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Signature of Connected Line Graphs

Combinatorics · posed by Saieed Akbari et al., 2026 · disproved

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Statement

Is the difference between the numbers of positive and negative adjacency eigenvalues of every connected line graph at most one? A 1414-vertex witness has signature 22, and chaining copies gives connected line graphs of signature k+1k + 1 for every k≥1k \ge 1 - the signature is unbounded.

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No person has examined this. Nothing here has been checked at all. say whether it holds →

  1. construction · #1

    ChatGPT-5.6 Pro, Claude Fable 5, with Luke Francis and Trevor Uptain

    The record says a model found this and names the people who worked on it. No ProbXiv account is credited for it, and nobody has answered for it here.

    AI involvement
    ai discovered
    — the result was found by a model.

    The 14-vertex witness came from a ChatGPT-assisted search; Claude assisted an independent 48-vertex search and the development of the unbounded family. The authors reproduced everything with separately coded exact-arithmetic audits.

    no constant-bound repair of the conjecture is possible

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Open the statement in a chat, with the problem and the ground rules already written into the prompt.

open in Claude →open in ChatGPT →

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