Specification, versioned

The theory, stated to be wrong

Six propositions about stability, each with its prior owners, its strongest objection, and the observation that would kill it.

v3.0, 8 October 2026 1 measurement: snapshot 1, agent domain 0 accepted external objections 4 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.
Tested in other sciences. Each test's rules were deposited before it ran: proposition 2 in the lake model, proposition 3 in the lake model, the ice ages, the economy and the fossil record, and proposition 4 on measles. The verdicts so far are survives, restricted, unresolved and, in the fossil record, killed, each on its domain's page. The orbits test ran twice, and neither run counts.
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.
Three senses of island: what the word means on this site.
The six propositions: each in full, with the domain it is stated for, how it can be tested, what would kill it, and its sources and objections.
Open objections: every objection that changed the text, and those still standing.
History: the versions, earlier wording, what was dropped, and the changelog.
Glossary, references and how to cite.

Index

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.	Basin-island, reduced to enclosure	The Map, test 1 (pre-registration r4, deposited)	snapshot 1 measured	#v3.0-p1
P2	The evidence rule	Looking stable is not evidence. Only recovery from a push shows an island is there.	Basin-island	The Map, test 2, fault-injection arm (pre-registration r4, deposited). The lake's tests E1 (restricted) and E2 (survives)	snapshot 1 measured	#v3.0-p2
P3	Exit statistics	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	killed in one domain	#v3.0-p3
P4	Cost	Where stability is held by a flow, it is paid for continuously, and whatever pays for it becomes the weak point.	All three	The measles runway test, deposited and run once: unresolved. Illustrated on the Cases page and across the sciences	test run	#v3.0-p4
P5	Transit	Survival is decided in the crossing, not on either island.	Basin-island and grid-island	None	framing, not testable yet	#v3.0-p5
P6	The era ratio	If the world changes faster than you can reconfigure, no map helps: get faster, park on the widest island, or hibernate.	Chart-island, at the scale of eras	Hamilton's regime-switching model, built and demonstrated on US output. Series not named	framing, not testable yet	#v3.0-p6

Three senses of island, declared

Chart-island: 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 domain pre-registration drafted, deposit pending instrument written and dated, protocol frozen locally, not yet run no instrument yet nothing to run framing, not testable yet no instrument, and not counted toward the tally The measurement count is one snapshot, in one domain. Tests in four more domains were deposited and run on 30 September 2026.

Propositions with an instrument path

Proposition 1#v3.0-p1

Sparsity

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.
Prior owners: Lewontin 1969. Holling 1973 on multiple stability domains. May 1972 and Gardner and Ashby 1970 on stability against size and connectance.
Economics precedents: 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.

Proposition 2#v3.0-p2

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, 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?

Sources and objections

Sense used: Basin-island.
Prior owners: Hastings et al. 2018 on long transients and ghost attractors. Menck et al. 2013 on basin stability. Scheffer et al. 2009.
Economics precedents: 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.

Proposition 3#v3.0-p3

Exit statistics

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?

Sources and objections

Sense used: Basin-island.
Prior owners: Kramers 1940. Van Valen 1973. Amburgey, Kelly and Barnett 1993, who found organizational hazard highest just after a change and falling with time since. Boettiger and Hastings 2012 on early-warning limits.
Economics precedents: 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.

Proposition 4#v3.0-p4

Cost

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.
Prior owners: Carlson and Doyle 2002 on robust yet fragile. Bronson et al. 2021 and Huang et al. 2022 on metastable failures. The Google SRE book, 2016. Martin 2004 inside viability theory.
Economics precedents: 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.

Proposition 5#v3.0-p5

Transit

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.
Killed by: Endpoint properties predicting transit success. Invariant preservation proving irrelevant.
Instrument: 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?

Sources and objections

Sense used: Basin-island and grid-island.
Prior owners: Refugia and metapopulation ecology. Neishtadt 1975 and Henrard 1982 on capture under a moving landscape. The graded continuity criterion in the author's paper The Preservation of the Continuity of the Self supplies the pre-specified invariants, and enters nowhere else on this site.
Economics precedents: 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.
Strongest objection: Not yet observable.

Proposition 6#v3.0-p6

The era ratio

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?

Sources and objections

Sense used: Chart-island, at the scale of eras.
Prior owners: Levins 1968 on environmental grain. Kussell and Leibler 2005 on sensing versus stochastic switching under environmental change.
Economics precedents: 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.	Amburgey, Kelly and Barnett 1993, via refutation round	Accepted. Proposition 3 scoped to agent systems.
2026-09-24	Exit through the stabilizer is the founding observation of the metastable-failures literature.	Bronson et al. 2021, via refutation round	Accepted. Proposition 4 split and credited.
2026-09-24	The era ratio has prior owners in evolutionary ecology.	Levins 1968 and Kussell and Leibler 2005	Accepted. Credited.
2026-09-24	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.
Deposits	2026-09-30	Pre-registrations deposited on Zenodo before any run: lake r1 (10.5281/zenodo.23065462), orbits r1 (10.5281/zenodo.23066015), ice-age r1 (10.5281/zenodo.23066235) and expansions X1 r1 (10.5281/zenodo.23066598). Snapshot 1's results bundle deposited as 10.5281/zenodo.23066893.	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
Dixit, A. K., and Pindyck, R. S. 1994. Investment under Uncertainty. Princeton University Press. https://doi.org/10.1515/9781400830176
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
Hanski, I. 1998. Metapopulation dynamics. Nature 396: 41–49. https://doi.org/10.1038/23876
Hastings, A., et al. 2018. Transient phenomena in ecology. Science 361(6406): eaat6412. https://doi.org/10.1126/science.aat6412
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
Holling, C. S. 1973. Resilience and stability of ecological systems. Annual Review of Ecology and Systematics 4: 1–23. https://doi.org/10.1146/annurev.es.04.110173.000245
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
Kramers, H. A. 1940. Brownian motion in a field of force and the diffusion model of chemical reactions. Physica 7(4): 284–304. https://doi.org/10.1016/S0031-8914(40)90098-2
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
May, R. M. 1972. Will a large complex system be stable? Nature 238: 413–414. https://doi.org/10.1038/238413a0
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
Scheffer, M., et al. 2009. Early-warning signals for critical transitions. Nature 461: 53–59. https://doi.org/10.1038/nature08227
Schelling, T. C. 1971. Dynamic models of segregation. Journal of Mathematical Sociology 1(2): 143–186. https://doi.org/10.1080/0022250X.1971.9989794
Van Valen, L. 1973. A new evolutionary law. Evolutionary Theory 1: 1–30. No DOI.
Young, H. P. 1993. The evolution of conventions. Econometrica 61(1): 57–84. https://doi.org/10.2307/2951778

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 Map, snapshot 1: pre-registration r4, with the harness's freeze lock, 10.5281/zenodo.22982434. The results, 10.5281/zenodo.23066893.
The lake tests, pre-registration r1: 10.5281/zenodo.23065462.
The orbits test, pre-registration r1: 10.5281/zenodo.23066015. Its one run is recorded as invalid.
The ice-age tests, pre-registration r1: 10.5281/zenodo.23066235.
Expansions X1, pre-registration r1: 10.5281/zenodo.23066598.
The orbits test, pre-registration r2, which corrects r1: 10.5281/zenodo.23071492.
The measles runway test of proposition 4, pre-registration r1: 10.5281/zenodo.23071574.

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.