{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:6IBCD7WHAXJNOBHFWMGQKD3EVG","short_pith_number":"pith:6IBCD7WH","schema_version":"1.0","canonical_sha256":"f20221fec705d2d704e5b30d050f64a99e3821f391106c994daaebf0d7f5cd7b","source":{"kind":"arxiv","id":"2508.08025","version":2},"attestation_state":"computed","paper":{"title":"Flagifying the Dowker Complex","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG"],"primary_cat":"math.AT","authors_text":"Marius Huber, Patrick Schnider","submitted_at":"2025-08-11T14:30:17Z","abstract_excerpt":"The Dowker complex $\\mathrm{D}_{R}(X,Y)$ is a simplicial complex capturing the topological interplay between two finite sets $X$ and $Y$ under some relation $R\\subseteq X\\times Y$. While its definition is asymmetric, the famous Dowker duality states that $\\mathrm{D}_{R}(X,Y)$ and $\\mathrm{D}_{R}(Y,X)$ have homotopy equivalent geometric realizations. We introduce the Dowker-Rips complex $\\mathrm{DR}_{R}(X,Y)$, defined as the flagification of the Dowker complex or, equivalently, as the maximal simplicial complex whose $1$-skeleton coincides with that of $\\mathrm{D}_{R}(X,Y)$. This is motivated b"},"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":"2508.08025","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2025-08-11T14:30:17Z","cross_cats_sorted":["cs.CG"],"title_canon_sha256":"d74730a9241a238a58571a6db075546acf04880ecf74dd743d7e4d0e1d3de5ae","abstract_canon_sha256":"1791b3574f249059dd550183e801bd65c18a94d922eaa401102226576eacfe05"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:56:06.274756Z","signature_b64":"qNm6n17w1vaY/H3MhGRkiWDKn7OElPEwdtwCTwM31R12X8gS3ePncaQLLEFL6oyTRVBuaoIRylj1kCcyl+PcCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f20221fec705d2d704e5b30d050f64a99e3821f391106c994daaebf0d7f5cd7b","last_reissued_at":"2026-07-05T11:56:06.274252Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:56:06.274252Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Flagifying the Dowker Complex","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG"],"primary_cat":"math.AT","authors_text":"Marius Huber, Patrick Schnider","submitted_at":"2025-08-11T14:30:17Z","abstract_excerpt":"The Dowker complex $\\mathrm{D}_{R}(X,Y)$ is a simplicial complex capturing the topological interplay between two finite sets $X$ and $Y$ under some relation $R\\subseteq X\\times Y$. While its definition is asymmetric, the famous Dowker duality states that $\\mathrm{D}_{R}(X,Y)$ and $\\mathrm{D}_{R}(Y,X)$ have homotopy equivalent geometric realizations. We introduce the Dowker-Rips complex $\\mathrm{DR}_{R}(X,Y)$, defined as the flagification of the Dowker complex or, equivalently, as the maximal simplicial complex whose $1$-skeleton coincides with that of $\\mathrm{D}_{R}(X,Y)$. This is motivated b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.08025","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2508.08025/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":"2508.08025","created_at":"2026-07-05T11:56:06.274320+00:00"},{"alias_kind":"arxiv_version","alias_value":"2508.08025v2","created_at":"2026-07-05T11:56:06.274320+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2508.08025","created_at":"2026-07-05T11:56:06.274320+00:00"},{"alias_kind":"pith_short_12","alias_value":"6IBCD7WHAXJN","created_at":"2026-07-05T11:56:06.274320+00:00"},{"alias_kind":"pith_short_16","alias_value":"6IBCD7WHAXJNOBHF","created_at":"2026-07-05T11:56:06.274320+00:00"},{"alias_kind":"pith_short_8","alias_value":"6IBCD7WH","created_at":"2026-07-05T11:56:06.274320+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2605.12509","citing_title":"Representing Higher-Order Networks: A Survey of Graph-Based Frameworks","ref_index":280,"is_internal_anchor":false},{"citing_arxiv_id":"2605.12509","citing_title":"Representing Higher-Order Networks: A Survey of Graph-Based Frameworks","ref_index":180,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/6IBCD7WHAXJNOBHFWMGQKD3EVG","json":"https://pith.science/pith/6IBCD7WHAXJNOBHFWMGQKD3EVG.json","graph_json":"https://pith.science/api/pith-number/6IBCD7WHAXJNOBHFWMGQKD3EVG/graph.json","events_json":"https://pith.science/api/pith-number/6IBCD7WHAXJNOBHFWMGQKD3EVG/events.json","paper":"https://pith.science/paper/6IBCD7WH"},"agent_actions":{"view_html":"https://pith.science/pith/6IBCD7WHAXJNOBHFWMGQKD3EVG","download_json":"https://pith.science/pith/6IBCD7WHAXJNOBHFWMGQKD3EVG.json","view_paper":"https://pith.science/paper/6IBCD7WH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2508.08025&json=true","fetch_graph":"https://pith.science/api/pith-number/6IBCD7WHAXJNOBHFWMGQKD3EVG/graph.json","fetch_events":"https://pith.science/api/pith-number/6IBCD7WHAXJNOBHFWMGQKD3EVG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6IBCD7WHAXJNOBHFWMGQKD3EVG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6IBCD7WHAXJNOBHFWMGQKD3EVG/action/storage_attestation","attest_author":"https://pith.science/pith/6IBCD7WHAXJNOBHFWMGQKD3EVG/action/author_attestation","sign_citation":"https://pith.science/pith/6IBCD7WHAXJNOBHFWMGQKD3EVG/action/citation_signature","submit_replication":"https://pith.science/pith/6IBCD7WHAXJNOBHFWMGQKD3EVG/action/replication_record"}},"created_at":"2026-07-05T11:56:06.274320+00:00","updated_at":"2026-07-05T11:56:06.274320+00:00"}