{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:3UMPKLYIXZLTKBEDXQZI4NDQLY","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"0bd977e92df77531511b8137219735cbbfede865001be27a1b4169a4b4cd61ba","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-05-17T01:32:55Z","title_canon_sha256":"4ddc4dd9fcab9d21e2bca0fca9d5750345e079d6256c0dc8a8ddec02fdc42355"},"schema_version":"1.0","source":{"id":"2605.17218","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.17218","created_at":"2026-05-20T00:03:45Z"},{"alias_kind":"arxiv_version","alias_value":"2605.17218v1","created_at":"2026-05-20T00:03:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.17218","created_at":"2026-05-20T00:03:45Z"},{"alias_kind":"pith_short_12","alias_value":"3UMPKLYIXZLT","created_at":"2026-05-20T00:03:45Z"},{"alias_kind":"pith_short_16","alias_value":"3UMPKLYIXZLTKBED","created_at":"2026-05-20T00:03:45Z"},{"alias_kind":"pith_short_8","alias_value":"3UMPKLYI","created_at":"2026-05-20T00:03:45Z"}],"graph_snapshots":[{"event_id":"sha256:c252ab9e727d0a59503f0feeb4a8a1d168c056469826247c15998db98b3ba9a8","target":"graph","created_at":"2026-05-20T00:03:45Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":4,"items":[{"attestation":"unclaimed","claim_id":"C1","kind":"strongest_claim","source":"verdict.strongest_claim","status":"machine_extracted","text":"there exists an absolute constant g0 such that, for every integer k≥3, every graph G with δ(G)≥k and g(G)≥g0 contains an induced subdivision of K_{k+1}"},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","text":"The proof depends on an induced variant of Mader's theorem (for every fixed s, η, D, every graph J with Δ(J)≤D, d(J)>s−2+η and sufficiently large girth contains an induced subdivision of K_s) whose own proof is not supplied in the abstract and is treated as a black-box ingredient."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"There exists an absolute constant g0 such that every graph with minimum degree at least k and girth at least g0 contains an induced subdivision of K_{k+1}."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"Graphs with minimum degree at least k and girth above a fixed constant contain an induced subdivision of K_{k+1}."}],"snapshot_sha256":"0d616829ca71eef9d52ea29b3a1573c22c1974389f9a2a2ef9d96cb5105642a4"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[{"findings_count":0,"name":"doi_title_agreement","ran_at":"2026-05-20T00:01:20.686340Z","status":"completed","version":"1.0.0"},{"findings_count":0,"name":"doi_compliance","ran_at":"2026-05-19T23:52:41.582939Z","status":"completed","version":"1.0.0"},{"findings_count":0,"name":"ai_meta_artifact","ran_at":"2026-05-19T22:33:23.715995Z","status":"skipped","version":"1.0.0"},{"findings_count":0,"name":"claim_evidence","ran_at":"2026-05-19T22:01:57.921650Z","status":"completed","version":"1.0.0"}],"endpoint":"/pith/2605.17218/integrity.json","findings":[],"snapshot_sha256":"beef8ec048002a99cbd68930251f10766127e125ac16119556757c869b462964","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we prove that there exists an absolute constant $g_0$ such that, for every integer $k\\ge 3$, every graph $G$ with $\\delta(G)\\ge k$ and $g(G)\\ge g_0$ contains an induced subdivision of $K_{k+1}$. This answers, in a strong sense, a problem asked by K\\\"uhn and Osthus (originally attributed to Shi). A main ingredient in our proof is an induced variant of Mader's theorem: for every fixed \\(s,\\eta,D\\), every graph \\(J\\) with \\(\\Delta(J)\\le D\\), \\(d(J)>s-2+\\eta\\) and sufficiently large girth contains an induced subdivision of \\(K_s\\).","authors_text":"Peiru Kuang, Yan Wang","cross_cats":[],"headline":"Graphs with minimum degree at least k and girth above a fixed constant contain an induced subdivision of K_{k+1}.","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-05-17T01:32:55Z","title":"Induced subdivisions in graphs of large girth"},"references":{"count":36,"internal_anchors":0,"resolved_work":36,"sample":[{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":1,"title":"N. Alon, S. Hoory and N. Linial, The Moore bound for irregular graphs,Graphs Combin.18(2002), no. 1, 53–57. 13","work_id":"d85af58a-9ef0-49c1-879d-7a5109709d26","year":2002},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":2,"title":"N. Alon and J. H. Spencer,The Probabilistic Method, Wiley, Hoboken, NJ, 4th ed., 2016","work_id":"ff8f57d4-2682-4499-8047-ab78a1dc692e","year":2016},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":3,"title":"Bollob´ as and A","work_id":"5b6ea3b9-f1af-44f6-b94a-b20896611bcd","year":1998},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":4,"title":"Buci´ c and R","work_id":"85551e65-18b0-4c66-bea3-bb495481e328","year":2024},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":5,"title":"Catlin, Haj´ os’ graph-coloring conjecture: variations and counterexamples,J","work_id":"04038b0f-aea4-4b2d-92ca-6f452b16ffb8","year":1979}],"snapshot_sha256":"c3c6dd06927198fe60acb6a0678ca5caf89c5374b7430e2451460fac6442862f"},"source":{"id":"2605.17218","kind":"arxiv","version":1},"verdict":{"created_at":"2026-05-19T23:35:39.186918Z","id":"d91ecf00-84cb-40ec-85cd-1597ef35b5ba","model_set":{"reader":"grok-4.3"},"one_line_summary":"There exists an absolute constant g0 such that every graph with minimum degree at least k and girth at least g0 contains an induced subdivision of K_{k+1}.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"Graphs with minimum degree at least k and girth above a fixed constant contain an induced subdivision of K_{k+1}.","strongest_claim":"there exists an absolute constant g0 such that, for every integer k≥3, every graph G with δ(G)≥k and g(G)≥g0 contains an induced subdivision of K_{k+1}","weakest_assumption":"The proof depends on an induced variant of Mader's theorem (for every fixed s, η, D, every graph J with Δ(J)≤D, d(J)>s−2+η and sufficiently large girth contains an induced subdivision of K_s) whose own proof is not supplied in the abstract and is treated as a black-box ingredient."}},"verdict_id":"d91ecf00-84cb-40ec-85cd-1597ef35b5ba"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:fc6283c13dc724a8e35f42086bfb7c916680e9bb549c563b3cc65bbdc972f5d4","target":"record","created_at":"2026-05-20T00:03:45Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"0bd977e92df77531511b8137219735cbbfede865001be27a1b4169a4b4cd61ba","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-05-17T01:32:55Z","title_canon_sha256":"4ddc4dd9fcab9d21e2bca0fca9d5750345e079d6256c0dc8a8ddec02fdc42355"},"schema_version":"1.0","source":{"id":"2605.17218","kind":"arxiv","version":1}},"canonical_sha256":"dd18f52f08be57350483bc328e34705e2fa79cdc1eea343af950f485479e4a5f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dd18f52f08be57350483bc328e34705e2fa79cdc1eea343af950f485479e4a5f","first_computed_at":"2026-05-20T00:03:45.796918Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:03:45.796918Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bgpzPrf4EBZIyU7nT40V8AVHc60kodCFYb3mYimyPlT0ZCuF+OgSS7FzX1/+QC/7VKt0Typ6tSFw75VKLaVsBQ==","signature_status":"signed_v1","signed_at":"2026-05-20T00:03:45.797985Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.17218","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fc6283c13dc724a8e35f42086bfb7c916680e9bb549c563b3cc65bbdc972f5d4","sha256:c252ab9e727d0a59503f0feeb4a8a1d168c056469826247c15998db98b3ba9a8"],"state_sha256":"c3e33cc21dc4279af4bfb21e4c011aef2c853c02e6b20a6c85f50577e791d07a"}