{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:FSQAN5RHS352ZUH5BREXUOOKG6","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":"66715bef1ede714286b5c710e04701aa46f38507b9dad74aa898060649680bd2","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2017-05-24T13:18:14Z","title_canon_sha256":"dda6598ba605cb6d8bbd142afeb680f7e1bde6439500e347ee9c99d0b4586eb3"},"schema_version":"1.0","source":{"id":"1705.08743","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.08743","created_at":"2026-05-18T00:31:12Z"},{"alias_kind":"arxiv_version","alias_value":"1705.08743v2","created_at":"2026-05-18T00:31:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.08743","created_at":"2026-05-18T00:31:12Z"},{"alias_kind":"pith_short_12","alias_value":"FSQAN5RHS352","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_16","alias_value":"FSQAN5RHS352ZUH5","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_8","alias_value":"FSQAN5RH","created_at":"2026-05-18T12:31:15Z"}],"graph_snapshots":[{"event_id":"sha256:26d9e0aa726a0878bb4f8983b6c3921228a8ff0a07f302c854aef611e495905d","target":"graph","created_at":"2026-05-18T00:31:12Z","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":"We show that Boolean matrix multiplication, computed as a sum of products of column vectors with row vectors, is essentially the same as Warshall's algorithm for computing the transitive closure matrix of a graph from its adjacency matrix.\n  Warshall's algorithm can be generalized to Floyd's algorithm for computing the distance matrix of a graph with weighted edges. We will generalize Boolean matrices in the same way, keeping matrix multiplication essentially equivalent to the Floyd-Warshall algorithm. This way, we get matrices over a semiring, which are similar to the so-called \"funny matrice","authors_text":"Michiel de Bondt","cross_cats":["cs.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2017-05-24T13:18:14Z","title":"Fast algorithms for anti-distance matrices as a generalization of Boolean matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.08743","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":"sha256:574cc97b52d0b6bceb995503b39c721c3c1c67606779253002f4edb6479ac754","target":"record","created_at":"2026-05-18T00:31:12Z","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":"66715bef1ede714286b5c710e04701aa46f38507b9dad74aa898060649680bd2","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2017-05-24T13:18:14Z","title_canon_sha256":"dda6598ba605cb6d8bbd142afeb680f7e1bde6439500e347ee9c99d0b4586eb3"},"schema_version":"1.0","source":{"id":"1705.08743","kind":"arxiv","version":2}},"canonical_sha256":"2ca006f62796fbacd0fd0c497a39ca37931c7360dcf119b52d1d1510244d1532","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2ca006f62796fbacd0fd0c497a39ca37931c7360dcf119b52d1d1510244d1532","first_computed_at":"2026-05-18T00:31:12.700385Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:31:12.700385Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RvxSSJ8z3opTPIt3Ia++A/NyPbP9lrdSuOEaGztZLLCK0HWxjxr6GzMkFVQJksuTETwiOutaq6WJkDFQ+/H/Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:31:12.701021Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.08743","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:574cc97b52d0b6bceb995503b39c721c3c1c67606779253002f4edb6479ac754","sha256:26d9e0aa726a0878bb4f8983b6c3921228a8ff0a07f302c854aef611e495905d"],"state_sha256":"71288d866084bbde2639f512ed9c60167e5489d1523ef061acdd6f27d06d291b"}