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Asymptotically attaining the Moore bound

Settles two conjectures. Theorem 1.1 proves Bollobas's asymptotic degree-diameter conjecture, in the stronger liminf form rather than the conjectured limsup. Corollary 1.2 proves Conjecture 3 of Cambie, Cames van Batenburg, de Joannis de Verclos and Kang on the edge variant, again in the stronger liminf form, and is tight for bipartite graphs.

Exact FrontierDelta

Prior state unknown→proved

Scope and record

Occurred: Aug 4, 2026

Delta type: SOURCE CLAIM

Assumptions: VibeMathed verification: lean-verified. Publication: preprint. AI contribution: ai-co-developed. Editorial metadata: CC BY 4.0; linked content retains its own rights.

Canonical aliases: Asymptotically attaining the Moore bound · Degree-Diameter Problem

Confidence: Not scored

Registry verification: lean verified · preprint · resolved

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Attribution

VibeMathed
registry · event recorded by

Wouter Cames van Batenburg
human · human collaborator

Samuel Korsky
human · human collaborator

GPT-5.6
model · ai model contributor · OpenAI

Evidence vector

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

Named evidence

VibeMathed record: Asymptotically attaining the Moore bound

specialist registry · passed

Lean 4 formalization at github.com/woutercvb/wewantmoore, checked by the site on 2026-08-06 at commit 32beb227. `DegreeDiameter.theorem_1_1` states Theorem 1.1 itself, as a limit of nKD k d / d^k, and `corollary_1_2` states Corollary 1.2; neither is a weakened lemma, and a second independent route is proved alongside each under `_via_big_cell`. No sorry or admit appears in the sources, and the committed axiom audit shows both final theorems resting only on propext, Classical.choice and Quot.sound. That audit is not taken on trust: the repository's CI builds the project from the pinned toolchain and manifest, regenerates the axiom and dependency reports, and fails if they differ from the committed ones. It passes on this commit. The formalization was itself AI-assisted, per the paper's disclosure, and the authors note it is not a line-by-line transcription: k = 1 is handled by the same construction rather than by complete graphs, and the order and cap asymptotics go through leading terms rather than the displayed O_k(q^-1) estimates.

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Asymptotically attaining the Moore bound

preprint · pending

Primary source named by the VibeMathed record. Presence in this import is not an independent mathematical verification.

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Asymptotically attaining the Moore bound — Lean 4 formalization

code · pending

code link supplied by the VibeMathed registry.

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Degree diameter problem

witness · pending

wikipedia link supplied by the VibeMathed registry.