Source authenticated

Sombor-Energy Conjecture

Registry resolution: candidate. Reported result type: disproved. The registry record and named primary source provide the statement and scope.

Exact FrontierDelta

disproved→disproved

Scope and record

Occurred: Oct 29, 2026

Delta type: REGISTRY REVISION

Assumptions: VibeMathed verification: unreviewed. Publication: announcement. AI contribution: ai-discovered. VibeMathed editorial classifications, scores, notes, relations, and dataset structure are CC BY 4.0. Source statements and linked content retain their own rights.

Canonical aliases: Sombor-Energy Conjecture · Sombor energy

Confidence: Not scored

Registry verification: unreviewed · announcement · candidate

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Attribution

VibeMathed
registry · event recorded by

GPT-5.6 Thinking
model · ai model contributor · OpenAI

Evidence vector

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

Named evidence

VibeMathed record: Sombor-Energy Conjecture

specialist registry · passed

The proof has been internally audited using exact calculations. The graph has nine vertices, fifteen distinct edges and degree sequence $(4,4,4,3,3,3,3,3,3)$ . Its connectivity, bipartition, Sombor matrix, product $B^{T}B$ , singular values, complete spectrum and energy $64$ were independently recomputed within the AI conversation. The result has not yet been checked by an independent graph-theory expert, peer reviewer or formal proof assistant. A literature search located the original conjecture, the 2023 partial-results paper and its 2024 corrigendum, but did not locate an equivalent connected counterexample. This search does not establish absolute priority, and no claim is made that this is the first or a new counterexample.

Source ↗

Sombor-Energy Conjecture

witness · pending

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

Source ↗

Lineage and corrections

Corrects Sombor-Energy Conjecture →

Supersedes Sombor-Energy Conjecture →

Sombor-Energy Conjecture parent of this event

Sombor-Energy Conjecture evidence for this event

Registry resolution: candidate. Reported result type: disproved. The registry record and named primary source provide the statement and scope. parent of this event

VibeMathed record: Sombor-Energy Conjecture evidence for this event

This event attributed to GPT-5.6 Thinking

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