{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:7ZUOZZ4IP6QLZA262RDDTRENVK","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"660d46f2b6fb94e23bb96e353868b895dff2470735c88501c7c3025887317a63","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2012-03-23T16:35:44Z","title_canon_sha256":"38ef040099dbd2b408130067d5d69db9134f46ded47f8fa5673c5d386dbf22f1"},"schema_version":"1.0","source":{"id":"1203.5288","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.5288","created_at":"2026-07-05T00:22:33Z"},{"alias_kind":"arxiv_version","alias_value":"1203.5288v4","created_at":"2026-07-05T00:22:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.5288","created_at":"2026-07-05T00:22:33Z"},{"alias_kind":"pith_short_12","alias_value":"7ZUOZZ4IP6QL","created_at":"2026-07-05T00:22:33Z"},{"alias_kind":"pith_short_16","alias_value":"7ZUOZZ4IP6QLZA26","created_at":"2026-07-05T00:22:33Z"},{"alias_kind":"pith_short_8","alias_value":"7ZUOZZ4I","created_at":"2026-07-05T00:22:33Z"}],"graph_snapshots":[{"event_id":"sha256:a6697dfd34cacd9d57d162c52cf72829da4b2a01602a628f521c7e4fe97e56c6","target":"graph","created_at":"2026-07-05T00:22:33Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1203.5288/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We explore the special structure of the top-dimensional homology of any compact triangulable space $X$ of dimension $d$. Since there are no $(d+1)$-dimensional cells, the top homology equals the top cycles and is thus a free abelian group. There is no obvious basis, but we show that there is a canonical embedding of the top homology into a canonical free abelian group which has a natural basis up to signs. This embedding structure is an invariant of $X$ up to homeomorphism. This circumstance gives the top homology the structure of an (orientable) matroid, where cycles in the sense of matroids ","authors_text":"Chandrika Sadanand, Dennis Sullivan, Nissim Ranade","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2012-03-23T16:35:44Z","title":"Structure on the Top Homology and Related Algorithms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.5288","kind":"arxiv","version":4},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:33f79e95537cfa37b3e369dd6344bfeef4164da9adbf4080a66075e90530d7b6","target":"record","created_at":"2026-07-05T00:22:33Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"660d46f2b6fb94e23bb96e353868b895dff2470735c88501c7c3025887317a63","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2012-03-23T16:35:44Z","title_canon_sha256":"38ef040099dbd2b408130067d5d69db9134f46ded47f8fa5673c5d386dbf22f1"},"schema_version":"1.0","source":{"id":"1203.5288","kind":"arxiv","version":4}},"canonical_sha256":"fe68ece7887fa0bc835ed44639c48daab0188ce5700145d63371a8a77e8907d1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fe68ece7887fa0bc835ed44639c48daab0188ce5700145d63371a8a77e8907d1","first_computed_at":"2026-07-05T00:22:33.199374Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:22:33.199374Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eWzpc7R5a0u0V+YfmnITw8TbG9BcWwr42opzVa84Yr77uov2EhU1raTLH58eMV9nSH3BbyGVYxa/CMg8+LteBw==","signature_status":"signed_v1","signed_at":"2026-07-05T00:22:33.199844Z","signed_message":"canonical_sha256_bytes"},"source_id":"1203.5288","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:33f79e95537cfa37b3e369dd6344bfeef4164da9adbf4080a66075e90530d7b6","sha256:a6697dfd34cacd9d57d162c52cf72829da4b2a01602a628f521c7e4fe97e56c6"],"state_sha256":"7dba29bae2f94a5335976972e559ac55326396ef0effed229f3edd8e768db7c5"}