{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:3QPTIXSSCZRRMCNTYGYBMLUSYY","short_pith_number":"pith:3QPTIXSS","schema_version":"1.0","canonical_sha256":"dc1f345e5216631609b3c1b0162e92c61a44a7a629999a6b3af84b441821ac83","source":{"kind":"arxiv","id":"2201.07595","version":1},"attestation_state":"computed","paper":{"title":"Strengthening a theorem of Meyniel","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Carl Feghali, Cl\\'ement Legrand-Duchesne, Franti\\v{s}ek Kardo\\v{s}, Quentin Deschamps, Th\\'eo Pierron","submitted_at":"2022-01-19T13:45:08Z","abstract_excerpt":"For an integer $k \\geq 1$ and a graph $G$, let $\\mathcal{K}_k(G)$ be the graph that has vertex set all proper $k$-colorings of $G$, and an edge between two vertices $\\alpha$ and~$\\beta$ whenever the coloring~$\\beta$ can be obtained from $\\alpha$ by a single Kempe change. A theorem of Meyniel from 1978 states that $\\mathcal{K}_5(G)$ is connected with diameter $O(5^{|V(G)|})$ for every planar graph $G$. We significantly strengthen this result, by showing that there is a positive constant $c$ such that $\\mathcal{K}_5(G)$ has diameter $O(|V(G)|^c)$ for every planar graph $G$."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2201.07595","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.CO","submitted_at":"2022-01-19T13:45:08Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"37d640e624d561fb70650cef7241ad14460e4c5b1fe89e026521842c64547c61","abstract_canon_sha256":"96a76a775b5dd109c4a7374aae86526824b7f1d2c9b10f6b69d6396b85c04a5d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:49:48.492251Z","signature_b64":"iIndaXXpScHDdqwyTeARomjkBXMxG8mwN+LsL9qaA+/5lwFBKGHwAJsD10HDh+f0MI53jibWlZiD7xNmdCHvDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dc1f345e5216631609b3c1b0162e92c61a44a7a629999a6b3af84b441821ac83","last_reissued_at":"2026-07-05T03:49:48.491918Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:49:48.491918Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Strengthening a theorem of Meyniel","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Carl Feghali, Cl\\'ement Legrand-Duchesne, Franti\\v{s}ek Kardo\\v{s}, Quentin Deschamps, Th\\'eo Pierron","submitted_at":"2022-01-19T13:45:08Z","abstract_excerpt":"For an integer $k \\geq 1$ and a graph $G$, let $\\mathcal{K}_k(G)$ be the graph that has vertex set all proper $k$-colorings of $G$, and an edge between two vertices $\\alpha$ and~$\\beta$ whenever the coloring~$\\beta$ can be obtained from $\\alpha$ by a single Kempe change. A theorem of Meyniel from 1978 states that $\\mathcal{K}_5(G)$ is connected with diameter $O(5^{|V(G)|})$ for every planar graph $G$. We significantly strengthen this result, by showing that there is a positive constant $c$ such that $\\mathcal{K}_5(G)$ has diameter $O(|V(G)|^c)$ for every planar graph $G$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2201.07595","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2201.07595/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2201.07595","created_at":"2026-07-05T03:49:48.491972+00:00"},{"alias_kind":"arxiv_version","alias_value":"2201.07595v1","created_at":"2026-07-05T03:49:48.491972+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2201.07595","created_at":"2026-07-05T03:49:48.491972+00:00"},{"alias_kind":"pith_short_12","alias_value":"3QPTIXSSCZRR","created_at":"2026-07-05T03:49:48.491972+00:00"},{"alias_kind":"pith_short_16","alias_value":"3QPTIXSSCZRRMCNT","created_at":"2026-07-05T03:49:48.491972+00:00"},{"alias_kind":"pith_short_8","alias_value":"3QPTIXSS","created_at":"2026-07-05T03:49:48.491972+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/3QPTIXSSCZRRMCNTYGYBMLUSYY","json":"https://pith.science/pith/3QPTIXSSCZRRMCNTYGYBMLUSYY.json","graph_json":"https://pith.science/api/pith-number/3QPTIXSSCZRRMCNTYGYBMLUSYY/graph.json","events_json":"https://pith.science/api/pith-number/3QPTIXSSCZRRMCNTYGYBMLUSYY/events.json","paper":"https://pith.science/paper/3QPTIXSS"},"agent_actions":{"view_html":"https://pith.science/pith/3QPTIXSSCZRRMCNTYGYBMLUSYY","download_json":"https://pith.science/pith/3QPTIXSSCZRRMCNTYGYBMLUSYY.json","view_paper":"https://pith.science/paper/3QPTIXSS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2201.07595&json=true","fetch_graph":"https://pith.science/api/pith-number/3QPTIXSSCZRRMCNTYGYBMLUSYY/graph.json","fetch_events":"https://pith.science/api/pith-number/3QPTIXSSCZRRMCNTYGYBMLUSYY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3QPTIXSSCZRRMCNTYGYBMLUSYY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3QPTIXSSCZRRMCNTYGYBMLUSYY/action/storage_attestation","attest_author":"https://pith.science/pith/3QPTIXSSCZRRMCNTYGYBMLUSYY/action/author_attestation","sign_citation":"https://pith.science/pith/3QPTIXSSCZRRMCNTYGYBMLUSYY/action/citation_signature","submit_replication":"https://pith.science/pith/3QPTIXSSCZRRMCNTYGYBMLUSYY/action/replication_record"}},"created_at":"2026-07-05T03:49:48.491972+00:00","updated_at":"2026-07-05T03:49:48.491972+00:00"}