{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:UJYCY6GWDN2FXAVDTBCGDMAB6O","short_pith_number":"pith:UJYCY6GW","schema_version":"1.0","canonical_sha256":"a2702c78d61b745b82a3984461b001f38935730345f2f6cdd9a8f11b7c8cd1ae","source":{"kind":"arxiv","id":"1510.06964","version":3},"attestation_state":"computed","paper":{"title":"On a conjecture of Mohar concerning Kempe equivalence of regular graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"Carl Feghali, Marthe Bonamy, Matthew Johnson, Nicolas Bousquet","submitted_at":"2015-10-23T15:06:51Z","abstract_excerpt":"Let $G$ be a graph with a vertex colouring $\\alpha$. Let $a$ and $b$ be two colours. Then a connected component of the subgraph induced by those vertices coloured either $a$ or $b$ is known as a Kempe chain. A colouring of $G$ obtained from $\\alpha$ by swapping the colours on the vertices of a Kempe chain is said to have been obtained by a Kempe change. Two colourings of $G$ are Kempe equivalent if one can be obtained from the other by a sequence of Kempe changes.\n  A conjecture of Mohar (2007) asserts that, for $k \\geq 3$, all $k$-colourings of a $k$-regular graph that is not complete are Kem"},"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":"1510.06964","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2015-10-23T15:06:51Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"52c42e4a0acfdb210d7fd504df97694705fbcf9a04f825573335b76eff16c01e","abstract_canon_sha256":"9e760bc5ca441102eb4bd46ab26981adc5e1d774e9f7825eee1a9987fbc59eb9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:04:05.807348Z","signature_b64":"Vs5g+fY/4fpVeh6fU14uEZwa3nXx8xBRD1ugzQlQEFqHBrqUaMVkU85wm5jiLAYNunA8iXjnzigJO/tgKTnRDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a2702c78d61b745b82a3984461b001f38935730345f2f6cdd9a8f11b7c8cd1ae","last_reissued_at":"2026-05-18T01:04:05.806842Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:04:05.806842Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On a conjecture of Mohar concerning Kempe equivalence of regular graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"Carl Feghali, Marthe Bonamy, Matthew Johnson, Nicolas Bousquet","submitted_at":"2015-10-23T15:06:51Z","abstract_excerpt":"Let $G$ be a graph with a vertex colouring $\\alpha$. Let $a$ and $b$ be two colours. Then a connected component of the subgraph induced by those vertices coloured either $a$ or $b$ is known as a Kempe chain. A colouring of $G$ obtained from $\\alpha$ by swapping the colours on the vertices of a Kempe chain is said to have been obtained by a Kempe change. Two colourings of $G$ are Kempe equivalent if one can be obtained from the other by a sequence of Kempe changes.\n  A conjecture of Mohar (2007) asserts that, for $k \\geq 3$, all $k$-colourings of a $k$-regular graph that is not complete are Kem"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.06964","kind":"arxiv","version":3},"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":"1510.06964","created_at":"2026-05-18T01:04:05.806913+00:00"},{"alias_kind":"arxiv_version","alias_value":"1510.06964v3","created_at":"2026-05-18T01:04:05.806913+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.06964","created_at":"2026-05-18T01:04:05.806913+00:00"},{"alias_kind":"pith_short_12","alias_value":"UJYCY6GWDN2F","created_at":"2026-05-18T12:29:44.643036+00:00"},{"alias_kind":"pith_short_16","alias_value":"UJYCY6GWDN2FXAVD","created_at":"2026-05-18T12:29:44.643036+00:00"},{"alias_kind":"pith_short_8","alias_value":"UJYCY6GW","created_at":"2026-05-18T12:29:44.643036+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/UJYCY6GWDN2FXAVDTBCGDMAB6O","json":"https://pith.science/pith/UJYCY6GWDN2FXAVDTBCGDMAB6O.json","graph_json":"https://pith.science/api/pith-number/UJYCY6GWDN2FXAVDTBCGDMAB6O/graph.json","events_json":"https://pith.science/api/pith-number/UJYCY6GWDN2FXAVDTBCGDMAB6O/events.json","paper":"https://pith.science/paper/UJYCY6GW"},"agent_actions":{"view_html":"https://pith.science/pith/UJYCY6GWDN2FXAVDTBCGDMAB6O","download_json":"https://pith.science/pith/UJYCY6GWDN2FXAVDTBCGDMAB6O.json","view_paper":"https://pith.science/paper/UJYCY6GW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1510.06964&json=true","fetch_graph":"https://pith.science/api/pith-number/UJYCY6GWDN2FXAVDTBCGDMAB6O/graph.json","fetch_events":"https://pith.science/api/pith-number/UJYCY6GWDN2FXAVDTBCGDMAB6O/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UJYCY6GWDN2FXAVDTBCGDMAB6O/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UJYCY6GWDN2FXAVDTBCGDMAB6O/action/storage_attestation","attest_author":"https://pith.science/pith/UJYCY6GWDN2FXAVDTBCGDMAB6O/action/author_attestation","sign_citation":"https://pith.science/pith/UJYCY6GWDN2FXAVDTBCGDMAB6O/action/citation_signature","submit_replication":"https://pith.science/pith/UJYCY6GWDN2FXAVDTBCGDMAB6O/action/replication_record"}},"created_at":"2026-05-18T01:04:05.806913+00:00","updated_at":"2026-05-18T01:04:05.806913+00:00"}