{"data":{"id":"kill-line-graph-signature-2026","statement_oneline":"The signature of a connected line graph is at most 1 (Akbari, Elphick, Kumar, Pragada, Tang, Discrete Math. 349 (2026) 114953, Conjecture 4.12).","renown":{"score":2,"rationale":"A 2026 conjecture from a published Discrete Mathematics paper; specialist renown.","scored_by":"founder"},"attackability":{"score":4,"rationale":"Cheap eigendecomposition oracle, equality cases as seeds; refuted within a year of publication.","subscores":{"finite_witness":5,"oracle_cost":5,"freshness":4,"seedability":4},"scored_by":"founder"},"ranking_score":8,"verification_tier":"pending-peer-review","ai_systems":["ChatGPT 5.6 Pro","Claude Fable 5"],"posed_by":null,"years_open":null,"notability":null,"source_trackers":["https://aimath.robertj1.com/"],"added":"2026-07-24","resolution_type":"counterexample","resolution_date":"2026-07-24","resolver":"Andrea Paone (Zenodo, 2026-07-22); Luke Francis and Trevor Uptain (arXiv, submitted 2026-07-24)","related_records":[{"label":"Paone, Zenodo V1 (first public deposit, 2026-07-22)","url":"https://doi.org/10.5281/zenodo.21499790"},{"label":"Paone, Zenodo V2 (unboundedness, 2026-07-24)","url":"https://doi.org/10.5281/zenodo.21534809"}],"method_note":"Found independently multiple times within days by different people using different AI systems. Exhaustive enumeration shows it is the unique subcubic counterexample on at most 14 vertices, so hunters seeking a minimal subcubic example were bound to converge on it.","evidence_note":"Independent contemporaneous discoveries of the same 14-vertex graph (isomorphism machine-verified). First public evidence: Paone, Zenodo V1, 2026-07-22, with unboundedness in V2 (2026-07-24) via a rooted-module route. Francis and Uptain proved unboundedness independently via a bridge lemma (signature k+1 on 14k vertices), arXiv:2607.22874 (submitted 2026-07-24, announced 2026-07-27); they state, and the source paper's authors can corroborate, that the 14-vertex example was communicated privately to those authors on 2026-07-20 and the unbounded family in correspondence of 2026-07-21 to 23. The source paper's authors additionally report receiving further independent copies of the same graph. Disclosure: this entry concerns work by the Board's operator. All edits are logged in the public status history, and the entry text was shared with all named parties for accuracy review.","last_verified_open":"2026-07-28","evidence_url":"https://arxiv.org/abs/2607.22874","status":"confirmed","effective_status":"confirmed","claims":[],"status_events":[{"id":"arxiv-live-kill-line-graph-signature-2026-07-28","conjecture_id":"kill-line-graph-signature-2026","status":"confirmed","date":"2026-07-28T00:00:00.000Z","actor":"human-admin","rationale":"arXiv abstract live and matching the claim; confirmed per policy; operator entry, see disclosure.","evidence_url":"https://arxiv.org/abs/2607.22874","note":"Set evidence_url to arXiv:2607.22874 and confirmed after abstract announcement."},{"id":"provenance-line-graph-signature-2026-07-27","conjecture_id":"kill-line-graph-signature-2026","status":"reported","date":"2026-07-27T00:00:00.000Z","actor":"human-admin","rationale":"provenance report from A. Paone, verified; corrected per dispute policy.","note":"Updated resolver attribution, related records, and provenance text."},{"id":"seed-kill-line-graph-signature-2026","conjecture_id":"kill-line-graph-signature-2026","status":"reported","date":"2026-07-24T00:00:00.000Z","actor":"human-admin","rationale":"Loaded from unified seed data.","note":"Loaded from unified seed data."}],"public_actions":[],"resolutions":[]},"notice":"Status is community- and machine-tracked and may lag. Verify independently before investing effort."}