{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:NWT2Y7XNUIPC3DPAVXEKQG6VXH","short_pith_number":"pith:NWT2Y7XN","canonical_record":{"source":{"id":"1208.5018","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2012-08-24T17:46:21Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"f3e3f13f2031aa1463cd553a98c098d8d361ce8274a2f78fd9c2bb921088d70e","abstract_canon_sha256":"5d6df90cff8a1869c5ede344240efca7e6856ef4ac5628bfe1ef861038721786"},"schema_version":"1.0"},"canonical_sha256":"6da7ac7eeda21e2d8de0adc8a81bd5b9d5dc73001455f3eacab63a2a35435f6b","source":{"kind":"arxiv","id":"1208.5018","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.5018","created_at":"2026-05-18T02:55:39Z"},{"alias_kind":"arxiv_version","alias_value":"1208.5018v4","created_at":"2026-05-18T02:55:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.5018","created_at":"2026-05-18T02:55:39Z"},{"alias_kind":"pith_short_12","alias_value":"NWT2Y7XNUIPC","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"NWT2Y7XNUIPC3DPA","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"NWT2Y7XN","created_at":"2026-05-18T12:27:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:NWT2Y7XNUIPC3DPAVXEKQG6VXH","target":"record","payload":{"canonical_record":{"source":{"id":"1208.5018","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2012-08-24T17:46:21Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"f3e3f13f2031aa1463cd553a98c098d8d361ce8274a2f78fd9c2bb921088d70e","abstract_canon_sha256":"5d6df90cff8a1869c5ede344240efca7e6856ef4ac5628bfe1ef861038721786"},"schema_version":"1.0"},"canonical_sha256":"6da7ac7eeda21e2d8de0adc8a81bd5b9d5dc73001455f3eacab63a2a35435f6b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:55:39.390701Z","signature_b64":"GY4TJaDL6LUsfUry+RlsQnONKfPAf2blxltMu+YUb1mbN5wBcQ5pnY7XenPifJVUOg/+G0KKLStQXt3HhryqCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6da7ac7eeda21e2d8de0adc8a81bd5b9d5dc73001455f3eacab63a2a35435f6b","last_reissued_at":"2026-05-18T02:55:39.390079Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:55:39.390079Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1208.5018","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":"2026-05-18T02:55:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nJJiwgIcUhXNnbq/LUj6lddgQeeYamduHIWoOFj2JtmgK0eF0u4+/s5KVexWyORvX3nXIACOGUCuDVIxALizAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T21:41:01.064053Z"},"content_sha256":"25a67e0d3b7796cc771049c7a3d0cf2783c3e93ef45a49bfbea7439aec6aa514","schema_version":"1.0","event_id":"sha256:25a67e0d3b7796cc771049c7a3d0cf2783c3e93ef45a49bfbea7439aec6aa514"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:NWT2Y7XNUIPC3DPAVXEKQG6VXH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Computing Topological Persistence for Simplicial Maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"cs.CG","authors_text":"Fengtao Fan, Tamal K. Dey, Yusu Wang","submitted_at":"2012-08-24T17:46:21Z","abstract_excerpt":"Algorithms for persistent homology and zigzag persistent homology are well-studied for persistence modules where homomorphisms are induced by inclusion maps. In this paper, we propose a practical algorithm for computing persistence under $\\mathbb{Z}_2$ coefficients for a sequence of general simplicial maps and show how these maps arise naturally in some applications of topological data analysis.\n  First, we observe that it is not hard to simulate simplicial maps by inclusion maps but not necessarily in a monotone direction. This, combined with the known algorithms for zigzag persistence, provi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.5018","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":""},"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":"2026-05-18T02:55:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"m0vIBh73NXRd2fSJatGkRyhHVFwKG3Vdfzy2a4IY+Wha0y8YL+yxC/F0W+HJeEg5Wy1czYQQCn7vM8oe9zNJAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T21:41:01.064716Z"},"content_sha256":"2eecf521619bc12dc659c6617cd05230bfef6c4375b080701661ddceece21a29","schema_version":"1.0","event_id":"sha256:2eecf521619bc12dc659c6617cd05230bfef6c4375b080701661ddceece21a29"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NWT2Y7XNUIPC3DPAVXEKQG6VXH/bundle.json","state_url":"https://pith.science/pith/NWT2Y7XNUIPC3DPAVXEKQG6VXH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NWT2Y7XNUIPC3DPAVXEKQG6VXH/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":"2026-05-26T21:41:01Z","links":{"resolver":"https://pith.science/pith/NWT2Y7XNUIPC3DPAVXEKQG6VXH","bundle":"https://pith.science/pith/NWT2Y7XNUIPC3DPAVXEKQG6VXH/bundle.json","state":"https://pith.science/pith/NWT2Y7XNUIPC3DPAVXEKQG6VXH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NWT2Y7XNUIPC3DPAVXEKQG6VXH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:NWT2Y7XNUIPC3DPAVXEKQG6VXH","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":"5d6df90cff8a1869c5ede344240efca7e6856ef4ac5628bfe1ef861038721786","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2012-08-24T17:46:21Z","title_canon_sha256":"f3e3f13f2031aa1463cd553a98c098d8d361ce8274a2f78fd9c2bb921088d70e"},"schema_version":"1.0","source":{"id":"1208.5018","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.5018","created_at":"2026-05-18T02:55:39Z"},{"alias_kind":"arxiv_version","alias_value":"1208.5018v4","created_at":"2026-05-18T02:55:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.5018","created_at":"2026-05-18T02:55:39Z"},{"alias_kind":"pith_short_12","alias_value":"NWT2Y7XNUIPC","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"NWT2Y7XNUIPC3DPA","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"NWT2Y7XN","created_at":"2026-05-18T12:27:16Z"}],"graph_snapshots":[{"event_id":"sha256:2eecf521619bc12dc659c6617cd05230bfef6c4375b080701661ddceece21a29","target":"graph","created_at":"2026-05-18T02:55:39Z","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"},"paper":{"abstract_excerpt":"Algorithms for persistent homology and zigzag persistent homology are well-studied for persistence modules where homomorphisms are induced by inclusion maps. In this paper, we propose a practical algorithm for computing persistence under $\\mathbb{Z}_2$ coefficients for a sequence of general simplicial maps and show how these maps arise naturally in some applications of topological data analysis.\n  First, we observe that it is not hard to simulate simplicial maps by inclusion maps but not necessarily in a monotone direction. This, combined with the known algorithms for zigzag persistence, provi","authors_text":"Fengtao Fan, Tamal K. Dey, Yusu Wang","cross_cats":["math.AT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2012-08-24T17:46:21Z","title":"Computing Topological Persistence for Simplicial Maps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.5018","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":"sha256:25a67e0d3b7796cc771049c7a3d0cf2783c3e93ef45a49bfbea7439aec6aa514","target":"record","created_at":"2026-05-18T02:55:39Z","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":"5d6df90cff8a1869c5ede344240efca7e6856ef4ac5628bfe1ef861038721786","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2012-08-24T17:46:21Z","title_canon_sha256":"f3e3f13f2031aa1463cd553a98c098d8d361ce8274a2f78fd9c2bb921088d70e"},"schema_version":"1.0","source":{"id":"1208.5018","kind":"arxiv","version":4}},"canonical_sha256":"6da7ac7eeda21e2d8de0adc8a81bd5b9d5dc73001455f3eacab63a2a35435f6b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6da7ac7eeda21e2d8de0adc8a81bd5b9d5dc73001455f3eacab63a2a35435f6b","first_computed_at":"2026-05-18T02:55:39.390079Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:55:39.390079Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GY4TJaDL6LUsfUry+RlsQnONKfPAf2blxltMu+YUb1mbN5wBcQ5pnY7XenPifJVUOg/+G0KKLStQXt3HhryqCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:55:39.390701Z","signed_message":"canonical_sha256_bytes"},"source_id":"1208.5018","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:25a67e0d3b7796cc771049c7a3d0cf2783c3e93ef45a49bfbea7439aec6aa514","sha256:2eecf521619bc12dc659c6617cd05230bfef6c4375b080701661ddceece21a29"],"state_sha256":"4cab0def0426841fd973d03bd1adce5227b890fd4749c9c70ca4cfd94bcc9c24"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EaVo+aGmr97wQSYASwsYuTrFBmf3okLNUqFlZiJu1rDMpwSMpw8d6GbpBiQj0urFxpcv7b+6u7vknaWDKn5sBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T21:41:01.068055Z","bundle_sha256":"44d235596001f5f10e96d9221a02586ae5b3697475cf194a4c165849d5e97102"}}