What was already known
Surjunctivity is known for sofic groups, but the universal finite-alphabet conjecture remained open. A companion characteristic-two direct-finiteness construction has a related automaton consequence from a different witness.
AI involvement
OpenAI credits an internal model with the odd-characteristic manuscript and Lean proof, building on its companion algebra-to-automaton argument.
The OpenAI release attributes the odd-characteristic construction and proof artifact to its internal model.
- Supporting source (github.com) — How the results were produced
Importance
The claimed automaton refutes Gottschalk’s universal surjunctivity conjecture.
Limitations
The Lean theorem covers the specified odd-characteristic witness. Its proof is source-reported and has no documented completed human check.
Technical verification
The source-reported Lean main theorem asserts both the prescribed odd-characteristic scalar defect and injectivity without surjectivity of the associated cellular automaton on all configurations. It matches this finite-alphabet surjunctivity counterexample, but was not rebuilt here.
Formal checking
Proof of OAI.OddKaplansky.main_theorem matched to the OddKaplansky Comparator MainClaim
- Checker
- Lean 4 kernel, as reported by the OpenAI math release
- Scope
- An injective nonsurjective cellular automaton on K^G for the specified odd-characteristic finite field and finitely generated group
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
No named human account of the odd-characteristic witness's construction is documented; Few is the evidence default.
Correction and publication history
The claimed automaton refutes Gottschalk’s universal surjunctivity conjecture.
Read this published revision