{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:63VFPPKBFR6SEDXFMPBQX6HUZD","short_pith_number":"pith:63VFPPKB","schema_version":"1.0","canonical_sha256":"f6ea57bd412c7d220ee563c30bf8f4c8eb3eae31dec0f1ce256b5982ca0d7394","source":{"kind":"arxiv","id":"1807.07920","version":1},"attestation_state":"computed","paper":{"title":"The Generalized Persistent Nerve Theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG"],"primary_cat":"math.AT","authors_text":"Donald R. Sheehy, Nicholas J. Cavanna","submitted_at":"2018-07-20T16:25:52Z","abstract_excerpt":"In this paper a parameterized generalization of a good cover filtration is introduced called an {\\epsilon}-good cover, defined as a cover filtration in which the reduced homology groups of the image of the inclusions between the intersections of the cover filtration at two scales {\\epsilon} apart are trivial. Assuming that one has an {\\epsilon}-good cover filtration of a finite simplicial filtration, we prove a tight bound on the bottleneck distance between the persistence diagrams of the nerve filtration and the simplicial filtration that is linear with respect to {\\epsilon} and the homology "},"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":"1807.07920","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2018-07-20T16:25:52Z","cross_cats_sorted":["cs.CG"],"title_canon_sha256":"ff2595c5cc1582a72bb2c88bcbd25f701e197c2c72d74507bb377d1c00ae647b","abstract_canon_sha256":"d4fcb185fe7a65d34b4712f8cf2f82a7217249f4ddcf4f458b49d7b65710ce5f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:10:15.295298Z","signature_b64":"xTd8zbviZ+5/8o4T4jyfOx8L+8cr4Po6X/6jFzTBOnERpilLXxKRGtdpw+WdhZXS6DB2zTf4NhKC23qLCVe7Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f6ea57bd412c7d220ee563c30bf8f4c8eb3eae31dec0f1ce256b5982ca0d7394","last_reissued_at":"2026-05-18T00:10:15.294623Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:10:15.294623Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Generalized Persistent Nerve Theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG"],"primary_cat":"math.AT","authors_text":"Donald R. Sheehy, Nicholas J. Cavanna","submitted_at":"2018-07-20T16:25:52Z","abstract_excerpt":"In this paper a parameterized generalization of a good cover filtration is introduced called an {\\epsilon}-good cover, defined as a cover filtration in which the reduced homology groups of the image of the inclusions between the intersections of the cover filtration at two scales {\\epsilon} apart are trivial. Assuming that one has an {\\epsilon}-good cover filtration of a finite simplicial filtration, we prove a tight bound on the bottleneck distance between the persistence diagrams of the nerve filtration and the simplicial filtration that is linear with respect to {\\epsilon} and the homology "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.07920","kind":"arxiv","version":1},"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":"1807.07920","created_at":"2026-05-18T00:10:15.294736+00:00"},{"alias_kind":"arxiv_version","alias_value":"1807.07920v1","created_at":"2026-05-18T00:10:15.294736+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.07920","created_at":"2026-05-18T00:10:15.294736+00:00"},{"alias_kind":"pith_short_12","alias_value":"63VFPPKBFR6S","created_at":"2026-05-18T12:32:08.215937+00:00"},{"alias_kind":"pith_short_16","alias_value":"63VFPPKBFR6SEDXF","created_at":"2026-05-18T12:32:08.215937+00:00"},{"alias_kind":"pith_short_8","alias_value":"63VFPPKB","created_at":"2026-05-18T12:32:08.215937+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/63VFPPKBFR6SEDXFMPBQX6HUZD","json":"https://pith.science/pith/63VFPPKBFR6SEDXFMPBQX6HUZD.json","graph_json":"https://pith.science/api/pith-number/63VFPPKBFR6SEDXFMPBQX6HUZD/graph.json","events_json":"https://pith.science/api/pith-number/63VFPPKBFR6SEDXFMPBQX6HUZD/events.json","paper":"https://pith.science/paper/63VFPPKB"},"agent_actions":{"view_html":"https://pith.science/pith/63VFPPKBFR6SEDXFMPBQX6HUZD","download_json":"https://pith.science/pith/63VFPPKBFR6SEDXFMPBQX6HUZD.json","view_paper":"https://pith.science/paper/63VFPPKB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1807.07920&json=true","fetch_graph":"https://pith.science/api/pith-number/63VFPPKBFR6SEDXFMPBQX6HUZD/graph.json","fetch_events":"https://pith.science/api/pith-number/63VFPPKBFR6SEDXFMPBQX6HUZD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/63VFPPKBFR6SEDXFMPBQX6HUZD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/63VFPPKBFR6SEDXFMPBQX6HUZD/action/storage_attestation","attest_author":"https://pith.science/pith/63VFPPKBFR6SEDXFMPBQX6HUZD/action/author_attestation","sign_citation":"https://pith.science/pith/63VFPPKBFR6SEDXFMPBQX6HUZD/action/citation_signature","submit_replication":"https://pith.science/pith/63VFPPKBFR6SEDXFMPBQX6HUZD/action/replication_record"}},"created_at":"2026-05-18T00:10:15.294736+00:00","updated_at":"2026-05-18T00:10:15.294736+00:00"}