{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:OJEKZMY6W4U5SE2ZI35QMXJHBK","short_pith_number":"pith:OJEKZMY6","schema_version":"1.0","canonical_sha256":"7248acb31eb729d9135946fb065d270a895bc41f83f2e8b1040e2705fdced8df","source":{"kind":"arxiv","id":"1810.02149","version":2},"attestation_state":"computed","paper":{"title":"Sparse Filtered Nerves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Morten Brun, Nello Blaser","submitted_at":"2018-10-04T11:29:42Z","abstract_excerpt":"Given a point cloud $P$ in Euclidean space and a positive parameter $t$ we can consider the $t$-neighborhood $P^{t}$ of $P$ consisting of points at distance less than $t$ to $P$. Homology of $P^{t}$ gives information about components, holes, voids etc. in $P^{t}$. The idea of persistent homology is that it may happen that we are interested in some of holes in the spaces $P^t$ that are not detected simultaneously in homology for a single value of $t$, but where each of these holes is detected for $t$ in a wide range.\n  When the dimension of the ambient Euclidean space is small, persistent homol"},"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":"1810.02149","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2018-10-04T11:29:42Z","cross_cats_sorted":[],"title_canon_sha256":"bcfe15c12d65a2d870e22cdb9f8eab4e3377a749001b46cedcbcc52c259e2678","abstract_canon_sha256":"9bf66c4f2851a7857c1c00f20ccb0ae218181d6b2f8071c9f70efbe0b0354aa0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:47:53.855037Z","signature_b64":"pYi2QJcrQjvOjYXNpvwmj+PuLvPElvCYEoPfxG5sbDHR3hHH/YX3BU2+ACfNxBkBpZ5KLyAnr6Yy2rwN7M9mCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7248acb31eb729d9135946fb065d270a895bc41f83f2e8b1040e2705fdced8df","last_reissued_at":"2026-05-17T23:47:53.854376Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:47:53.854376Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sparse Filtered Nerves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Morten Brun, Nello Blaser","submitted_at":"2018-10-04T11:29:42Z","abstract_excerpt":"Given a point cloud $P$ in Euclidean space and a positive parameter $t$ we can consider the $t$-neighborhood $P^{t}$ of $P$ consisting of points at distance less than $t$ to $P$. Homology of $P^{t}$ gives information about components, holes, voids etc. in $P^{t}$. The idea of persistent homology is that it may happen that we are interested in some of holes in the spaces $P^t$ that are not detected simultaneously in homology for a single value of $t$, but where each of these holes is detected for $t$ in a wide range.\n  When the dimension of the ambient Euclidean space is small, persistent homol"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.02149","kind":"arxiv","version":2},"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":"1810.02149","created_at":"2026-05-17T23:47:53.854480+00:00"},{"alias_kind":"arxiv_version","alias_value":"1810.02149v2","created_at":"2026-05-17T23:47:53.854480+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.02149","created_at":"2026-05-17T23:47:53.854480+00:00"},{"alias_kind":"pith_short_12","alias_value":"OJEKZMY6W4U5","created_at":"2026-05-18T12:32:43.782077+00:00"},{"alias_kind":"pith_short_16","alias_value":"OJEKZMY6W4U5SE2Z","created_at":"2026-05-18T12:32:43.782077+00:00"},{"alias_kind":"pith_short_8","alias_value":"OJEKZMY6","created_at":"2026-05-18T12:32:43.782077+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/OJEKZMY6W4U5SE2ZI35QMXJHBK","json":"https://pith.science/pith/OJEKZMY6W4U5SE2ZI35QMXJHBK.json","graph_json":"https://pith.science/api/pith-number/OJEKZMY6W4U5SE2ZI35QMXJHBK/graph.json","events_json":"https://pith.science/api/pith-number/OJEKZMY6W4U5SE2ZI35QMXJHBK/events.json","paper":"https://pith.science/paper/OJEKZMY6"},"agent_actions":{"view_html":"https://pith.science/pith/OJEKZMY6W4U5SE2ZI35QMXJHBK","download_json":"https://pith.science/pith/OJEKZMY6W4U5SE2ZI35QMXJHBK.json","view_paper":"https://pith.science/paper/OJEKZMY6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1810.02149&json=true","fetch_graph":"https://pith.science/api/pith-number/OJEKZMY6W4U5SE2ZI35QMXJHBK/graph.json","fetch_events":"https://pith.science/api/pith-number/OJEKZMY6W4U5SE2ZI35QMXJHBK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OJEKZMY6W4U5SE2ZI35QMXJHBK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OJEKZMY6W4U5SE2ZI35QMXJHBK/action/storage_attestation","attest_author":"https://pith.science/pith/OJEKZMY6W4U5SE2ZI35QMXJHBK/action/author_attestation","sign_citation":"https://pith.science/pith/OJEKZMY6W4U5SE2ZI35QMXJHBK/action/citation_signature","submit_replication":"https://pith.science/pith/OJEKZMY6W4U5SE2ZI35QMXJHBK/action/replication_record"}},"created_at":"2026-05-17T23:47:53.854480+00:00","updated_at":"2026-05-17T23:47:53.854480+00:00"}