Islands of Stability, the lake: pre-registration (r1)

This deposit fixes, before any of them is run, three model tests of the propositions of Islands of Stability (islandsofstability.com), in the standard model of a shallow lake that can be clear or turbid (Carpenter, Ludwig and Brock, 1999). Tests E1 and E2 bear on proposition 2, the evidence rule: whether pushing the lake locates the edge of its clear state better than watching it, and whether either can tell a doomed lake that looks safe from a safe one. Test E3 bears on proposition 3, exit statistics: whether exits from the clear state are memoryless (E3a), whether the mean stay grows exponentially rather than linearly with the basin's depth (E3b), and how many exits a warning signal can anticipate (E3c). Where theory already predicts an answer, the document says so. Nothing in this deposit has been run. The tests' random seeds are the first 16 hexadecimal digits of the SHA-256 of this record's DOI, so they could not have been chosen after seeing results. run_tests.py requires the DOI and refuses to run unless every frozen file matches lock.json. Contents of bundle.zip (SHA256SUMS lists a hash for every file): PREREGISTRATION.md: the frozen document (r1), also uploaded on its own; PREREGISTRATION-draft.md is the draft (r0), kept for the record. lock.json and freeze.py: the SHA-256 of every frozen file, and the check (python freeze.py --verify). lake.py, experiments.py, design.py, run_tests.py: the model, the tests and the runner (python run_tests.py --doi ). tests/: unit tests (python -m pytest -q tests). results/design.json and results/pilot-e3c-control*.json: design numbers from the equations, and the disclosed pilot of test E3c's positive control (section 8 of the document). Related: the pre-registration of the site's first instrument, snapshot 1 of the Map (10.5281/zenodo.22982434). Drafted with Claude (Anthropic), an AI assistant; every decision recorded in the document was made by the author.