{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:UOSXQW3HJTXB2DIWDTR565DEI6","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"1b3100e9a379dd12d6c667e6b85b3843e95f88c5fb5ff135dd1542b5c9d359a3","cross_cats_sorted":["cs.CG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AT","submitted_at":"2021-08-19T17:51:53Z","title_canon_sha256":"8a28380448d625cd969dd182cbd7bc25f07f7aa9f7775d67e78820ef4fcb271d"},"schema_version":"1.0","source":{"id":"2108.08831","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2108.08831","created_at":"2026-07-05T03:07:31Z"},{"alias_kind":"arxiv_version","alias_value":"2108.08831v2","created_at":"2026-07-05T03:07:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2108.08831","created_at":"2026-07-05T03:07:31Z"},{"alias_kind":"pith_short_12","alias_value":"UOSXQW3HJTXB","created_at":"2026-07-05T03:07:31Z"},{"alias_kind":"pith_short_16","alias_value":"UOSXQW3HJTXB2DIW","created_at":"2026-07-05T03:07:31Z"},{"alias_kind":"pith_short_8","alias_value":"UOSXQW3H","created_at":"2026-07-05T03:07:31Z"}],"graph_snapshots":[{"event_id":"sha256:22b4240764c3792941ac6f9be96e695ab233cf98c8e25880b71476eaeac02b01","target":"graph","created_at":"2026-07-05T03:07:31Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2108.08831/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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","authors_text":"Chad Giusti, Gregory Henselman-Petrusek, Haibin Hang, Lori Ziegelmeier","cross_cats":["cs.CG"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AT","submitted_at":"2021-08-19T17:51:53Z","title":"U-match factorization: sparse homological algebra, lazy cycle representatives, and dualities in persistent (co)homology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2108.08831","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:4bbdc2df08ac9671f3f4659417825a0fc54c341617f8a57f87056e88ffcd1881","target":"record","created_at":"2026-07-05T03:07:31Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"1b3100e9a379dd12d6c667e6b85b3843e95f88c5fb5ff135dd1542b5c9d359a3","cross_cats_sorted":["cs.CG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AT","submitted_at":"2021-08-19T17:51:53Z","title_canon_sha256":"8a28380448d625cd969dd182cbd7bc25f07f7aa9f7775d67e78820ef4fcb271d"},"schema_version":"1.0","source":{"id":"2108.08831","kind":"arxiv","version":2}},"canonical_sha256":"a3a5785b674cee1d0d161ce3df7464479e1b0a1ffe699d8e1870fa6c9603a92c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a3a5785b674cee1d0d161ce3df7464479e1b0a1ffe699d8e1870fa6c9603a92c","first_computed_at":"2026-07-05T03:07:31.433225Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:07:31.433225Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UU33g4c39sOi+Ai5VwFXvCGgOkI7EEwYMBmgYhxCe1YVe307ktnD1x1gVNtxSkjqL8QQaeIdlwUqDu/xlUsWBg==","signature_status":"signed_v1","signed_at":"2026-07-05T03:07:31.433616Z","signed_message":"canonical_sha256_bytes"},"source_id":"2108.08831","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4bbdc2df08ac9671f3f4659417825a0fc54c341617f8a57f87056e88ffcd1881","sha256:22b4240764c3792941ac6f9be96e695ab233cf98c8e25880b71476eaeac02b01"],"state_sha256":"4e3e6155174517aea6f1bc989e689101077573a76ca665536772296453b095ad"}