{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:UOSXQW3HJTXB2DIWDTR565DEI6","short_pith_number":"pith:UOSXQW3H","schema_version":"1.0","canonical_sha256":"a3a5785b674cee1d0d161ce3df7464479e1b0a1ffe699d8e1870fa6c9603a92c","source":{"kind":"arxiv","id":"2108.08831","version":2},"attestation_state":"computed","paper":{"title":"U-match factorization: sparse homological algebra, lazy cycle representatives, and dualities in persistent (co)homology","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.CG"],"primary_cat":"math.AT","authors_text":"Chad Giusti, Gregory Henselman-Petrusek, Haibin Hang, Lori Ziegelmeier","submitted_at":"2021-08-19T17:51:53Z","abstract_excerpt":"Persistent homology is a leading tool in topological data analysis (TDA). Many problems in TDA can be solved via homological -- and indeed, linear -- algebra. However, matrices in this domain are typically large, with rows and columns numbered in billions. Low-rank approximation of such arrays typically destroys essential information; thus, new mathematical and computational paradigms are needed for very large, sparse matrices.\n  We present the U-match matrix factorization scheme to address this challenge. U-match has two desirable features. First, it admits a compressed storage format that re"},"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":"2108.08831","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AT","submitted_at":"2021-08-19T17:51:53Z","cross_cats_sorted":["cs.CG"],"title_canon_sha256":"8a28380448d625cd969dd182cbd7bc25f07f7aa9f7775d67e78820ef4fcb271d","abstract_canon_sha256":"1b3100e9a379dd12d6c667e6b85b3843e95f88c5fb5ff135dd1542b5c9d359a3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:07:31.433616Z","signature_b64":"UU33g4c39sOi+Ai5VwFXvCGgOkI7EEwYMBmgYhxCe1YVe307ktnD1x1gVNtxSkjqL8QQaeIdlwUqDu/xlUsWBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a3a5785b674cee1d0d161ce3df7464479e1b0a1ffe699d8e1870fa6c9603a92c","last_reissued_at":"2026-07-05T03:07:31.433225Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:07:31.433225Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"U-match factorization: sparse homological algebra, lazy cycle representatives, and dualities in persistent (co)homology","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.CG"],"primary_cat":"math.AT","authors_text":"Chad Giusti, Gregory Henselman-Petrusek, Haibin Hang, Lori Ziegelmeier","submitted_at":"2021-08-19T17:51:53Z","abstract_excerpt":"Persistent homology is a leading tool in topological data analysis (TDA). Many problems in TDA can be solved via homological -- and indeed, linear -- algebra. However, matrices in this domain are typically large, with rows and columns numbered in billions. Low-rank approximation of such arrays typically destroys essential information; thus, new mathematical and computational paradigms are needed for very large, sparse matrices.\n  We present the U-match matrix factorization scheme to address this challenge. U-match has two desirable features. First, it admits a compressed storage format that re"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2108.08831","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2108.08831/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":"2108.08831","created_at":"2026-07-05T03:07:31.433279+00:00"},{"alias_kind":"arxiv_version","alias_value":"2108.08831v2","created_at":"2026-07-05T03:07:31.433279+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2108.08831","created_at":"2026-07-05T03:07:31.433279+00:00"},{"alias_kind":"pith_short_12","alias_value":"UOSXQW3HJTXB","created_at":"2026-07-05T03:07:31.433279+00:00"},{"alias_kind":"pith_short_16","alias_value":"UOSXQW3HJTXB2DIW","created_at":"2026-07-05T03:07:31.433279+00:00"},{"alias_kind":"pith_short_8","alias_value":"UOSXQW3H","created_at":"2026-07-05T03:07:31.433279+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/UOSXQW3HJTXB2DIWDTR565DEI6","json":"https://pith.science/pith/UOSXQW3HJTXB2DIWDTR565DEI6.json","graph_json":"https://pith.science/api/pith-number/UOSXQW3HJTXB2DIWDTR565DEI6/graph.json","events_json":"https://pith.science/api/pith-number/UOSXQW3HJTXB2DIWDTR565DEI6/events.json","paper":"https://pith.science/paper/UOSXQW3H"},"agent_actions":{"view_html":"https://pith.science/pith/UOSXQW3HJTXB2DIWDTR565DEI6","download_json":"https://pith.science/pith/UOSXQW3HJTXB2DIWDTR565DEI6.json","view_paper":"https://pith.science/paper/UOSXQW3H","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2108.08831&json=true","fetch_graph":"https://pith.science/api/pith-number/UOSXQW3HJTXB2DIWDTR565DEI6/graph.json","fetch_events":"https://pith.science/api/pith-number/UOSXQW3HJTXB2DIWDTR565DEI6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UOSXQW3HJTXB2DIWDTR565DEI6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UOSXQW3HJTXB2DIWDTR565DEI6/action/storage_attestation","attest_author":"https://pith.science/pith/UOSXQW3HJTXB2DIWDTR565DEI6/action/author_attestation","sign_citation":"https://pith.science/pith/UOSXQW3HJTXB2DIWDTR565DEI6/action/citation_signature","submit_replication":"https://pith.science/pith/UOSXQW3HJTXB2DIWDTR565DEI6/action/replication_record"}},"created_at":"2026-07-05T03:07:31.433279+00:00","updated_at":"2026-07-05T03:07:31.433279+00:00"}