{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:WSSBWSJPJNFXAZ53RLEN2ERWRN","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":"7341e06d8f32694f00dad2520a60107ef584591bd13c86ca1e009d31a1c6ec07","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.SC","submitted_at":"2025-05-09T09:02:34Z","title_canon_sha256":"567130cf7fa3d31f54499a0d020769e53adcc08a9b20d0dd7c320397ca16333e"},"schema_version":"1.0","source":{"id":"2505.05896","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.05896","created_at":"2026-07-05T11:00:49Z"},{"alias_kind":"arxiv_version","alias_value":"2505.05896v1","created_at":"2026-07-05T11:00:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.05896","created_at":"2026-07-05T11:00:49Z"},{"alias_kind":"pith_short_12","alias_value":"WSSBWSJPJNFX","created_at":"2026-07-05T11:00:49Z"},{"alias_kind":"pith_short_16","alias_value":"WSSBWSJPJNFXAZ53","created_at":"2026-07-05T11:00:49Z"},{"alias_kind":"pith_short_8","alias_value":"WSSBWSJP","created_at":"2026-07-05T11:00:49Z"}],"graph_snapshots":[{"event_id":"sha256:ffc6368bac5d78c2c0867af75565a92e1d12d0959301cf2d4881751c9a1d2d20","target":"graph","created_at":"2026-07-05T11:00:49Z","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/2505.05896/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Moosbauer and Poole have recently shown that the multiplication of two $5\\times 5$ matrices requires no more than 93 multiplications in the (possibly non-commutative) coefficient ring, and that the multiplication of two $6\\times 6$ matrices requires no more than 153 multiplications. Taking these multiplication schemes as starting points, we found improved matrix multiplication schemes for various rectangular matrix formats using a flip graph search.","authors_text":"Isaac Wood, Manuel Kauers","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.SC","submitted_at":"2025-05-09T09:02:34Z","title":"Consequences of the Moosbauer-Poole Algorithms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.05896","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":"sha256:4be7c86e1c288e58ef3d69eeac57c3f2edcff2c243a43af9a38e35c45a1dd7be","target":"record","created_at":"2026-07-05T11:00:49Z","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":"7341e06d8f32694f00dad2520a60107ef584591bd13c86ca1e009d31a1c6ec07","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.SC","submitted_at":"2025-05-09T09:02:34Z","title_canon_sha256":"567130cf7fa3d31f54499a0d020769e53adcc08a9b20d0dd7c320397ca16333e"},"schema_version":"1.0","source":{"id":"2505.05896","kind":"arxiv","version":1}},"canonical_sha256":"b4a41b492f4b4b7067bb8ac8dd12368b6448607ac0ef2298f39e4fc370e08f6e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b4a41b492f4b4b7067bb8ac8dd12368b6448607ac0ef2298f39e4fc370e08f6e","first_computed_at":"2026-07-05T11:00:49.472660Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:00:49.472660Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lN0mXI+Pa6gQJtYQE/SSBSRaBtTfd9b02ijiDy49fdtqjHT1FzDxJWPd4K7XkuwItSpwr9J4rTo5enarSAFfCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:00:49.473155Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.05896","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4be7c86e1c288e58ef3d69eeac57c3f2edcff2c243a43af9a38e35c45a1dd7be","sha256:ffc6368bac5d78c2c0867af75565a92e1d12d0959301cf2d4881751c9a1d2d20"],"state_sha256":"8b4e160f81f7cadcac2993cefeef0f8f31ef08c16af8b16989d42045fbfe7c04"}