{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:DBLZWM5GJ747FODLOATITQZ46T","short_pith_number":"pith:DBLZWM5G","schema_version":"1.0","canonical_sha256":"18579b33a64ff9f2b86b702689c33cf4fb7118dd7b2ce4419044eb6160c24e09","source":{"kind":"arxiv","id":"2506.10909","version":1},"attestation_state":"computed","paper":{"title":"Dowker's theorem for higher-order relations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Chad Giusti, Iris H. R. Yoon, Melvin Vaupel, Michael Robinson, Nikolas Schonsheck, Radmila Sazdanovic, Vin de Silva, Vladimir Itskov","submitted_at":"2025-06-12T17:19:38Z","abstract_excerpt":"Given a relation $R \\subseteq I \\times J$ between two sets, Dowker's Theorem (1952) states that the homology groups of two associated simplicial complexes, now known as Dowker complexes, are isomorphic. In its modern form, the full result asserts a functorial homotopy equivalence between the two Dowker complexes. What can be said about relations defined on three or more sets? We present a simple generalization to multiway relations of the form $R \\subseteq I_1 \\times I_2 \\times \\cdots \\times I_m$. The theorem asserts functorial homotopy equivalences between $m$ multiway Dowker complexes and a "},"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":"2506.10909","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AT","submitted_at":"2025-06-12T17:19:38Z","cross_cats_sorted":[],"title_canon_sha256":"005eb94e919411b7706cad7fbb2fb19a24a39ee8491751dbb66f6ea4570dbd5d","abstract_canon_sha256":"f188bf201c28be55c79eaba2cad5e6b444358d715138a6747f91b200d50375e1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-09T02:08:31.017462Z","signature_b64":"/QrRAfkS1kwJPdHqL72rr5XoEIAet7QY/BVUicetqgjlpeqL+y71uRmwCXeA7nPjkfyboytH9KU6cppQFJXVDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"18579b33a64ff9f2b86b702689c33cf4fb7118dd7b2ce4419044eb6160c24e09","last_reissued_at":"2026-06-09T02:08:31.016157Z","signature_status":"signed_v1","first_computed_at":"2026-06-09T02:08:31.016157Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Dowker's theorem for higher-order relations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Chad Giusti, Iris H. R. Yoon, Melvin Vaupel, Michael Robinson, Nikolas Schonsheck, Radmila Sazdanovic, Vin de Silva, Vladimir Itskov","submitted_at":"2025-06-12T17:19:38Z","abstract_excerpt":"Given a relation $R \\subseteq I \\times J$ between two sets, Dowker's Theorem (1952) states that the homology groups of two associated simplicial complexes, now known as Dowker complexes, are isomorphic. In its modern form, the full result asserts a functorial homotopy equivalence between the two Dowker complexes. What can be said about relations defined on three or more sets? We present a simple generalization to multiway relations of the form $R \\subseteq I_1 \\times I_2 \\times \\cdots \\times I_m$. The theorem asserts functorial homotopy equivalences between $m$ multiway Dowker complexes and a "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.10909","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/2506.10909/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":"2506.10909","created_at":"2026-06-09T02:08:31.016362+00:00"},{"alias_kind":"arxiv_version","alias_value":"2506.10909v1","created_at":"2026-06-09T02:08:31.016362+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.10909","created_at":"2026-06-09T02:08:31.016362+00:00"},{"alias_kind":"pith_short_12","alias_value":"DBLZWM5GJ747","created_at":"2026-06-09T02:08:31.016362+00:00"},{"alias_kind":"pith_short_16","alias_value":"DBLZWM5GJ747FODL","created_at":"2026-06-09T02:08:31.016362+00:00"},{"alias_kind":"pith_short_8","alias_value":"DBLZWM5G","created_at":"2026-06-09T02:08:31.016362+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/DBLZWM5GJ747FODLOATITQZ46T","json":"https://pith.science/pith/DBLZWM5GJ747FODLOATITQZ46T.json","graph_json":"https://pith.science/api/pith-number/DBLZWM5GJ747FODLOATITQZ46T/graph.json","events_json":"https://pith.science/api/pith-number/DBLZWM5GJ747FODLOATITQZ46T/events.json","paper":"https://pith.science/paper/DBLZWM5G"},"agent_actions":{"view_html":"https://pith.science/pith/DBLZWM5GJ747FODLOATITQZ46T","download_json":"https://pith.science/pith/DBLZWM5GJ747FODLOATITQZ46T.json","view_paper":"https://pith.science/paper/DBLZWM5G","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2506.10909&json=true","fetch_graph":"https://pith.science/api/pith-number/DBLZWM5GJ747FODLOATITQZ46T/graph.json","fetch_events":"https://pith.science/api/pith-number/DBLZWM5GJ747FODLOATITQZ46T/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DBLZWM5GJ747FODLOATITQZ46T/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DBLZWM5GJ747FODLOATITQZ46T/action/storage_attestation","attest_author":"https://pith.science/pith/DBLZWM5GJ747FODLOATITQZ46T/action/author_attestation","sign_citation":"https://pith.science/pith/DBLZWM5GJ747FODLOATITQZ46T/action/citation_signature","submit_replication":"https://pith.science/pith/DBLZWM5GJ747FODLOATITQZ46T/action/replication_record"}},"created_at":"2026-06-09T02:08:31.016362+00:00","updated_at":"2026-06-09T02:08:31.016362+00:00"}