What was already known
The 2018 MathOverflow question asked for a pair with two negative Liouville signs. Mangerel proved that the product λ(a)λ(N−a) is not constant for N≥11, which yields opposite-sign pairs but not the two-negative conclusion. Lingsen Meng later gave an independent stronger four-sign-pattern result and credited this earlier even-case proof.
AI involvement
VibeMathed records the submitter’s account that ChatGPT-6 Astra chose and proved the result and produced its Lean formalization. The repository has no human byline but does not independently document this division of work.
VibeMathed records the submitter’s account that ChatGPT-6 Astra chose and proved the result and produced its Lean formalization. The repository has no human byline but does not independently document this division of work. The AI-led assessment rests on that submitter attribution; absence of a human byline alone does not prove autonomy.
Importance
Answers the Liouville Goldbach question for every admissible even integer.
Limitations
The later independent argument does not itself check the original AI proof. VibeMathed records that the submitter attributed problem selection, proof and Lean formalization to an AI model; the unbylined repository does not independently specify the model’s role.
Technical verification
The repository reports a completed Lean 4/mathlib theorem `liouville_goldbach` with standard axioms and successful pinned CI; VibeMathed reviewed the theorem statement against the posed question. This is a source-reported check of the exact selected theorem; AIProofWatch did not rerun the build.
Formal checking
The repository reports a completed Lean 4/mathlib theorem `liouville_goldbach` with standard axioms and successful pinned CI; VibeMathed reviewed the theorem statement against the posed question.
- Checker
- Lean 4 / mathlib, source-reported CI; VibeMathed statement review
- Scope
- Every even integer N>2 is a sum of positive integers a and b for which the Liouville function satisfies λ(a)=λ(b)=−1.
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
Few is the default when evidence for a higher level is insufficient. The reviewed sources do not name a person who explains the central proof. Few is the default from missing documentation, not a finding that a person cannot understand it.
Correction and publication history
Primary paper, formal statement, prior work and submitter attribution reviewed for non-notifying local inclusion.
Read this published revision