{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:PFHKKKEX3QD5SV4YKWFVBZRCVG","short_pith_number":"pith:PFHKKKEX","schema_version":"1.0","canonical_sha256":"794ea52897dc07d95798558b50e622a9a8897cabb6121b26174d77a6eb9e10ea","source":{"kind":"arxiv","id":"1408.2812","version":2},"attestation_state":"computed","paper":{"title":"Homomorphism reconfiguration via homotopy","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.CC","authors_text":"Marcin Wrochna","submitted_at":"2014-08-12T19:19:08Z","abstract_excerpt":"We consider the following problem for a fixed graph H: given a graph G and two H-colorings of G, i.e. homomorphisms from G to H, can one be transformed (reconfigured) into the other by changing one color at a time, maintaining an H-coloring throughout. This is the same as finding a path in the Hom(G,H) complex. For H=K_k this is the problem of finding paths between k-colorings, which was shown to be in P for k<=3 and PSPACE-complete otherwise by Cereceda et al. 2011. We generalize the positive side of this dichotomy by providing an algorithm that solves the problem in polynomial time for any H"},"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":"1408.2812","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CC","submitted_at":"2014-08-12T19:19:08Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"96dee0572b290051ffa3b9988509ee5a51e025968a729ca77f6e0c197b487b05","abstract_canon_sha256":"5f930f3a2d2f20b655f5da02724d665b9e7630ab397f99f51d93ed51d9003884"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:47:59.540110Z","signature_b64":"0WaVRbwoNQAizVPvRoDD9s6i2TiFkBDTDDjrJii5dc11ZetzvMuCsJ8ddClxyXivaXIZ8bPzVxL2MmKL13pRAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"794ea52897dc07d95798558b50e622a9a8897cabb6121b26174d77a6eb9e10ea","last_reissued_at":"2026-05-18T00:47:59.539536Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:47:59.539536Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Homomorphism reconfiguration via homotopy","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.CC","authors_text":"Marcin Wrochna","submitted_at":"2014-08-12T19:19:08Z","abstract_excerpt":"We consider the following problem for a fixed graph H: given a graph G and two H-colorings of G, i.e. homomorphisms from G to H, can one be transformed (reconfigured) into the other by changing one color at a time, maintaining an H-coloring throughout. This is the same as finding a path in the Hom(G,H) complex. For H=K_k this is the problem of finding paths between k-colorings, which was shown to be in P for k<=3 and PSPACE-complete otherwise by Cereceda et al. 2011. We generalize the positive side of this dichotomy by providing an algorithm that solves the problem in polynomial time for any H"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.2812","kind":"arxiv","version":2},"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":"1408.2812","created_at":"2026-05-18T00:47:59.539622+00:00"},{"alias_kind":"arxiv_version","alias_value":"1408.2812v2","created_at":"2026-05-18T00:47:59.539622+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.2812","created_at":"2026-05-18T00:47:59.539622+00:00"},{"alias_kind":"pith_short_12","alias_value":"PFHKKKEX3QD5","created_at":"2026-05-18T12:28:43.426989+00:00"},{"alias_kind":"pith_short_16","alias_value":"PFHKKKEX3QD5SV4Y","created_at":"2026-05-18T12:28:43.426989+00:00"},{"alias_kind":"pith_short_8","alias_value":"PFHKKKEX","created_at":"2026-05-18T12:28:43.426989+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/PFHKKKEX3QD5SV4YKWFVBZRCVG","json":"https://pith.science/pith/PFHKKKEX3QD5SV4YKWFVBZRCVG.json","graph_json":"https://pith.science/api/pith-number/PFHKKKEX3QD5SV4YKWFVBZRCVG/graph.json","events_json":"https://pith.science/api/pith-number/PFHKKKEX3QD5SV4YKWFVBZRCVG/events.json","paper":"https://pith.science/paper/PFHKKKEX"},"agent_actions":{"view_html":"https://pith.science/pith/PFHKKKEX3QD5SV4YKWFVBZRCVG","download_json":"https://pith.science/pith/PFHKKKEX3QD5SV4YKWFVBZRCVG.json","view_paper":"https://pith.science/paper/PFHKKKEX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1408.2812&json=true","fetch_graph":"https://pith.science/api/pith-number/PFHKKKEX3QD5SV4YKWFVBZRCVG/graph.json","fetch_events":"https://pith.science/api/pith-number/PFHKKKEX3QD5SV4YKWFVBZRCVG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PFHKKKEX3QD5SV4YKWFVBZRCVG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PFHKKKEX3QD5SV4YKWFVBZRCVG/action/storage_attestation","attest_author":"https://pith.science/pith/PFHKKKEX3QD5SV4YKWFVBZRCVG/action/author_attestation","sign_citation":"https://pith.science/pith/PFHKKKEX3QD5SV4YKWFVBZRCVG/action/citation_signature","submit_replication":"https://pith.science/pith/PFHKKKEX3QD5SV4YKWFVBZRCVG/action/replication_record"}},"created_at":"2026-05-18T00:47:59.539622+00:00","updated_at":"2026-05-18T00:47:59.539622+00:00"}