{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:T4SJZRXU2RR2JDPRAKJNYPXASY","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":"835d7e8f4b94cb7443520c87dac229f38cf4634a2567baf3ee17afd0facd5399","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-12-23T02:14:58Z","title_canon_sha256":"3aa2aea0aa55eab2359cdb901681af19749aee0bf1ba279ebb41ac3d9b7cb172"},"schema_version":"1.0","source":{"id":"1312.6454","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.6454","created_at":"2026-05-18T02:19:25Z"},{"alias_kind":"arxiv_version","alias_value":"1312.6454v2","created_at":"2026-05-18T02:19:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.6454","created_at":"2026-05-18T02:19:25Z"},{"alias_kind":"pith_short_12","alias_value":"T4SJZRXU2RR2","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"T4SJZRXU2RR2JDPR","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"T4SJZRXU","created_at":"2026-05-18T12:27:59Z"}],"graph_snapshots":[{"event_id":"sha256:cc08f7e45bf838598582b4466b1e39dfc6860dcf59d662a4ebff461db32965af","target":"graph","created_at":"2026-05-18T02:19:25Z","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"},"paper":{"abstract_excerpt":"Sheaves and sheaf cohomology are powerful tools in computational topology, greatly generalizing persistent homology. We develop an algorithm for simplifying the computation of cellular sheaf cohomology via (discrete) Morse-theoretic techniques. As a consequence, we derive efficient techniques for distributed computation of (ordinary) cohomology of a cell complex.","authors_text":"Justin Curry, Robert Ghrist, Vidit Nanda","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-12-23T02:14:58Z","title":"Discrete Morse theory for computing cellular sheaf cohomology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.6454","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:e62f47250a4c613b7fe9289a04450f0649baf62b18bdd6ff1bacb47702f27da3","target":"record","created_at":"2026-05-18T02:19:25Z","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":"835d7e8f4b94cb7443520c87dac229f38cf4634a2567baf3ee17afd0facd5399","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-12-23T02:14:58Z","title_canon_sha256":"3aa2aea0aa55eab2359cdb901681af19749aee0bf1ba279ebb41ac3d9b7cb172"},"schema_version":"1.0","source":{"id":"1312.6454","kind":"arxiv","version":2}},"canonical_sha256":"9f249cc6f4d463a48df10292dc3ee0962fc6ee32966abfa147e521861b3bf4d6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9f249cc6f4d463a48df10292dc3ee0962fc6ee32966abfa147e521861b3bf4d6","first_computed_at":"2026-05-18T02:19:25.741001Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:19:25.741001Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"J7/nyL4+Xx1WjsDhX7slHRnBwVHQvTaaQ3r091JOivgUyLNOKu0/1FKJDnH5bYIVyYc4GQfCqD5EDRKZVhKSBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:19:25.741945Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.6454","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e62f47250a4c613b7fe9289a04450f0649baf62b18bdd6ff1bacb47702f27da3","sha256:cc08f7e45bf838598582b4466b1e39dfc6860dcf59d662a4ebff461db32965af"],"state_sha256":"e4c5bbddeb0b7c2f557db397efc660185cc0aafd97d060f49408db5ff93d5701"}