{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:4O7VA43TUBNTUKYQOO445RW3G6","short_pith_number":"pith:4O7VA43T","schema_version":"1.0","canonical_sha256":"e3bf507373a05b3a2b1073b9cec6db37b7f2cfb5a8d7d0256ee4e9978f9a7d78","source":{"kind":"arxiv","id":"1903.05619","version":1},"attestation_state":"computed","paper":{"title":"A polynomial version of Cereceda's conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"Marc Heinrich, Nicolas Bousquet","submitted_at":"2019-03-13T17:34:55Z","abstract_excerpt":"Let $k$ and $d$ be such that $k \\ge d+2$. Consider two $k$-colourings of a $d$-degenerate graph $G$. Can we transform one into the other by recolouring one vertex at each step while maintaining a proper coloring at any step? Cereceda et al. answered that question in the affirmative, and exhibited a recolouring sequence of exponential length. However, Cereceda conjectured that there should exist one of quadratic length.\n  The $k$-reconfiguration graph of $G$ is the graph whose vertices are the proper $k$-colourings of $G$, with an edge between two colourings if they differ on exactly one vertex"},"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":"1903.05619","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2019-03-13T17:34:55Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"f1c5999867d6a968fdec825520c08e39062c21887a08265ed43df88e39f49cf1","abstract_canon_sha256":"2774a4fb26a3628c864cbebd6e3d14d27dc1d2bbbabe5284166d9541600d84fb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:51:20.454451Z","signature_b64":"SmOOSfBQhT/RtJ/iffeARjV4J84TvQR34nM6uW64od03rhjigGcATSXkIUeq0M5l1fPKcHmM6aWJnBi36NJwCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e3bf507373a05b3a2b1073b9cec6db37b7f2cfb5a8d7d0256ee4e9978f9a7d78","last_reissued_at":"2026-05-17T23:51:20.453906Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:51:20.453906Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A polynomial version of Cereceda's conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"Marc Heinrich, Nicolas Bousquet","submitted_at":"2019-03-13T17:34:55Z","abstract_excerpt":"Let $k$ and $d$ be such that $k \\ge d+2$. Consider two $k$-colourings of a $d$-degenerate graph $G$. Can we transform one into the other by recolouring one vertex at each step while maintaining a proper coloring at any step? Cereceda et al. answered that question in the affirmative, and exhibited a recolouring sequence of exponential length. However, Cereceda conjectured that there should exist one of quadratic length.\n  The $k$-reconfiguration graph of $G$ is the graph whose vertices are the proper $k$-colourings of $G$, with an edge between two colourings if they differ on exactly one vertex"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.05619","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":""},"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":"1903.05619","created_at":"2026-05-17T23:51:20.453995+00:00"},{"alias_kind":"arxiv_version","alias_value":"1903.05619v1","created_at":"2026-05-17T23:51:20.453995+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.05619","created_at":"2026-05-17T23:51:20.453995+00:00"},{"alias_kind":"pith_short_12","alias_value":"4O7VA43TUBNT","created_at":"2026-05-18T12:33:10.108867+00:00"},{"alias_kind":"pith_short_16","alias_value":"4O7VA43TUBNTUKYQ","created_at":"2026-05-18T12:33:10.108867+00:00"},{"alias_kind":"pith_short_8","alias_value":"4O7VA43T","created_at":"2026-05-18T12:33:10.108867+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"1907.01863","citing_title":"Linear transformations between colorings in chordal graphs","ref_index":3,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/4O7VA43TUBNTUKYQOO445RW3G6","json":"https://pith.science/pith/4O7VA43TUBNTUKYQOO445RW3G6.json","graph_json":"https://pith.science/api/pith-number/4O7VA43TUBNTUKYQOO445RW3G6/graph.json","events_json":"https://pith.science/api/pith-number/4O7VA43TUBNTUKYQOO445RW3G6/events.json","paper":"https://pith.science/paper/4O7VA43T"},"agent_actions":{"view_html":"https://pith.science/pith/4O7VA43TUBNTUKYQOO445RW3G6","download_json":"https://pith.science/pith/4O7VA43TUBNTUKYQOO445RW3G6.json","view_paper":"https://pith.science/paper/4O7VA43T","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1903.05619&json=true","fetch_graph":"https://pith.science/api/pith-number/4O7VA43TUBNTUKYQOO445RW3G6/graph.json","fetch_events":"https://pith.science/api/pith-number/4O7VA43TUBNTUKYQOO445RW3G6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4O7VA43TUBNTUKYQOO445RW3G6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4O7VA43TUBNTUKYQOO445RW3G6/action/storage_attestation","attest_author":"https://pith.science/pith/4O7VA43TUBNTUKYQOO445RW3G6/action/author_attestation","sign_citation":"https://pith.science/pith/4O7VA43TUBNTUKYQOO445RW3G6/action/citation_signature","submit_replication":"https://pith.science/pith/4O7VA43TUBNTUKYQOO445RW3G6/action/replication_record"}},"created_at":"2026-05-17T23:51:20.453995+00:00","updated_at":"2026-05-17T23:51:20.453995+00:00"}