{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:NM35QTSS43PYRJN2KKJR4X4LOQ","short_pith_number":"pith:NM35QTSS","schema_version":"1.0","canonical_sha256":"6b37d84e52e6df88a5ba52931e5f8b74322acf0b4426731516916dbc92f93f28","source":{"kind":"arxiv","id":"1608.06956","version":3},"attestation_state":"computed","paper":{"title":"An Approximate Nerve Theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Dejan Govc, Primoz Skraba","submitted_at":"2016-08-24T20:18:17Z","abstract_excerpt":"The Nerve Theorem relates the topological type of a suitably nice space with the nerve of a good cover of that space. It has many variants, such as to consider acyclic covers and numerous applications in topology including applied and computational topology. The goal of this paper is to relax the notion of a good cover to an approximately good cover, or more precisely, we introduce the notion of an $\\varepsilon$-acyclic cover. We use persistent homology to make this rigorous and prove tight bounds between the persistent homology of a space endowed with a function and the persistent homology of"},"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":"1608.06956","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2016-08-24T20:18:17Z","cross_cats_sorted":[],"title_canon_sha256":"c5f81cf8279aa2b5fe73e3c24abf5cda4f025a2537f736216a1b0e8f8fd6a351","abstract_canon_sha256":"7c708062ea916fdecc4b96e2af123057cf83fbef11dffcfb3eff284fde9968e8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:46:16.426265Z","signature_b64":"qazuvYkyjuerxsbtRRRENXp4UPVwMmhYe/adCQ9pXRLnmyGXh/mlUxoan60o0WQOJVfzG6ROdMokN37LkRBaCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6b37d84e52e6df88a5ba52931e5f8b74322acf0b4426731516916dbc92f93f28","last_reissued_at":"2026-05-18T00:46:16.425735Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:46:16.425735Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An Approximate Nerve Theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Dejan Govc, Primoz Skraba","submitted_at":"2016-08-24T20:18:17Z","abstract_excerpt":"The Nerve Theorem relates the topological type of a suitably nice space with the nerve of a good cover of that space. It has many variants, such as to consider acyclic covers and numerous applications in topology including applied and computational topology. The goal of this paper is to relax the notion of a good cover to an approximately good cover, or more precisely, we introduce the notion of an $\\varepsilon$-acyclic cover. We use persistent homology to make this rigorous and prove tight bounds between the persistent homology of a space endowed with a function and the persistent homology of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.06956","kind":"arxiv","version":3},"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":"1608.06956","created_at":"2026-05-18T00:46:16.425828+00:00"},{"alias_kind":"arxiv_version","alias_value":"1608.06956v3","created_at":"2026-05-18T00:46:16.425828+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.06956","created_at":"2026-05-18T00:46:16.425828+00:00"},{"alias_kind":"pith_short_12","alias_value":"NM35QTSS43PY","created_at":"2026-05-18T12:30:32.724797+00:00"},{"alias_kind":"pith_short_16","alias_value":"NM35QTSS43PYRJN2","created_at":"2026-05-18T12:30:32.724797+00:00"},{"alias_kind":"pith_short_8","alias_value":"NM35QTSS","created_at":"2026-05-18T12:30:32.724797+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/NM35QTSS43PYRJN2KKJR4X4LOQ","json":"https://pith.science/pith/NM35QTSS43PYRJN2KKJR4X4LOQ.json","graph_json":"https://pith.science/api/pith-number/NM35QTSS43PYRJN2KKJR4X4LOQ/graph.json","events_json":"https://pith.science/api/pith-number/NM35QTSS43PYRJN2KKJR4X4LOQ/events.json","paper":"https://pith.science/paper/NM35QTSS"},"agent_actions":{"view_html":"https://pith.science/pith/NM35QTSS43PYRJN2KKJR4X4LOQ","download_json":"https://pith.science/pith/NM35QTSS43PYRJN2KKJR4X4LOQ.json","view_paper":"https://pith.science/paper/NM35QTSS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1608.06956&json=true","fetch_graph":"https://pith.science/api/pith-number/NM35QTSS43PYRJN2KKJR4X4LOQ/graph.json","fetch_events":"https://pith.science/api/pith-number/NM35QTSS43PYRJN2KKJR4X4LOQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NM35QTSS43PYRJN2KKJR4X4LOQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NM35QTSS43PYRJN2KKJR4X4LOQ/action/storage_attestation","attest_author":"https://pith.science/pith/NM35QTSS43PYRJN2KKJR4X4LOQ/action/author_attestation","sign_citation":"https://pith.science/pith/NM35QTSS43PYRJN2KKJR4X4LOQ/action/citation_signature","submit_replication":"https://pith.science/pith/NM35QTSS43PYRJN2KKJR4X4LOQ/action/replication_record"}},"created_at":"2026-05-18T00:46:16.425828+00:00","updated_at":"2026-05-18T00:46:16.425828+00:00"}