{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:7ZUOZZ4IP6QLZA262RDDTRENVK","short_pith_number":"pith:7ZUOZZ4I","canonical_record":{"source":{"id":"1203.5288","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2012-03-23T16:35:44Z","cross_cats_sorted":[],"title_canon_sha256":"38ef040099dbd2b408130067d5d69db9134f46ded47f8fa5673c5d386dbf22f1","abstract_canon_sha256":"660d46f2b6fb94e23bb96e353868b895dff2470735c88501c7c3025887317a63"},"schema_version":"1.0"},"canonical_sha256":"fe68ece7887fa0bc835ed44639c48daab0188ce5700145d63371a8a77e8907d1","source":{"kind":"arxiv","id":"1203.5288","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:7ZUOZZ4IP6QLZA262RDDTRENVK","target":"record","payload":{"canonical_record":{"source":{"id":"1203.5288","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2012-03-23T16:35:44Z","cross_cats_sorted":[],"title_canon_sha256":"38ef040099dbd2b408130067d5d69db9134f46ded47f8fa5673c5d386dbf22f1","abstract_canon_sha256":"660d46f2b6fb94e23bb96e353868b895dff2470735c88501c7c3025887317a63"},"schema_version":"1.0"},"canonical_sha256":"fe68ece7887fa0bc835ed44639c48daab0188ce5700145d63371a8a77e8907d1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:22:33.199844Z","signature_b64":"eWzpc7R5a0u0V+YfmnITw8TbG9BcWwr42opzVa84Yr77uov2EhU1raTLH58eMV9nSH3BbyGVYxa/CMg8+LteBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fe68ece7887fa0bc835ed44639c48daab0188ce5700145d63371a8a77e8907d1","last_reissued_at":"2026-07-05T00:22:33.199374Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:22:33.199374Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1203.5288","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T00:22:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PgMzM61SJtH5BeaN3Cz+7r3MpK0aYaGaegpSR9W7thrMNhCJOlVNSAga/yNqhSvl6vbD+3ToJDCGW4S0dSLcCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T11:21:16.151383Z"},"content_sha256":"33f79e95537cfa37b3e369dd6344bfeef4164da9adbf4080a66075e90530d7b6","schema_version":"1.0","event_id":"sha256:33f79e95537cfa37b3e369dd6344bfeef4164da9adbf4080a66075e90530d7b6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:7ZUOZZ4IP6QLZA262RDDTRENVK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Structure on the Top Homology and Related Algorithms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Chandrika Sadanand, Dennis Sullivan, Nissim Ranade","submitted_at":"2012-03-23T16:35:44Z","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 "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.5288","kind":"arxiv","version":4},"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/1203.5288/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T00:22:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OB2lkHd1AUq2pFAdUR/K6qOqdqnaPeUD/bTg0khoH03NFbpabfyExSxrFCJFyP3v33OmNtaLX8v267s1aKcWCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T11:21:16.151912Z"},"content_sha256":"a6697dfd34cacd9d57d162c52cf72829da4b2a01602a628f521c7e4fe97e56c6","schema_version":"1.0","event_id":"sha256:a6697dfd34cacd9d57d162c52cf72829da4b2a01602a628f521c7e4fe97e56c6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7ZUOZZ4IP6QLZA262RDDTRENVK/bundle.json","state_url":"https://pith.science/pith/7ZUOZZ4IP6QLZA262RDDTRENVK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7ZUOZZ4IP6QLZA262RDDTRENVK/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-05T11:21:16Z","links":{"resolver":"https://pith.science/pith/7ZUOZZ4IP6QLZA262RDDTRENVK","bundle":"https://pith.science/pith/7ZUOZZ4IP6QLZA262RDDTRENVK/bundle.json","state":"https://pith.science/pith/7ZUOZZ4IP6QLZA262RDDTRENVK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7ZUOZZ4IP6QLZA262RDDTRENVK/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"66LaFcs8APp0Za4A0u3Vs5vr9BexmxqFXFyh/nkMAnXB3FJh/0YlYtCi0vmvPoy3d/PVRIDPzS/WRvAJuu3+CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-05T11:21:16.157224Z","bundle_sha256":"0bd89081d37e38b93b018522493a304461a7c86718bc1644741e760f299e9814"}}