Source authenticated

The Laplacian $S_{n,n}$ conjecture

True: no simple graph on $n \ge 2$ vertices has Laplacian spectrum $\{0,1,\ldots,n-1\}$ . The paper closes the range left between the two previously settled regimes, $n \le 15$ and $n \ge 6\,649\,688\,933$ .

Exact FrontierDelta

Prior state unknown→proved

Scope and record

Occurred: Sep 22, 2026

Delta type: SOURCE CLAIM

Assumptions: VibeMathed verification: unreviewed. Publication: preprint. AI contribution: ai-co-developed. 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: The Laplacian $S_{n,n}$ conjecture · Laplacian $S_{n,n}$ conjecture

Confidence: Not scored

Registry verification: unreviewed · preprint · resolved

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Attribution

VibeMathed
registry · event recorded by

ChatGPT-6 Astra
model · ai model contributor · OpenAI

Nathaniel Johnston
human · human collaborator

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Named evidence

VibeMathed record: The Laplacian $S_{n,n}$ conjecture

specialist registry · passed

Checked here on 27 September 2026 against arXiv:2609.26895, posted 22 September. The abstract states the conjecture, records that it was already proved for $2 \le n \le 15$ and for $n \ge 6\,649\,688\,933$ , and claims all remaining cases, so the entry's Resolved is the paper's own claim about the full range rather than an extrapolation. The mathematics was not checked here; five days old, no referee, no formalisation. Nathaniel Johnston works in this area.

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The Laplacian $S_{n,n}$ conjecture

preprint · pending

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

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This event attributed to ChatGPT-6 Astra

The Laplacian $S_{n,n}$ conjecture evidence for this event

The Laplacian $S_{n,n}$ conjecture parent of this event

VibeMathed record: The Laplacian $S_{n,n}$ conjecture evidence for this event

This event attributed to Nathaniel Johnston

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