{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:RD7UP7HEYYP7AS2RFCGVCW646M","short_pith_number":"pith:RD7UP7HE","schema_version":"1.0","canonical_sha256":"88ff47fce4c61ff04b51288d515bdcf33a5aaac711c7e77f2f0d6b40406b403e","source":{"kind":"arxiv","id":"2412.17482","version":1},"attestation_state":"computed","paper":{"title":"Poisson approximation of large-lifetime cycles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Christian Hirsch, Moritz Otto, Nikolaj Nyvold Lundbye","submitted_at":"2024-12-23T11:16:50Z","abstract_excerpt":"In topological data analysis, the notions of persistent homology, birthtime, lifetime, and deathtime are used to assign and capture relevant cycles (i.e., topological features) of a point cloud, such as loops and cavities. In particular, cycles with a large lifetime are of special interest. In this paper, we study such large-lifetime cycles when the point cloud is modeled as a Poisson point process. First, we consider the case with no bound on the deathtime, where we establish Poisson convergence of the centers of large-lifetime features on the 2-dimensional flat torus. Afterwards, by imposing"},"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":"2412.17482","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-12-23T11:16:50Z","cross_cats_sorted":[],"title_canon_sha256":"6c224b515e6f56aed1b9a329e4f824f45a5be602749833de0841239bc0a1cd58","abstract_canon_sha256":"c1a09846fd76f094e164a90e2d662a5fb89927711c56852a3774c449b7978fa6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:53:23.086414Z","signature_b64":"DdMu5JUY6iWAsCB0HQM7gHAY7Uv0o5hPN0AFIapkBwaoET18GmuQ4bpvICi3kTzWhrPTIsrRPFoinIHZ4hS2DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"88ff47fce4c61ff04b51288d515bdcf33a5aaac711c7e77f2f0d6b40406b403e","last_reissued_at":"2026-07-05T09:53:23.086059Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:53:23.086059Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Poisson approximation of large-lifetime cycles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Christian Hirsch, Moritz Otto, Nikolaj Nyvold Lundbye","submitted_at":"2024-12-23T11:16:50Z","abstract_excerpt":"In topological data analysis, the notions of persistent homology, birthtime, lifetime, and deathtime are used to assign and capture relevant cycles (i.e., topological features) of a point cloud, such as loops and cavities. In particular, cycles with a large lifetime are of special interest. In this paper, we study such large-lifetime cycles when the point cloud is modeled as a Poisson point process. First, we consider the case with no bound on the deathtime, where we establish Poisson convergence of the centers of large-lifetime features on the 2-dimensional flat torus. Afterwards, by imposing"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.17482","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2412.17482/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2412.17482","created_at":"2026-07-05T09:53:23.086117+00:00"},{"alias_kind":"arxiv_version","alias_value":"2412.17482v1","created_at":"2026-07-05T09:53:23.086117+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.17482","created_at":"2026-07-05T09:53:23.086117+00:00"},{"alias_kind":"pith_short_12","alias_value":"RD7UP7HEYYP7","created_at":"2026-07-05T09:53:23.086117+00:00"},{"alias_kind":"pith_short_16","alias_value":"RD7UP7HEYYP7AS2R","created_at":"2026-07-05T09:53:23.086117+00:00"},{"alias_kind":"pith_short_8","alias_value":"RD7UP7HE","created_at":"2026-07-05T09:53:23.086117+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/RD7UP7HEYYP7AS2RFCGVCW646M","json":"https://pith.science/pith/RD7UP7HEYYP7AS2RFCGVCW646M.json","graph_json":"https://pith.science/api/pith-number/RD7UP7HEYYP7AS2RFCGVCW646M/graph.json","events_json":"https://pith.science/api/pith-number/RD7UP7HEYYP7AS2RFCGVCW646M/events.json","paper":"https://pith.science/paper/RD7UP7HE"},"agent_actions":{"view_html":"https://pith.science/pith/RD7UP7HEYYP7AS2RFCGVCW646M","download_json":"https://pith.science/pith/RD7UP7HEYYP7AS2RFCGVCW646M.json","view_paper":"https://pith.science/paper/RD7UP7HE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2412.17482&json=true","fetch_graph":"https://pith.science/api/pith-number/RD7UP7HEYYP7AS2RFCGVCW646M/graph.json","fetch_events":"https://pith.science/api/pith-number/RD7UP7HEYYP7AS2RFCGVCW646M/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RD7UP7HEYYP7AS2RFCGVCW646M/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RD7UP7HEYYP7AS2RFCGVCW646M/action/storage_attestation","attest_author":"https://pith.science/pith/RD7UP7HEYYP7AS2RFCGVCW646M/action/author_attestation","sign_citation":"https://pith.science/pith/RD7UP7HEYYP7AS2RFCGVCW646M/action/citation_signature","submit_replication":"https://pith.science/pith/RD7UP7HEYYP7AS2RFCGVCW646M/action/replication_record"}},"created_at":"2026-07-05T09:53:23.086117+00:00","updated_at":"2026-07-05T09:53:23.086117+00:00"}