{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:FDY2K4ZBMZZ64PJ2PH7B2KWRJ2","short_pith_number":"pith:FDY2K4ZB","schema_version":"1.0","canonical_sha256":"28f1a573216673ee3d3a79fe1d2ad14e97bd3f2ae69290d593bd9db697605167","source":{"kind":"arxiv","id":"2408.16716","version":1},"attestation_state":"computed","paper":{"title":"Sparse Approximation of the Subdivision-Rips Bifiltration for Doubling Metrics","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.CG"],"primary_cat":"math.AT","authors_text":"Kenneth McCabe, Michael Lesnick","submitted_at":"2024-08-29T17:07:40Z","abstract_excerpt":"The Vietoris-Rips filtration, the standard filtration on metric data in topological data analysis, is notoriously sensitive to outliers. Sheehy's subdivision-Rips bifiltration $\\mathcal{SR}(-)$ is a density-sensitive refinement that is robust to outliers in a strong sense, but whose 0-skeleton has exponential size. For $X$ a finite metric space of constant doubling dimension and fixed $\\epsilon>0$, we construct a $(1+\\epsilon)$-homotopy interleaving approximation of $\\mathcal{SR}(X)$ whose $k$-skeleton has size $O(|X|^{k+2})$. For $k\\geq 1$ constant, the $k$-skeleton can be computed in time $O"},"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":"2408.16716","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AT","submitted_at":"2024-08-29T17:07:40Z","cross_cats_sorted":["cs.CG"],"title_canon_sha256":"c3b7607bd2d109be0b6f2627575fb8b6014ebe4f128c318a1dc66296a5f8e2c6","abstract_canon_sha256":"58cc8cce9319c8adb5bad05a19622a6bfd74c495a15e38f3e1fc2f65fb303fcc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:00:45.449532Z","signature_b64":"e8SSVedjsGSrh9TzwoLGGynVghUcYnuXnAhfgGwhUGu4QTgjLJVi1Lrja5X+VQvOClPZIUfbGmjYLhSVojpCAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"28f1a573216673ee3d3a79fe1d2ad14e97bd3f2ae69290d593bd9db697605167","last_reissued_at":"2026-07-05T09:00:45.449056Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:00:45.449056Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sparse Approximation of the Subdivision-Rips Bifiltration for Doubling Metrics","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.CG"],"primary_cat":"math.AT","authors_text":"Kenneth McCabe, Michael Lesnick","submitted_at":"2024-08-29T17:07:40Z","abstract_excerpt":"The Vietoris-Rips filtration, the standard filtration on metric data in topological data analysis, is notoriously sensitive to outliers. Sheehy's subdivision-Rips bifiltration $\\mathcal{SR}(-)$ is a density-sensitive refinement that is robust to outliers in a strong sense, but whose 0-skeleton has exponential size. For $X$ a finite metric space of constant doubling dimension and fixed $\\epsilon>0$, we construct a $(1+\\epsilon)$-homotopy interleaving approximation of $\\mathcal{SR}(X)$ whose $k$-skeleton has size $O(|X|^{k+2})$. For $k\\geq 1$ constant, the $k$-skeleton can be computed in time $O"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2408.16716","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/2408.16716/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":"2408.16716","created_at":"2026-07-05T09:00:45.449112+00:00"},{"alias_kind":"arxiv_version","alias_value":"2408.16716v1","created_at":"2026-07-05T09:00:45.449112+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2408.16716","created_at":"2026-07-05T09:00:45.449112+00:00"},{"alias_kind":"pith_short_12","alias_value":"FDY2K4ZBMZZ6","created_at":"2026-07-05T09:00:45.449112+00:00"},{"alias_kind":"pith_short_16","alias_value":"FDY2K4ZBMZZ64PJ2","created_at":"2026-07-05T09:00:45.449112+00:00"},{"alias_kind":"pith_short_8","alias_value":"FDY2K4ZB","created_at":"2026-07-05T09:00:45.449112+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2607.06524","citing_title":"Lower Bounds for Approximating the Vietoris-Rips Filtration","ref_index":34,"is_internal_anchor":true},{"citing_arxiv_id":"2604.07022","citing_title":"An Algebraic Introduction to Persistence","ref_index":148,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/FDY2K4ZBMZZ64PJ2PH7B2KWRJ2","json":"https://pith.science/pith/FDY2K4ZBMZZ64PJ2PH7B2KWRJ2.json","graph_json":"https://pith.science/api/pith-number/FDY2K4ZBMZZ64PJ2PH7B2KWRJ2/graph.json","events_json":"https://pith.science/api/pith-number/FDY2K4ZBMZZ64PJ2PH7B2KWRJ2/events.json","paper":"https://pith.science/paper/FDY2K4ZB"},"agent_actions":{"view_html":"https://pith.science/pith/FDY2K4ZBMZZ64PJ2PH7B2KWRJ2","download_json":"https://pith.science/pith/FDY2K4ZBMZZ64PJ2PH7B2KWRJ2.json","view_paper":"https://pith.science/paper/FDY2K4ZB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2408.16716&json=true","fetch_graph":"https://pith.science/api/pith-number/FDY2K4ZBMZZ64PJ2PH7B2KWRJ2/graph.json","fetch_events":"https://pith.science/api/pith-number/FDY2K4ZBMZZ64PJ2PH7B2KWRJ2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FDY2K4ZBMZZ64PJ2PH7B2KWRJ2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FDY2K4ZBMZZ64PJ2PH7B2KWRJ2/action/storage_attestation","attest_author":"https://pith.science/pith/FDY2K4ZBMZZ64PJ2PH7B2KWRJ2/action/author_attestation","sign_citation":"https://pith.science/pith/FDY2K4ZBMZZ64PJ2PH7B2KWRJ2/action/citation_signature","submit_replication":"https://pith.science/pith/FDY2K4ZBMZZ64PJ2PH7B2KWRJ2/action/replication_record"}},"created_at":"2026-07-05T09:00:45.449112+00:00","updated_at":"2026-07-05T09:00:45.449112+00:00"}