{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:KNUIL5HJWJKIGFVOPCEZMETVET","short_pith_number":"pith:KNUIL5HJ","schema_version":"1.0","canonical_sha256":"536885f4e9b2548316ae788996127524e9cae8ac5bd6ea0a54122b9e4681245a","source":{"kind":"arxiv","id":"1509.04347","version":2},"attestation_state":"computed","paper":{"title":"Maximally Persistent Cycles in Random Geometric Complexes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.CO"],"primary_cat":"math.PR","authors_text":"Matthew Kahle, Omer Bobrowski, Primoz Skraba","submitted_at":"2015-09-14T22:43:02Z","abstract_excerpt":"We initiate the study of persistent homology of random geometric simplicial complexes. Our main interest is in maximally persistent cycles of degree-$k$ in persistent homology, for a either the \\cech or the Vietoris--Rips filtration built on a uniform Poisson process of intensity $n$ in the unit cube $[0,1]^d$. This is a natural way of measuring the largest \"$k$-dimensional hole\" in a random point set. This problem is in the intersection of geometric probability and algebraic topology, and is naturally motivated by a probabilistic view of topological inference.\n  We show that for all $d \\ge 2$"},"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":"1509.04347","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-09-14T22:43:02Z","cross_cats_sorted":["math.AT","math.CO"],"title_canon_sha256":"0375cfb0a02b217b69911074c4036d6d8214e713d12c2e4fb1710bda1bf07e14","abstract_canon_sha256":"70ae4f9e973a55dd7ce61aa8fce13c6b93598cc50b2d5c4dcd12f3cf1e1f65d6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:14:52.941889Z","signature_b64":"6XyAkP4yuffoluf9tTJVWcjYmreSdMgJAZSpPkw9IXP4bWA2Gf9hRPj4x6BZg6e5cHG114D4T3lt5etqI4EiBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"536885f4e9b2548316ae788996127524e9cae8ac5bd6ea0a54122b9e4681245a","last_reissued_at":"2026-05-18T01:14:52.941426Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:14:52.941426Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Maximally Persistent Cycles in Random Geometric Complexes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.CO"],"primary_cat":"math.PR","authors_text":"Matthew Kahle, Omer Bobrowski, Primoz Skraba","submitted_at":"2015-09-14T22:43:02Z","abstract_excerpt":"We initiate the study of persistent homology of random geometric simplicial complexes. Our main interest is in maximally persistent cycles of degree-$k$ in persistent homology, for a either the \\cech or the Vietoris--Rips filtration built on a uniform Poisson process of intensity $n$ in the unit cube $[0,1]^d$. This is a natural way of measuring the largest \"$k$-dimensional hole\" in a random point set. This problem is in the intersection of geometric probability and algebraic topology, and is naturally motivated by a probabilistic view of topological inference.\n  We show that for all $d \\ge 2$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.04347","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":"1509.04347","created_at":"2026-05-18T01:14:52.941495+00:00"},{"alias_kind":"arxiv_version","alias_value":"1509.04347v2","created_at":"2026-05-18T01:14:52.941495+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.04347","created_at":"2026-05-18T01:14:52.941495+00:00"},{"alias_kind":"pith_short_12","alias_value":"KNUIL5HJWJKI","created_at":"2026-05-18T12:29:29.992203+00:00"},{"alias_kind":"pith_short_16","alias_value":"KNUIL5HJWJKIGFVO","created_at":"2026-05-18T12:29:29.992203+00:00"},{"alias_kind":"pith_short_8","alias_value":"KNUIL5HJ","created_at":"2026-05-18T12:29:29.992203+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/KNUIL5HJWJKIGFVOPCEZMETVET","json":"https://pith.science/pith/KNUIL5HJWJKIGFVOPCEZMETVET.json","graph_json":"https://pith.science/api/pith-number/KNUIL5HJWJKIGFVOPCEZMETVET/graph.json","events_json":"https://pith.science/api/pith-number/KNUIL5HJWJKIGFVOPCEZMETVET/events.json","paper":"https://pith.science/paper/KNUIL5HJ"},"agent_actions":{"view_html":"https://pith.science/pith/KNUIL5HJWJKIGFVOPCEZMETVET","download_json":"https://pith.science/pith/KNUIL5HJWJKIGFVOPCEZMETVET.json","view_paper":"https://pith.science/paper/KNUIL5HJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1509.04347&json=true","fetch_graph":"https://pith.science/api/pith-number/KNUIL5HJWJKIGFVOPCEZMETVET/graph.json","fetch_events":"https://pith.science/api/pith-number/KNUIL5HJWJKIGFVOPCEZMETVET/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KNUIL5HJWJKIGFVOPCEZMETVET/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KNUIL5HJWJKIGFVOPCEZMETVET/action/storage_attestation","attest_author":"https://pith.science/pith/KNUIL5HJWJKIGFVOPCEZMETVET/action/author_attestation","sign_citation":"https://pith.science/pith/KNUIL5HJWJKIGFVOPCEZMETVET/action/citation_signature","submit_replication":"https://pith.science/pith/KNUIL5HJWJKIGFVOPCEZMETVET/action/replication_record"}},"created_at":"2026-05-18T01:14:52.941495+00:00","updated_at":"2026-05-18T01:14:52.941495+00:00"}