{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:KY7JMQPSSADHGLF6CDGR4JYOCQ","short_pith_number":"pith:KY7JMQPS","schema_version":"1.0","canonical_sha256":"563e9641f29006732cbe10cd1e270e1421ad94f01e10c893561b9140aa195ebd","source":{"kind":"arxiv","id":"1005.4411","version":2},"attestation_state":"computed","paper":{"title":"Homology of the Boolean Complex","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.CO","authors_text":"Bridget Eileen Tenner, Kari Ragnarsson","submitted_at":"2010-05-24T20:02:54Z","abstract_excerpt":"We construct and analyze an explicit basis for the homology of the boolean complex of a Coxeter system. This gives combinatorial meaning to the spheres in the wedge sum describing the homotopy type of the complex. We assign a set of derangements to any finite simple graph. For each derangement, we construct a corresponding element in the homology of the complex, and the collection of these elements forms a basis for the homology of the boolean complex. In this manner, the spheres in the wedge sum describing the homotopy type of the complex can be represented by a set of derangements. We give 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":"1005.4411","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-05-24T20:02:54Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"65dae112d0228b859dbd9a312c17894bd367b1db984bc901febd5ac155b822c4","abstract_canon_sha256":"ebfa4fb7cebe66c63d367642e5667e05b2dfc96b197c29be1fcbb3d861ed0809"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:25:25.963270Z","signature_b64":"xwG+v72WbZ4aGrUv20ChUbtXiDqQl9864Y5/hOUnGvaSqqZFv7DbK/aEFpmR5WbTWB3jFgXBXPuXNdjagnk5CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"563e9641f29006732cbe10cd1e270e1421ad94f01e10c893561b9140aa195ebd","last_reissued_at":"2026-05-18T04:25:25.962481Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:25:25.962481Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Homology of the Boolean Complex","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.CO","authors_text":"Bridget Eileen Tenner, Kari Ragnarsson","submitted_at":"2010-05-24T20:02:54Z","abstract_excerpt":"We construct and analyze an explicit basis for the homology of the boolean complex of a Coxeter system. This gives combinatorial meaning to the spheres in the wedge sum describing the homotopy type of the complex. We assign a set of derangements to any finite simple graph. For each derangement, we construct a corresponding element in the homology of the complex, and the collection of these elements forms a basis for the homology of the boolean complex. In this manner, the spheres in the wedge sum describing the homotopy type of the complex can be represented by a set of derangements. We give a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.4411","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":"1005.4411","created_at":"2026-05-18T04:25:25.962599+00:00"},{"alias_kind":"arxiv_version","alias_value":"1005.4411v2","created_at":"2026-05-18T04:25:25.962599+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1005.4411","created_at":"2026-05-18T04:25:25.962599+00:00"},{"alias_kind":"pith_short_12","alias_value":"KY7JMQPSSADH","created_at":"2026-05-18T12:26:09.077623+00:00"},{"alias_kind":"pith_short_16","alias_value":"KY7JMQPSSADHGLF6","created_at":"2026-05-18T12:26:09.077623+00:00"},{"alias_kind":"pith_short_8","alias_value":"KY7JMQPS","created_at":"2026-05-18T12:26:09.077623+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/KY7JMQPSSADHGLF6CDGR4JYOCQ","json":"https://pith.science/pith/KY7JMQPSSADHGLF6CDGR4JYOCQ.json","graph_json":"https://pith.science/api/pith-number/KY7JMQPSSADHGLF6CDGR4JYOCQ/graph.json","events_json":"https://pith.science/api/pith-number/KY7JMQPSSADHGLF6CDGR4JYOCQ/events.json","paper":"https://pith.science/paper/KY7JMQPS"},"agent_actions":{"view_html":"https://pith.science/pith/KY7JMQPSSADHGLF6CDGR4JYOCQ","download_json":"https://pith.science/pith/KY7JMQPSSADHGLF6CDGR4JYOCQ.json","view_paper":"https://pith.science/paper/KY7JMQPS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1005.4411&json=true","fetch_graph":"https://pith.science/api/pith-number/KY7JMQPSSADHGLF6CDGR4JYOCQ/graph.json","fetch_events":"https://pith.science/api/pith-number/KY7JMQPSSADHGLF6CDGR4JYOCQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KY7JMQPSSADHGLF6CDGR4JYOCQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KY7JMQPSSADHGLF6CDGR4JYOCQ/action/storage_attestation","attest_author":"https://pith.science/pith/KY7JMQPSSADHGLF6CDGR4JYOCQ/action/author_attestation","sign_citation":"https://pith.science/pith/KY7JMQPSSADHGLF6CDGR4JYOCQ/action/citation_signature","submit_replication":"https://pith.science/pith/KY7JMQPSSADHGLF6CDGR4JYOCQ/action/replication_record"}},"created_at":"2026-05-18T04:25:25.962599+00:00","updated_at":"2026-05-18T04:25:25.962599+00:00"}