What was already known
White's 2022 lower bound was c_E > 0.379005. The separate AlphaEvolve, TTT-Discover and other AI-assisted advances improve upper bounds and do not establish this lower bound.
AI involvement
Liam Price's public comment says GPT Pro improved the lower bound and links the proof note and certificate. This supports a central model role in the retained bound but does not establish task-only autonomy or allocate each lemma and computational step.
Liam Price attributes the improved bound to GPT Pro in his dated public comment. The proof note and certificate are human-posted, but the precise division of mathematical work is not documented.
Importance
Narrows the interval for a longstanding extremal-combinatorics constant through a new certified lower bound; the optimal value remains open.
Limitations
The author gives only a brief public attribution to GPT Pro, so the exact division of mathematical work between model and human is not documented. The repository reports a successful Arb check over 172 mean bins and supplies a proof note for the analytic and discrete transfer; the VibeMathed reviewer reports rerunning the finite certificate, not auditing the transfer proof. The Erdős problem tracker had not incorporated this lower bound into its standing table at review time.
Technical verification
The repository reports Arb verification of the finite dual certificate over 172 mean bins, and VibeMathed reports independently rerunning that finite checker. The analytic reduction and step-function transfer in the note have not received documented rigorous review, so the full lower-bound claim is only partially checked.
- Supporting source (github.com) — README, certificate status
Independent checking
VibeMathed reports rerunning the Arb verifier on all 172 mean bins at commit 6bc610e; this checks the finite certificate, not the analytic transfer proof.
- Checker
- VibeMathed reviewer
- Scope
- Finite Arb dual certificate over 172 mean bins at target 0.38055470; excludes the proof note's continuous-to-finite transfer
- Basis
- Reported by the linked checker
Human understanding
The available author comment and proof note explain the claimed derivation but do not document a human explanation of how the GPT-generated certificate or central optimization was discovered. Few is the evidence default, not a positive finding that people lack understanding.
Correction and publication history
Distinct lower-bound claim checked against the primary proof note, author attribution, prior White bound and independent finite-certificate replay; non-notifying local inclusion.
Read this published revision