Source authenticated

Levit–Mandrescu Unimodality Conjecture

A graph on $n$ vertices is very well-covered if every maximal independent set has size $n/2$. Levit and Mandrescu conjectured that the independence polynomial $i(G,x)$ of every very well-covered graph is unimodal, i.e. its coefficient sequence is nondecreasing and then nonincreasing.

Exact FrontierDelta

Prior state unknown→disproved

Scope and record

Occurred: Jul 22, 2026

Delta type: SOURCE CLAIM

Assumptions: VibeMathed verification: unreviewed. Publication: announcement. AI contribution: ai-discovered. Imported under CC BY 4.0.

Canonical aliases: Levit–Mandrescu Unimodality Conjecture · Levit–Mandrescu Unimodality

Confidence: Not scored

Registry verification: unreviewed · announcement · resolved

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Attribution

VibeMathed
registry · event recorded by

Lucas B.
human · human collaborator

GPT-5.6 Sol
model · ai model contributor

Claude Fable 5
model · ai model contributor

Evidence vector

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

Named evidence

VibeMathed record: Levit–Mandrescu Unimodality Conjecture

specialist registry · passed

Announced on LinkedIn by Lucas B. (Head of AI Research, Jump Trading); no preprint yet, and the reviewers credited are internal to the team rather than independent. The stated polynomial was recomputed with exact integer arithmetic: $a_{1094} > a_{1095} < a_{1096}$ holds, so the polynomial given is genuinely not unimodal, and its low-order coefficients ($a_0 = 1$, $a_1 = 4074$) are consistent with a graph on 4,074 vertices. What remains unchecked is that the whiskered graph's independence polynomial equals the polynomial stated.

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Levit–Mandrescu Unimodality Conjecture

witness · pending

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

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Lineage and corrections

This event attributed to Lucas B.

This event attributed to Claude Fable 5

This event attributed to GPT-5.6 Sol

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