What was already known
Gurvich and Naumova proved partial cases and reduced the possible counterexamples, but the full base-three partition conjecture remained open.
AI involvement
JD Jones chose and directed the problem. Codex GPT-6 agents developed the proof constructions, finite certificates and Lean implementation, adapting published sequence formulas with credit.
The disclosure credits Codex agents with the substantial proof constructions and searches while Jones supplied direction and the target.
Importance
Proves the full base-three existence statement for every n.
Limitations
The result does not cover other bases, uniqueness or counts of partitions. The source reports Lean, Comparator and proof-replay checks; no independent human mathematical check is documented.
Technical verification
The source reports a complete Lean 4 proof of the exact m=3 statement, finite certificates checked by decide, symbolic unbounded families, a transitive axiom audit and Comparator/independent-kernel replay.
Formal checking
The source reports a complete Lean 4 proof of the exact m=3 statement, finite certificates checked by decide, symbolic unbounded families, a transitive axiom audit and Comparator/independent-kernel replay. This review did not rerun them.
- Checker
- Lean 4 kernel, Palomar Comparator and NanoDa
- Scope
- GurvichNaumova.partition_into_powers_of_three for every natural n
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
The repository gives a proof account, but no person's explanation or independent human review of the central six-family and contraction mechanism is documented; Few is an evidence-gap default.
Correction and publication history
Proves the full base-three existence statement for every n.
Read this published revision