{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:VDQSRDRCDR6TSWH66OKQC3TFKH","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":"2d2c86fad78eeb69e06b784bbea88d420403a29209f90a72bc66e87beac3c32e","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AT","submitted_at":"2023-03-20T15:22:58Z","title_canon_sha256":"baa14a9a833f385ca1b1c5ae77558b3545a08fc5dfeba969ea1af38f61a082bb"},"schema_version":"1.0","source":{"id":"2303.11193","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2303.11193","created_at":"2026-07-05T06:37:13Z"},{"alias_kind":"arxiv_version","alias_value":"2303.11193v2","created_at":"2026-07-05T06:37:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2303.11193","created_at":"2026-07-05T06:37:13Z"},{"alias_kind":"pith_short_12","alias_value":"VDQSRDRCDR6T","created_at":"2026-07-05T06:37:13Z"},{"alias_kind":"pith_short_16","alias_value":"VDQSRDRCDR6TSWH6","created_at":"2026-07-05T06:37:13Z"},{"alias_kind":"pith_short_8","alias_value":"VDQSRDRC","created_at":"2026-07-05T06:37:13Z"}],"graph_snapshots":[{"event_id":"sha256:ba4c5aeea62abb65168f1ddde74e12b5f15b7e799841b97b68d96c8646c4859a","target":"graph","created_at":"2026-07-05T06:37:13Z","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/2303.11193/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Clearing is a simple but effective optimization for the standard algorithm of persistent homology (PH), which dramatically improves the speed and scalability of PH computations for Vietoris--Rips filtrations. Due to the quick growth of the boundary matrices of a Vietoris--Rips filtration with increasing dimension, clearing is only effective when used in conjunction with a dual (cohomological) variant of the standard algorithm. This approach has not previously been applied successfully to the computation of two-parameter PH.\n  We introduce a cohomological algorithm for computing minimal free re","authors_text":"Fabian Lenzen, Michael Lesnick, Ulrich Bauer","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AT","submitted_at":"2023-03-20T15:22:58Z","title":"Efficient two-parameter persistence computation via cohomology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.11193","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:a07039ebe796454bc7aafebc680f862f5744915a08ed97fba61e498e29953dcf","target":"record","created_at":"2026-07-05T06:37:13Z","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":"2d2c86fad78eeb69e06b784bbea88d420403a29209f90a72bc66e87beac3c32e","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AT","submitted_at":"2023-03-20T15:22:58Z","title_canon_sha256":"baa14a9a833f385ca1b1c5ae77558b3545a08fc5dfeba969ea1af38f61a082bb"},"schema_version":"1.0","source":{"id":"2303.11193","kind":"arxiv","version":2}},"canonical_sha256":"a8e1288e221c7d3958fef395016e6551ef081adf21689a83b2cae0664936006b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a8e1288e221c7d3958fef395016e6551ef081adf21689a83b2cae0664936006b","first_computed_at":"2026-07-05T06:37:13.200406Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:37:13.200406Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VuXsVB3094Tr3fpXjMFXGvmHhyILpZXWd02o5ljXeRuFcUg9E+uS/v6p5CcKAN8C78Y6iAl91q7Zr6fzTpWeCA==","signature_status":"signed_v1","signed_at":"2026-07-05T06:37:13.200866Z","signed_message":"canonical_sha256_bytes"},"source_id":"2303.11193","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a07039ebe796454bc7aafebc680f862f5744915a08ed97fba61e498e29953dcf","sha256:ba4c5aeea62abb65168f1ddde74e12b5f15b7e799841b97b68d96c8646c4859a"],"state_sha256":"906d6e8900382080044b1c183d207f9d2c45d48997e13dd659265858b4b70c20"}