What was already known
Shallit, Shur and Zorcic conjectured this length-set stability, proved nonexistence at lengths 3 and 6, and supplied prior morphism constructions and a finite sufficient criterion.
AI involvement
The primary theorem note credits dot, an OpenAI agent, with the central boundary-marker strengthening, complete length coverage, a new length-12 seed and the strict length-five obstruction. The project reports separate AI review, without human expert endorsement.
The pinned theorem note credits dot, an OpenAI agent, with the boundary-marker strengthening, complete length coverage, new length-12 seed and strict length-five obstruction. Prior constructions and a sufficient criterion are credited to Shallit, Shur and Zorcic. The project’s separate reviewer is also AI; no human expert endorsement is documented.
Importance
Settles the stated stability question in the interval from (8/3)^+ to 3 and identifies a genuine change at the strict 8/3 endpoint.
Limitations
No Lean formalization or completed independent check of the universal hand proof is documented. Finite scripts and a separate brute-force review cover the seed, length-five endpoint and bounded inputs, not all morphisms or input words. Other threshold intervals remain open.
Technical verification
Exact finite controls report the length-12 seed conditions, 128 normalized length-five exclusions and selected bounded input tests. A separate AI review accepts the universal written proof, but neither a Lean proof nor a completed human check of the all-input argument is documented. The finite checks support only their stated cases; AIProofWatch did not rerun them.
Independent checking
A separate AI checker reports exact controls for the fixed length-12 seed and normalized length-five exclusions; VibeMathed reports additional bounded brute-force checks. These do not verify the universal hand proof.
- Checker
- Separate AI finite checker, as reported in the source package
- Scope
- The fixed length-12 seed, the four reduced length-five cases and bounded cubefree inputs.
- Basis
- Reported by the linked checker
Human understanding
Few is the default when evidence for a higher level is insufficient. No named person is documented explaining the central argument. Editorial reading or a separate AI review does not establish human understanding. Few is the default from missing evidence, not a finding that people cannot explain it.
Correction and publication history
Pinned primary claim, prior baseline, AI attribution and checking scope reviewed for local inclusion without notification.
Read this published revision