The quiet years are its standard economic example.
Thin bars: the annualized growth of US real output in each quarter, in percent. Shaded bands are NBER recessions. Line: the standard deviation of growth over the previous five years. Dashed: the standard deviation over 1960 to 1983 and over 1984 to mid-2007. Bars beyond the scale are marked in orange. Data: BEA, via FRED.
From 1960 to 1983 the annualized growth of US output swung around its average with a standard deviation of 4.3 points. From 1984 to mid-2007 the swings shrank to 2.0, 2.1 times smaller. Then, in the fourth quarter of 2008, output fell at an annualized rate of 8.9 percent.
The calm measured how quietly output moved, not how hard the economy was to push off course. Hyman Minsky had argued that stability itself breeds the borrowing that ends it. Whether he was right about 2008 is argued still. What the record shows is that twenty-three calm years were not evidence of depth.
How long does a regime last?
Proposition 6 turns on how long the world stays in one regime before it changes. In 1989 James Hamilton showed how to estimate that from a series alone: let the economy switch at random between a regime of growth and a regime of decline, each with its own average, and find the switching chances that best explain the data. A regime that stays with chance p each quarter lasts, on average, 1 / (1 − p) quarters. The theory page names his method as the candidate instrument for proposition 6. Here it is, built and run on the series Hamilton used, US output, in its simplest form: two averages, one spread, no lags.
Line: the chance, estimated from output alone, that the economy was in its low-growth regime each quarter. Shaded: NBER recessions, which the fit never saw. The dotted line marks where one fit ends and the other begins: 1951 to 1984, Hamilton's own window, and 1985 to 2019, stopping before the pandemic's quarters.
In Hamilton's own window, 1951 to 1984, the fit finds a low regime, with output shrinking 0.18 percent a quarter on average, that lasts 4.0 quarters, and a high one, growing 1.32 percent a quarter, that lasts 9.3. It never saw the NBER's dates, yet it puts 92 percent of their recession quarters in the low regime, and 14 percent of the other quarters. From 1985 to 2019 the high regime's expected length is 59.0 quarters, 6.3 times as long, and the fit puts 55 percent of recession quarters in the low regime and none of the others.
Hamilton's original form, with four lags, reaches two different optima from the 18 starting points tried on today's revised data for 1951 to 1984, and the highest is not a recession regime: its low regime lasts 1.1 quarters and holds 12 percent of recession quarters. Started from his published estimates, the same model settles at 4.2 and 9.3 quarters, close to his own, at a slightly lower likelihood. The answer depends on the specification as well as the series.
What this is not. Proposition 6 bets that AI shortens the regimes of AI-exposed sectors. US output is not such a series, and the author has not named one. Were US output the series, the lengthening shown here would count against the proposition, since "era proxies stable or lengthening" is one of its falsifiers. So the instrument is built, and its series is still to be chosen and frozen, together with its specification, before any estimate on it counts.
A peg and its runway
A country that fixes its currency to the dollar has made an island: the exchange rate stays put while everything around it moves. The island is not free. Whenever more money wants to leave than to come in, the central bank must sell dollars from its reserves to hold the rate. That is proposition 4's picture exactly: depth bought by continuous spending against a drift, and a stabilizer, the reserves, that becomes the weak point. Version 0.2 of the theory defines the runway for such an island: how long the reserves would last at the rate they are being spent, measured before, and apart from, how the island ends.
Paul Krugman's 1979 model of a currency crisis turns this into a clock. Below, the central bank starts with some reserves and loses a steady amount each month. Speculators know the peg cannot outlast the reserves, so they do not wait for the last dollar: they attack when what is left equals what can leave at once.
A model, not data. On a clock: reserves over time (Krugman 1979, in the linear form of Flood and Garber 1984). The dashed line is the date the reserves would run out if nobody saw it coming. At any moment: when 600 model pegs fall if each month brings the same chance of a self-fulfilling attack, the kind of crisis Maurice Obstfeld described in 1996. The red curve is the memoryless prediction.
The two stories are proposition 3's two cases in one currency. On a clock, the peg ends by exhausting a reserve, and its age tells you how long it has left: version 0.2 names exactly this as no counterexample. At any moment, the end is memoryless, and a peg that has held for five years is as likely to fall next month as one set up last month. Real crises have mixed the two.
Real runways can be measured. The World Bank records, for most low- and middle-income countries, their reserves and their short-term foreign debt, the money that can leave within a year if lenders stop rolling it over. Reserves divided by that debt is a runway in years. The chart counts, for every year in which a currency had held within 2 percent against the dollar for two years, whether a crash followed within two years: a fall of at least a quarter of its value in a year, by Frankel and Rose's 1996 definition.
Share of years, with a currency held steady against the dollar, that were followed by a currency crash within two years, by the runway at the end of the year: on the left, reserves over short-term debt, and on the right, reserves in months of imports. Above each bar: crashes, and years counted. Data: World Bank, World Development Indicators.
The World Bank's data give 986 years in which a currency had held within 2 percent against the dollar for two years and the country's short-term debt is recorded. Where reserves covered less than half a year of that debt, a crash followed within two years in 15 of 92 years, 16.3 percent, and where they covered two years or more, in 15 of 591, 2.5 percent. In between, 10.2 percent and 7.7 percent. Counted in months of imports, the runway shows no such gradient: 4.4 percent under three months, 2.1 percent from three to six, 3.7 percent above six.
The runway that predicts is the one measured against the outflow that threatens: for a peg, money leaving, not imports arriving. That is the definition's point, a reserve against its own net outflow, and it is an illustration, not a test. The pattern has been known to economists since the crises of the 1990s, and nothing here was fixed before looking.
A sea between rich and poor?
Over the long run, is there an island of wealth, with a sea around it that countries cross only rarely? In the 1990s Danny Quah found the world's income distribution splitting into two peaks, a rich club and a poor one. Later decades brought fast growth to many poor countries. The Maddison Project's estimates of income per person, back to 1950 for 141 countries, show what happened.
How 141 countries are spread by income per person, as a share of the United States' in the same year, on a log scale. Solid: the year chosen below. Dashed: 1950. Shaded: between a quarter and a half of US income. Smoothed with the same kernel in every year. Data: Maddison Project Database 2023, via Our World in Data.
The Maddison estimates cover 141 countries in every one of the years shown. With the smoothing used here, every year has three or more peaks: in 1950 near 7, 19 and 57 percent of US income per person, in 2022 near 3, 19 and 67 percent. The band between a quarter and a half of US income held between 12 percent and 18 percent of the countries in every year. From one year shown to the next, 92 percent of countries below the band stayed below it and 94 percent of those above stayed above. Of those in the band, 66 percent were still there, 19 percent had moved up and 15 percent had fallen back.
Twelve countries crossed from below a quarter of US income per person in 1950 to above half in 2022: Singapore, Saudi Arabia, Taiwan, Oman, South Korea, Bahrain, Japan, Puerto Rico, Malta, Spain, Cyprus and Seychelles. One fell the other way: Venezuela, from 56 percent to 9.
The middle band is thinner than either side but never empty, and it holds its countries less firmly: that is a passage more than a sea. Proposition 5 says survival is decided in the crossing, not on either shore. The growth miracles made the crossing in a generation or two. Others started it and fell back. What decided each crossing, whether institutions, oil, education or luck, is what growth economists argue about, and this chart cannot say.
Cost line and fragility line
Cost line. A peg is paid for in reserves whenever money leaves, and in high interest rates when reserves run short. An expansion is paid for in credit and confidence that must keep being renewed. A rich country's place is kept by continuous investment. The oil states that crossed on oil rents hold it only while the oil flows.
Fragility line. For a peg, the runway: reserves against the money that can leave within a year. For an expansion, what builds up while it runs, which the dates alone cannot show.
Incomes cluster: countries sit mostly in three groups, and the ends keep more than nine in ten of their countries from one decade to the next. The band between is thinner, not empty. A resemblance of form.
The Great Moderation: swings in output halved for twenty-three years, then 2008. Calm was measured, depth was not. The canonical false island among the proposition's economics precedents.
Before 1919, expansions grew more likely to end with age, and since 1945 contractions have. Postwar expansions are borderline. No depth measure, and public, well-studied dates: description. Test X1, on expansions in 42 countries and the first written against version 0.2's wording, ran after its deposit: expansions aged, short of the bar set in advance.
A peg is held by a throughput, reserves spent against a drain, and in the World Bank's data a short runway, measured beforehand, was followed by crashes more often. The model shows the reserve as the weak point. Illustration: the pattern was known and nothing was fixed before looking.
A dozen countries crossed from below a quarter of US income per person to above half since 1950, and one fell the whole way back. The middle band holds its countries less firmly than either end.
The instrument is built: Hamilton's model estimates how long regimes last, shown on US output, where the high-growth regime's expected length rose several times over after 1984. Not the proposition's series, which is not named.
instrument built, series not named
Source and method
Business-cycle dates: the NBER's Business Cycle Dating Committee, from the NBER, business_cycle_dates.json, 2,303 bytes, SHA-256 675edfab232057b6d05dc460afee504013d40d12dd206ea70bb73a79e6481551, copied with attribution, as the NBER permits. Output: US real GDP, quarterly, from the Bureau of Economic Analysis via FRED, 1947Q2 to 2026Q2, 6,527 bytes, SHA-256 519d65c05941022da119fdcbc95976d6865e94b9cc4a8248239e20d7b898e5fc, public domain. Reserves, short-term debt and exchange rates: the World Bank's World Development Indicators (updated 2026-07-13), three files of 69,340, 95,745 and 68,087 bytes, CC BY 4.0. Incomes: the Maddison Project Database 2023 (Bolt and van Zanden, 2024), in Our World in Data's copy with its minor processing, 567,429 bytes, SHA-256 3764bd2ceff342198e539a27a87ec85bc2679ed8fc40c09f430a70a21fcdf27b, CC BY 4.0. All retrieved 2026-09-29. Every file's checksum is recorded, and the code refuses any other file.
Method. Phases are counted in months from the NBER's dates. Weibull shapes are maximum-likelihood estimates with profile-likelihood intervals, the running expansion treated as censored. Growth is the quarterly change in log output. Hamilton's model is fitted with statsmodels from 18 fixed starting points, keeping the highest likelihood. A crash is a loss of at least 25 percent of a currency's value against the dollar in a year, at least 10 points more than the year before, and the first in three years (Frankel and Rose, 1996). Incomes are relative to the United States in the same year, smoothed with one Gaussian kernel for all years. All of it is description: the data are public, and nothing was fixed before looking.
Draft site. The death rates, glucose tests and measles counts are real data. The herd-immunity curve is a model you can change. No medical advice.
Islands across the sciences · medicine and public health · real data and a model
Health
A life, a blood-sugar system, a population against a virus: which states last, what it takes to test them, and what keeps them.
Sense of island: basin-islandData: NCHS, NHANES, CDCOne test run, of proposition 4
Physiology has its own word for an island of stability: homeostasis, the body holding its temperature, its blood sugar and its blood pressure within narrow bounds against everything that pushes them. This page takes three cases with public data: how the chance of dying changes over a life, how medicine tests blood sugar by pushing it, and how a population keeps measles out. It describes populations and models, and it gives no medical advice.
If a human life were an island in the sense of proposition 3, the chance of dying in the coming year would be the same at every age. It is not, and the way it is not is instructive.
The chance that a person of each age dies within a year, United States, 2022, on a log scale. The dashed line is a straight-line fit from 30 to 90, Gompertz's law. Data: National Center for Health Statistics, United States Life Tables, 2022.
In 2022 a newborn's chance of dying before its first birthday was 0.56 percent. The chance fell to its lowest, 0.010 percent, at age 10, about 56 times lower. From 30 to 90 it rises along a nearly straight line on this scale, doubling every 9.3 years (the line accounts for 98.5 percent of the variation in the logarithm), and at 99 it is 33 percent a year.
The curve is a bathtub. On its left, the chance of dying falls through childhood: the frailest die first, and the rest grow sturdier as they grow. On its right it rises at a steady pace, doubling again and again: the body wears. Neither side is memoryless, and version 0.2 of the theory names both: differences in depth, which make a group's hazard fall, and exhaustion, which makes it rise on schedule. A life is not an island of given depth under a steady disturbance, so proposition 3's condition is not met here, as with the stars that leave the main sequence when their fuel runs out. The steady doubling has a name, Gompertz's law, from 1825. The flattening some demographers see at the very oldest ages is still argued over, partly as frailty again.
Watching and pushing
Proposition 2 says that looking stable is not evidence. Only recovery from a push is. Medicine has long worked this way in at least one place. Fasting blood sugar is a resting measure: how the system looks when left alone. The glucose tolerance test is a push: the patient drinks 75 grams of glucose, and the test measures how far the level has come back down two hours later. That is a measured recovery from a perturbation, which is exactly how the proposition says an island is established.
US adults aged 20 and over without treated diabetes, grouped by fasting blood sugar (rows). Each row is split by where their blood sugar stood two hours after the 75-gram drink: normal, raised, or in the diabetic range. Weighted to the population. Data: NHANES 2015–2016.
1,670 adults aged 20 and over in the survey's glucose-challenge subsample had both results, drank the whole drink and had the second blood draw 105 to 135 minutes after it. Among those whose fasting blood sugar was normal, 7.1 percent (95 percent interval 4.7 to 9.5) had a raised or diabetic-range result after the drink. Of those whose result after the drink was in the diabetic range, 52 percent (95 percent interval 43 to 60) had fasting blood sugar below the diabetic cut-off of 126 mg/dL: by the resting test alone, they would not have counted as diabetic.
The push finds what watching misses. Fasting glucose and longer-term averages remain the everyday tests because they are simpler: the push costs two hours and a sweet drink. That trade, between what a push costs and what it reveals, is the one proposition 2 asks every field to make knowingly.
An island paid for by every birth cohort
Herd immunity is an island a population holds: measles cannot spread when too few people can catch it. It is held by a throughput. Every year a new cohort is born susceptible and has to be vaccinated for the island to hold. That is proposition 4's case exactly: stability bought by continuous spending, decaying when the spending stops, with the fragility in the stabilizer, the vaccination program itself.
Reported measles cases in the United States each year, on a log scale. Gaps are years without a figure in the series. The vaccine was licensed in 1963, and measles was declared eliminated in 2000, meaning no continuous spread for a year. Data: CDC and earlier US government sources, via Our World in Data.
From 1950 to 1962, before the vaccine, the United States recorded an average of 525,730 measles cases a year and 475 deaths. From 2001 to 2018 the median was 79 cases a year, and the most 667, in 2014. In 2019 there were 1,274, and in 2025 2,289.
How long can an island like this last once coverage falls? The model below answers with version 0.2's runway: the gap between the share of people who can catch measles and the share at which it can spread, divided by the rate at which unvaccinated newborns fill that gap. It is known from coverage alone, before any outbreak.
A model, not data: one well-mixed population, born and dying at a steady rate, starting just after elimination with 5 percent able to catch measles. Blue: the share that can catch it. Red dashed: 1 / R0, above which one imported case can start an outbreak.
With each case infecting 15 others in a population where everyone could catch it, measles can spread once more than 6.7 percent can catch it, so the island needs at least 93 percent of each cohort vaccinated. In the model, starting from 5 percent able to catch it: at 95 percent coverage the threshold is never crossed. At 90 percent the runway is 30 years, at 70 percent (coverage found in some communities) 5 years, and with no vaccination at all 1.3 years.
The runway is long, so the erosion is silent. For years after coverage falls nothing happens, and the island looks as safe as ever, which is proposition 2 again. When the outbreak comes it runs through the gap in the program, not through any change in the virus. Real populations are not well mixed: communities with low coverage have much shorter runways than the national average suggests, and that is where outbreaks start.
The runway test, country by country
Proposition 4 says an island held by a flow drains when the flow falls short. A test deposited before it ran asked whether, across every country with the records, an outbreak-free spell is more likely to end when more children have been born unvaccinated since it began. If depth were a stock, set when the spell began, that inflow would not matter.
The test ran once, on 30 September 2026, after its rules were deposited as 10.5281/zenodo.23071574. Its bootstrap seed comes from that identifier.
Test
Bears on
Verdict
What was found
Does an outbreak-free spell end sooner when more children are born unvaccinated?
Across 276 outbreak-free spells in 138 countries, 166 of which ended in an outbreak, each percentage point of the population born unvaccinated since a spell began multiplied its chance of ending by 1.12 (1.02 to 1.27). Survival needed the interval's lower end above 1.10, and a kill its upper end below 1.10.
Reported without a verdict, as the rules require:
Counting the children who missed the second dose instead, from 2000 on: 1.05 (0.95 to 1.15), over 209 spells.
Spells by the decade they began: 1980s 6 (4 ended), 1990s 37 (15 ended), 2000s 92 (65 ended), 2010s 86 (57 ended), 2020s 55 (25 ended).
The model's runway at each spell's start: 128 spells began with coverage above the level at which the model's threshold is ever crossed, and 67 of those still ended in an outbreak. The other 148 had a median runway of 7.3 years. Spells that ended lasted a median of 3 years at risk.
The interval lies above 1, so the chance of an outbreak did rise with the unvaccinated inflow, in the direction the flow reading predicts. The test could not show an effect as large as the rules asked for, so the verdict is unresolved, as registered. Reported cases depend on surveillance, mass vaccination campaigns are not in routine coverage, and a national average hides the pockets where outbreaks start. All three blur the relation.
Warnings before a seizure?
Proposition 3 also says that some exits are noise-induced, with no warning, which bounds any early-warning instrument's recall below one. Epilepsy is where that has been tested hardest. If a seizure were a tipping point approached slowly, the brain's signals should slow down before it, as the lake's do before it turns. A study of long recordings from 28 people with epilepsy found no such slowing before 105 seizures (Wilkat, Rings and Lehnertz, Chaos, 2019). Forecasting has turned to other signals, such as the daily and multi-day cycles in seizure risk (Baud and colleagues, Nature Communications, 2018). Open recordings of brain activity would allow a frozen test of the same question with the lake's method. It is not drafted.
Cost line and fragility line
Cost line. Homeostasis is paid for in energy, every second. Blood sugar is held by insulin, made and spent after every meal. Herd immunity is held by vaccinating every new birth cohort.
Fragility line. For herd immunity, the runway: how long until the share who can catch measles passes the threshold, at current coverage. For blood sugar, what only the push shows: how fast the level comes back.
The glucose tolerance test is a push. In the national survey it found diabetic-range results that fasting glucose missed in about half of the cases. Illustration on real data. The test's use in medicine long predates the proposition.
The death rate by age is a bathtub: frailty on the left, wear on the right. A life is not an island of given depth under a steady disturbance, so the condition is not met. Seizures came without the slowing that would warn of them in the study cited, consistent with exits that give no warning.
Herd immunity is held by vaccinating every birth cohort. In the model, the runway is known from coverage alone, before any outbreak. Illustration, and tested once on real data from countries worldwide: unresolved. The chance of an outbreak rose with the unvaccinated inflow, short of the effect the rules required.
Death rates: the life table for the total population of the United States, 2022, from the National Center for Health Statistics (Arias and Xu, National Vital Statistics Reports 74, 2025), SHA-256 04e961f8668f1e863ca5bcd53586eec4b65735c89eb1a4301361f71d35a9d0fd, public domain. Glucose: NHANES 2015–2016, files DEMO_I, GLU_I and OGTT_I, from the National Center for Health Statistics, public domain. Measles: reported US cases, 1919 to 2025, and deaths, in Our World in Data's series compiled from CDC and earlier US government sources, SHA-256 6d483e76cc59033b1fa9c74eba9de33e5747b3d336096b078c4c4b27989792d2, CC BY 4.0. All retrieved 2026-09-29. Every file's size and checksum is recorded, and the code refuses any other file.
Method. The Gompertz line is a least-squares fit of the logarithm of the yearly death probability on age, from 30 to 90. Glucose shares are weighted with the challenge subsample's weights, with 95 percent intervals by Taylor linearization over the survey's strata and sampling units. Categories follow the American Diabetes Association (fasting: under 100, 100 to 125, 126 and over, and for two hours: under 140, 140 to 199, 200 and over, in mg/dL). People taking insulin or diabetes pills were not given the challenge. The herd-immunity model is one well-mixed population with births and deaths at a rate of one seventy-fifth a year. All of it is description.
Draft site. The freezing curves are real data. The tray of droplets is a simulation with illustrative rates, not measurements.
Islands across the sciences · chemistry · real data and an illustration
Metastable water
Water can stay liquid well below its freezing point, waiting for something to start the ice. Diamond sits on an island it should not be on, and stays for ages.
Sense of island: basin-islandReal freezing curves and a simulationTests no proposition
Below 0 °C, ice is the stable form of water, yet a clean droplet can stay liquid far colder than that: small, pure droplets in clouds stay liquid down to about −38 °C before they freeze on their own. The liquid is not stable. It is stuck. To freeze, a droplet first needs a tiny crystal to form by chance, and a crystal that small costs more energy than it saves, so it usually melts again. Until one grows past that hump, the liquid persists. Diamond is the same story on a longer clock: at the Earth's surface graphite is the stable form of carbon, but the hump between them is so high that diamonds keep.
Why this is a clean case for the site. A supercooled droplet looks perfectly stable on every passive measure: it sits there, clear and liquid. Only a push, a speck of ice or a sharp knock, shows that it was never on the island it seemed to be on. That is proposition 2's evidence rule in its simplest physical form. And a tray of droplets freezing one by one is proposition 3's question, and its strongest objection, in a form you can watch.
Freeze a tray of droplets
Each blue dot is a supercooled droplet. It turns white when it freezes. Every droplet has its own chance per second of freezing, which never changes while it stays liquid. In the identical tray, all droplets have the same chance. In the mixed tray, some carry a speck of dust that helps ice start, so their chance is higher. The right panel shows, second by second, what share of the droplets still liquid freezes: the tray's hazard.
The tray: blue is liquid, white is frozen.
The tray's hazard: the share of still-liquid droplets freezing each second, against time.
With identical droplets the hazard stays flat: a droplet that has stayed liquid for a long time is no safer than one poured a moment ago. That is proposition 3's memoryless exit. With mixed droplets the hazard falls: the dusty droplets freeze first, and the longer the tray waits, the more of what remains is clean. No droplet grows safer with age, but the tray does. This is the same trap as the firm data, and ice-nucleation researchers argue about it in the same terms: whether freezing is stochastic, a constant chance per droplet, or singular, set by each droplet's own impurities.
The seed crystal is the push. Drop one into a supercooled droplet and it freezes at once, however long it had survived: its persistence was never evidence that it was stable.
Real droplets in a wind tunnel
The tray above is a simulation. Szakáll and colleagues measured the real thing. In a vertical wind tunnel in Mainz they floated supercooled droplets about 0.7 millimeters across, one at a time, each in a rising stream of air held at a single temperature below zero. Each droplet was water carrying particles of one material that helps ice start, a mineral dust or a plant fiber. Each run floated 70 droplets, one after another, and counted the share still liquid as time passed.
The record holds 34 such runs for six of the seven materials: kaolinite, montmorillonite, feldspar, Sahara dust, microcrystalline cellulose and fibrous cellulose. Each run held one temperature, from −11.9 down to −23.9 °C, and was followed for up to 34 seconds. The run that went furthest ended with 15 percent of its droplets still liquid.
The share of each run's droplets still liquid against time, on a log scale. Each line is one run, labeled with its temperature and how many milligrams of material each millilitre of water carried. Data: Szakáll, Debertshäuser, Lackner, Mayer, Eppers and Diehl (2021), CC BY 4.0.
On this scale a constant chance of freezing draws a straight line, as the identical tray does, and the authors read the runs that way, as the exponential fall the stochastic view of freezing predicts. From separate experiments in an acoustic levitator, where drops were cooled steadily, they also classed every material as a mixture of particles that start ice more or less easily, the multiple-component case, although for illite NX the difference from a single component was not significant. That is the mixed tray. Droplets that differ in what they carry differ in depth, the exception proposition 3 names, and here it is already shown. So these curves cannot test the proposition, and no test is drafted on them. A test would need the same droplet frozen again and again, which these experiments did not do. Jakobsson and colleagues (2022) did, tracking about 3,000 drops through repeated cooling and holds at one temperature. Their raw data were downloaded on 8 October 2026, and a test of proposition 3 on them is being drafted. The data stay unanalyzed until its rules are frozen.
Cost line and fragility line
Cost line. Nothing is spent to keep a droplet liquid or a diamond a diamond: the hump is a stock, like the nuclear and orbital islands.
Fragility line. A single speck: one ice crystal or one potent dust grain ends a supercooled droplet at once, and the colder the droplet, the smaller the speck that will do it.
Identical droplets freeze memorylessly. Mixed droplets show a falling hazard from frailty alone, the objection that withdrew the organizational reading. Real wind-tunnel runs are shown without a verdict: their materials are mixtures, a difference in depth already shown.
The real freezing curves: Szakáll, Debertshäuser, Lackner, Mayer, Eppers and Diehl, Atmospheric Chemistry and Physics 21, 3289-3316 (2021), doi:10.5194/acp-21-3289-2021, with the data behind its figures in Zenodo record 10.5281/zenodo.4436153 (CC BY 4.0). The page draws the six files of runs at one temperature as published, each checked against its SHA-256 checksum, and does not fit them.
The simulation: 400 droplets, each freezing in any 0.05-second step with probability 1 − e−r·0.05, where r is its constant rate per second. Identical tray: every droplet r = 0.1. Mixed tray: a quarter carry a speck, with r = 0.8, and the rest r = 0.05. These rates are illustrative, chosen so the effect is visible in under a minute. Real rates depend steeply on temperature and droplet size. The hazard is the share of still-liquid droplets that froze in each one-second bin. The −38 °C limit for pure droplets freezing on their own: Koop and Murray, Journal of Chemical Physics 145, 211915 (2016). The stochastic and singular views of ice nucleation: Vali, Atmospheric Chemistry and Physics 14, 5271 (2014).
Draft site. The model records and the dates of the laws are real data. This page tests no proposition.
Islands across the sciences · law and policy · real data
AI governance
Rules for a technology whose frontier moves every few months. Two clocks, and what the site's era ratio makes of them.
Sense of island: chart-island, at the scale of erasData: Epoch AI, EUR-Lex, Federal RegisterTests no proposition
A rule in force is a configuration that holds: an island the rule-makers built, and one they can move only by making a new rule. The technology it governs has islands of its own, eras in which one kind of model leads until the next overtakes it. Proposition 6 says that whether anyone can navigate between islands depends on how long the environment's eras last compared with how long the navigator takes to reconfigure. AI governance is where the site's own bet about that ratio is most direct, so this page puts real numbers on both sides.
This page takes no position on any law or bill, and forecasts nothing. The ratio below is an illustration: proposition 6's series is not named, and nothing here is frozen or tested.
Epoch AI estimates how much computing power went into training the notable AI models of each year. The largest estimate so far is a running record, and each time a new model beats it, the frontier moves.
Training compute of notable AI models since 2010, on a log scale, from Epoch AI's estimates. The line steps up each time a model set a new record. The shaded span is the EU's AI Act from proposal to entry into force, the ticks at the foot are the dates its rules apply, the bar at the top is the US executive order's time in force, and the dashed lines are the two laws' compute thresholds.
Since 2010, 24 models have each set a new record for the computing power used to train an AI model, in Epoch AI's list of frontier models. A record held for a median of 132 days, about 4 months, and never longer than 583 days, the tenure of GNMT (Google, September 2016). The current record, GPT-6 Astra (OpenAI, about 1027 operations), was published on 3 September 2026. Epoch's wider list of notable models gives the same records except in 2021, where it does not count Wu Dao 2.0 and has Jurassic-1-Jumbo in its place.
The rule-makers' clock
The European Commission proposed the AI Act on 21 April 2021. It entered into force on 1 August 2024, 1,198 days later. While it was being made, the compute record changed hands 6 times: from GPT-3 175B (davinci), about 3.1 × 1023 operations, when it was proposed, to Gemini 1.0 Ultra, about 5.0 × 1025, when it entered into force.
The Act presumes that a general-purpose model carries systemic risk once its training used more than 1025 operations. The frontier first passed that line with GPT-4, in March 2023, before the Act was adopted. The record now stands at about 1027.
In the United States, Executive Order 14110, signed on 30 October 2023, required reports on any model trained with more than 1026 operations. It was rescinded on 20 January 2025, after 448 days. The first model in Epoch AI's data past that line, Grok 3, was published 28 days after that.
The era ratio, with real numbers
Proposition 6 divides the environment's regime dwell time by the organization's reconfiguration time. Above one, choosing an island and planning the crossing matter. Near one, timing dominates. Below one, no navigation strategy works, and three moves remain: shorten the reconfiguration time, park on the widest reachable island, or hibernate.
Taking the compute record's median tenure, 132 days, as the environment's regime dwell time, and the Act's 1,198 days from proposal to force as the rule-makers' reconfiguration time, the ratio is about 0.11. Counting to the Act's general application instead, 1,929 days, it is about 0.07.
On these numbers the rule-makers sit well below one. The Act's own text reaches for the first move where it can: the Commission may change its compute threshold with a delegated act, a faster route than a new law, and its recitals say the threshold should be adjusted over time. Its classification of systems by their use, rather than by how they are built, can be read as the second move, a wide island. Whether either is enough is not something this page can say.
Two cautions. The compute record is one measure of the technology's eras, not the measure: capability, cost and deployment keep clocks of their own. And the EU is one rule-maker among many.
A push written into law
Proposition 2 says that looking stable is not evidence. Only recovery from a push shows an island is there. The AI Act asks for both kinds of evidence from the providers of the most capable general-purpose models. Article 55 requires them to evaluate their models with standardized protocols, including adversarial testing, which is a push, and to track and report serious incidents, which is watching. The site draws no conclusion from this about the Act. It illustrates the distinction proposition 2 makes.
A crossing with a timetable
Proposition 5 says survival is decided in the passage between islands. A transit has a duration, a reserve burn rate, and a minimum set of things that must be carried across. Most transitions leave the duration to chance. The AI Act fixes it in law.
The Act entered into force on 1 August 2024 and set its own crossing, in steps:
2 February 2025, 6 months in: first provisions apply.
2 August 2025, 12 months in: rules for general-purpose models apply.
2 August 2026, 24 months in: general application.
2 August 2027, 36 months in: last provisions apply.
Only the first of proposition 5's three quantities is written down. The reserve spent and what is carried across are not measured here.
Illustrated with real data. The compute record's tenure against the time the Act took to make, a ratio well below one.
illustration, real data
Source and method
Models: Epoch AI, Data on AI Models, frontier and notable models, retrieved 30 September 2026 (CC BY 4.0). A record is a model whose training compute beat every earlier one with a published estimate. The estimates are Epoch AI's, and some leading models have none. Laws: Regulation (EU) 2024/1689, Official Journal of the European Union, 12 July 2024, and the Commission's proposal COM(2021) 206 on EUR-Lex. Executive Orders 14110 and 14148 in the Federal Register. The dates are the Act's as adopted.
Draft site. Snapshot 1 of the AI-agent map is measured, and tests in five other sciences have verdicts.5 of 7 launch conditions met →
Five systems that were called stable and were sitting on a boundary, coded under one protocol, with the evidence that existed before the failure.
5 cases, draft, one per type1 control candidate, 2 requiredForecasts: 4 open, with probabilitiesSecond coder: none yet
Nothing on this page is a measurement. The cases are readings of public investigation records, coded by the author under the protocol below and not yet checked by a second coder. The forecasts are dated claims that have not resolved. Both are plans for being wrong in public. Neither is a result.
The base-rate problem. Evidence dated before a failure exists in nearly every system, including ones that never failed. Field five is hindsight with a timestamp unless controls carry the same field and are coded blind to outcome. That is why two coded controls are a launch condition, not an appendix.
The protocol
Every case carries the same seven fields. A case that cannot fill the fifth field is not a false island. It is hindsight, and it is left out.
Claim. The statement that the system was stable, quoted or paraphrased, with who made it.
Stabilizer. What was holding the system up.
Fragility location. Where the stabilizer concentrated risk.
What broke. The failure, in a sentence or two.
Evidence dated before the failure. The column that separates a false island from hindsight. Documents, reports, or warnings that carry a date earlier than the failure.
Type. One of five: subsidized, plateau, unobservable cliff, no passage, or exit through the stabilizer. The five types are defined below.
Sources. The documents the coding rests on. Named, not linked, until verified.
The five types
Subsidized
Stability purchased by a hidden stabilizer that concentrates fragility in one component.
Plateau
A system running near its edge whose instruments hid the proximity, so apparent stability was stickiness.
Unobservable cliff
The boundary lay outside the range the design considered and outside routine measurement.
No passage
No route back once the transition began. The failure was in the transit.
Exit through the stabilizer
The stabilizer itself was the path by which the system left the island.
Selection
The five cases were chosen one per type, deliberately, so that each type has a worked example. That is a design choice, not a coincidence, and it means the set cannot show how often each type occurs.
Cases considered and not selected:
Candidate
Reason not selected
Challenger, 1986
The pre-dated evidence is so widely known that the field-five test would be trivial.
Deepwater Horizon, 2010
The timeline has several contested accounts, so the pre-dated column cannot be filled without adjudication.
Chernobyl, 1986
The stability claim was not public in the sense the protocol requires.
The base-rate argument applies to case selection as much as to controls, so the selection is published.
Rules. Regulator-grade or investigator-grade timelines only. No verdicts on live systems here. Those go to the forecasts below with a named resolver. No second human coder exists yet. Where a model coded a case blind to the thesis, that is stated. Every case and every control is to be coded blind to outcome by two independent coders, and the agreement statistic is published. Until then, each case is a single reading by the author. These five are drafts and their sources are to be verified before publication. No claimant with whom the author is in an active hiring or sales conversation. Additions and withdrawals for that reason are logged privately. The public log shows only the row count.
The five cases
Five drafts, in the order they were coded. Each was coded by the author from the sources named. No case has yet been coded by a model blind to the thesis. When one is, the case will say so. Numbers quoted inside the cases are taken from the named sources and are to be verified with them.
Exit through the stabilizer. 19 July 2024
CrowdStrike
Claim
Endpoint protection as the enterprise's immune system, updated continuously. A paraphrase of the vendor's framing, repeated by customers and analysts, not a single quotation.
Stabilizer
A kernel-level sensor with rapid content updates.
Fragility location
The update channel itself, which reached about 8.5 million Windows hosts at once.
What broke
A content update, Channel File 291, crashed hosts at boot. Airlines, hospitals and banks lost service.
Typed as exit through the stabilizer. It is not a metastable failure in the sense of Bronson et al., since it had no sustaining loop and ended when the trigger was reverted. Those are two different classifications: the type answers how the island was left, the Bronson question answers whether the failure sustained itself.
Evidence dated before
In April 2024 a sensor update crashed Debian servers at one customer, and in June 2024 Red Hat warned of kernel panics involving the sensor on RHEL 9.4, with similar reports on Rocky Linux. One later analysis attributed the Linux crashes to a kernel bug exposed by the sensor rather than to the sensor itself. Either way, the same delivery channel had produced boot failures three months before 19 July. Verified against The Register and Computing, July 2024.
Sources
CrowdStrike's preliminary post-incident review and root cause analysis, August 2024. Microsoft's estimate of affected hosts.
Status
draft, one field verified
Subsidized island. October 2018 to March 2019
Boeing 737 MAX
Claim
A re-engined airframe that handles like its predecessor, so no new type rating. Boeing's position to the regulator and to airline customers, paraphrased.
Stabilizer
MCAS, software that trimmed the nose down.
Fragility location
A single angle-of-attack sensor input, not described to pilots.
What broke
Lion Air 610 and Ethiopian 302.
Evidence dated before
After Lion Air, the FAA's own risk analysis projected further fatal accidents over the fleet's life without a fix, and the type kept flying.
Sources
The House Transportation Committee report, 2020. The FAA TARAM analysis as reported by the committee. The NTSB safety recommendation report, 2019, and the Ethiopian and Indonesian final accident reports.
Status
draft, sources to be verified
Unobservable cliff. 11 March 2011
Fukushima Daiichi
Claim
Sea defences and backup power sized to the design-basis tsunami. TEPCO's position, accepted by the regulator, paraphrased.
Stabilizer
Diesel generators and switchgear in basements behind defenses built to a 5.7-meter design-basis tsunami. Verified: TEPCO interim report, December 2011.
Fragility location
Backup power sited below the flood line.
What broke
A tsunami far above the design basis flooded the generators. Station blackout, then three meltdowns.
Evidence dated before
TEPCO's 2008 internal estimate of a tsunami above 15 meters at the site, not acted on.
Sources
The Diet's independent investigation commission report, 2012. The IAEA report, 2015.
Status
draft, one field verified
Plateau. 14 August 2003
Northeast blackout
Claim
A grid operated within limits, with alarms to warn operators of trouble. The operating assumption at the utility and its reliability coordinator, as reconstructed by the task force, paraphrased.
Stabilizer
The control-room alarm and state-estimation software.
Fragility location
The alarm processor, which failed silently, so operators worked without alarms for over an hour.
What broke
Overloaded lines sagged into untrimmed trees and tripped in sequence. The cascade reached about 50 million customers.
Evidence dated before
Vegetation management gaps and reliability findings in the years before, per the task force. Prior alarm issues (to verify).
Sources
The US-Canada Power System Outage Task Force final report, 2004.
Status
draft, sources to be verified
No passage. 1 August 2012
Knight Capital
Claim
A tested router deployment with a rollback plan. Knight's internal assumption, as described in the SEC order, paraphrased.
Stabilizer
A manual deployment to eight servers.
Fragility location
A repurposed flag that reactivated dormant code on the one server the deployment missed, and no fast route back.
What broke
About 440 million dollars of unintended orders in about 45 minutes.
Evidence dated before
97 automated emails before the market opened flagging the error, not acted on, per the SEC order.
Sources
SEC administrative order, October 2013.
Status
draft, sources to be verified
Control candidate. April 2011
Control candidate: Netflix during the April 2011 AWS outage
Five failures alone cannot test the protocol. Claimed islands that held are required as controls, at least two of them, coded under the same seven fields, so the fields can be seen to separate the two outcomes. Netflix's reported continuity through the multi-day Amazon Web Services outage of April 2011 is the candidate. It is a candidate only. It has not been coded, its claim and stabilizer have not been written up, and its sources have not been collected. If it fails the protocol on inspection, another control will be sought and the substitution logged by date.
Status
candidate, not yet coded
Controls
The protocol requires at least two claimed islands that held under a documented shock, with investigator-grade timelines, coded by a coder who receives the pre-shock timeline without the ending. Netflix during the April 2011 AWS outage is the first candidate. A second is to be nominated before launch.
Rejected candidates
Candidate
Reason rejected
Theranos
A fraud, not a stability claim. The protocol admits only claims made in good faith about a system's resilience.
Y2K
A predicted failure that did not occur. There was no claimed island, so it fits neither the cases nor the controls.
Rejected candidates are published so the selection can be checked.
Forecasts
Dated forward forecasts with named public resolvers and a stated probability. Scored once a year by hit rate and by mean Brier score, without base-rate subtraction. Forecasts that resolve on the author's own harness (F1 and F2) form a self-resolved pool, scored and reported separately from the independently resolved pool (F3 and F4). The self-resolved share of the scored set is capped at half. Regime-level calls are to be placed on Long Bets under the author's name. One is listed below, not yet placed. A forecast enters the table of open forecasts only with frozen wording, a resolver, a deadline, and a probability.
Four open forecasts with probabilities, none resolved. "Resolves by" is the deadline for scoring, not a prediction of when the event occurs. "p" is the stated probability.
#
Forecast
Resolver
p
Resolves by
Status
F1
Snapshot 2's viable fraction on the same task will be no larger than snapshot 1's.
The harness's public logs self-resolved
0.6
2027-09
open
F2
Rerun jitter on the hosted model will exceed 5 percentage points on at least one of three cells (50 reruns each). This is jitter, not sampling error.
The harness's public logs self-resolved
0.7
2026-11
open
F3
Among federal Chief AI Officers designated under OMB M-24-10, the dedicated role reporting to the CIO will show the shortest median observed tenure at a 2028 re-snapshot.
Public agency records
0.55
2028-06
open
F4
Within eighteen months, at least one published postmortem of a correlated multi-provider outage will show that multi-model routing sold as resilience did not prevent customer-visible failure.
Published postmortems
0.65
2028-03
open
Listed, not scored
Item
Why unscored
Gartner's June 2025 prediction that over 40 percent of agentic AI projects will be canceled by the end of 2027.
No public resolver.
A Long Bets entry that by 2030 a majority of S&P 500 firms that announced an enterprise AI operating model in 2024 will have changed it.
Not yet placed.
A proxy for regime dwell time in AI-exposed software categories showing shortening between 2024 and 2027.
No verdicts on already-failed systems beyond the five coded cases. The list grows only when a new case passes the protocol, including the fifth field.
No right of reply theatre. The sources are public investigations. Anyone named can point to the record, and any correction is logged by date.
No scraping of incident databases. Cases are read one at a time from primary documents.
No claimant with whom the author is in an active hiring or sales conversation. Additions and withdrawals for that reason are logged privately. The public log shows only the row count.
Draft site. Snapshot 1 of the AI-agent map is measured, and tests in five other sciences have verdicts.5 of 7 launch conditions met →
The map has been rerun. The issue carries the heatmap, the noise floor, and the five quantities: viable fraction (descriptive), upper tool edge, boundary width, recovery time, fault-axis shape (descriptive). It also says which proposition moved, if any.
02
A case
One false island, coded under the protocol, with the evidence that existed before the failure, each item dated.
03
A resolution
A forecast has resolved, hit or miss. The issue carries the result and the changelog entry it produced.
If none of the three has happened, no issue goes out.
Planned issues
Planned, illustrative. None of these issues has been written or sent. Dates are targets and will move with the work.
Issue 1 is a measurement, the noise floor and rerun jitter, so the first thing subscribers receive is a number. The specification and the pre-registration are announced on the Theory changelog and inside issue 1. They are not an issue of their own.
Issue
Planned
Subject
Kind
1
October 2026
The noise floor: 200 reruns of one cell
Snapshot
2
November 2026
Snapshot 1: band, continent, or below resolution
Snapshot
3
December 2026
Case 1: CrowdStrike, coded, with two controls
Case
4
Early 2027
Case 2: Knight Capital, coded
Case
5
September 2027
Resolution day 1
Resolution
Dates shift with the deposit date. If the pre-registration is deposited on 6 October 2026, snapshot 1 is due by 15 November 2026.
Islands of Stability