{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2001:YOPCJUDXJVSPNC2CEBD5THFCHH","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":"915edb6835c8f7c2ebeb5c73b55364b2cb3c4cd55d931af2d297835c790af10c","cross_cats_sorted":["math.CO"],"license":"","primary_cat":"math.AT","submitted_at":"2001-10-30T09:51:12Z","title_canon_sha256":"34b35d858b7c8e91ff75e61b42c821d04f019f949ca3d9a9af8a3e8bb641fc2f"},"schema_version":"1.0","source":{"id":"math/0110314","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0110314","created_at":"2026-05-18T04:21:51Z"},{"alias_kind":"arxiv_version","alias_value":"math/0110314v1","created_at":"2026-05-18T04:21:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0110314","created_at":"2026-05-18T04:21:51Z"},{"alias_kind":"pith_short_12","alias_value":"YOPCJUDXJVSP","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"YOPCJUDXJVSPNC2C","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"YOPCJUDX","created_at":"2026-05-18T12:25:50Z"}],"graph_snapshots":[{"event_id":"sha256:1fcd3f2d5aaad2907024932fde7fcc94f27f9c8a5cee011f058d80428b5559b5","target":"graph","created_at":"2026-05-18T04:21:51Z","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":"In this note, working in the context of simplicial sets, we give a detailed study of the complexity for computing chain level Steenrod squares, in terms of the number of face operators required. This analysis is based on the combinatorial formulation given in [R. Gonzalez-Diaz, P. Real. A Combinatorial Method for Computing Steenrod Squares. J. of Pure and Applied Algebra, 139 (1999) 89-108]. As an application, we give here an algorithm for computing cup-$i$ products over integers on a simplicial complex at chain level.","authors_text":"Pedro Real, Rocio Gonzalez-Diaz","cross_cats":["math.CO"],"headline":"","license":"","primary_cat":"math.AT","submitted_at":"2001-10-30T09:51:12Z","title":"Computing Cocycles on Simplicial Complexes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0110314","kind":"arxiv","version":1},"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:e82bc6b47c7db97219dcd9aee233053f514d74062ed060b66efbe551e1c71a43","target":"record","created_at":"2026-05-18T04:21:51Z","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":"915edb6835c8f7c2ebeb5c73b55364b2cb3c4cd55d931af2d297835c790af10c","cross_cats_sorted":["math.CO"],"license":"","primary_cat":"math.AT","submitted_at":"2001-10-30T09:51:12Z","title_canon_sha256":"34b35d858b7c8e91ff75e61b42c821d04f019f949ca3d9a9af8a3e8bb641fc2f"},"schema_version":"1.0","source":{"id":"math/0110314","kind":"arxiv","version":1}},"canonical_sha256":"c39e24d0774d64f68b422047d99ca239c877bd663da34cde7771023da236b28a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c39e24d0774d64f68b422047d99ca239c877bd663da34cde7771023da236b28a","first_computed_at":"2026-05-18T04:21:51.948230Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:21:51.948230Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BLQzJa/d0D0at1jVEZQJ5/a0HFCM8ddlfxREVoAgKYTO8peyYKhL10mskAP0eiJjymZXEinLImYbfjx+yDUfBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:21:51.948852Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0110314","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e82bc6b47c7db97219dcd9aee233053f514d74062ed060b66efbe551e1c71a43","sha256:1fcd3f2d5aaad2907024932fde7fcc94f27f9c8a5cee011f058d80428b5559b5"],"state_sha256":"e582f843f4c1a870b73202995c544d0b56ca306aa1738b75a6ae9a6c4ac48408"}