Islands of Stability Twelve domains, one set of questions
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.
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.
The MapAI governance
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.
Two clocksNuclear physics
The chart of every known nucleus, from the published evaluation: the island the site is named after, and the table's errors, corrected.
The chart of nuclidesEcology
The standard model of a lake that can be clear or murky. Push it in your browser. Three tests of propositions 2 and 3, run once, with their verdicts.
The lakeOrbits
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.
OrbitsStars
Gaia's chart of 228,623 nearby stars: where stars spend their lives, and an island paid for by burning fuel beside one that costs nothing.
StarsClimate
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.
Ice-age flipsEvolution
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.
The fossil recordOrganizations
US Census data on firm deaths by age, and why a falling death rate cannot say whether firms grow safer or the fragile die first.
Firm survivalEconomics
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 economyHealth
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.
HealthChemistry
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.
Metastable waterWhere each proposition stands
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.