{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:O6SW4PHF3HJDOO4MKODH4BQXUW","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":"6c46f32f0301362b97fa22ffcd937d61d6526babaf4bb986163313d4009fcb34","cross_cats_sorted":[],"license":"","primary_cat":"quant-ph","submitted_at":"2004-09-06T13:37:37Z","title_canon_sha256":"78f254c4f8615112da1a849a9d36dbacda9acfe49bf77005d58cc7e01d083c77"},"schema_version":"1.0","source":{"id":"quant-ph/0409035","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"quant-ph/0409035","created_at":"2026-07-04T14:46:40Z"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/0409035v2","created_at":"2026-07-04T14:46:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/0409035","created_at":"2026-07-04T14:46:40Z"},{"alias_kind":"pith_short_12","alias_value":"O6SW4PHF3HJD","created_at":"2026-07-04T14:46:40Z"},{"alias_kind":"pith_short_16","alias_value":"O6SW4PHF3HJDOO4M","created_at":"2026-07-04T14:46:40Z"},{"alias_kind":"pith_short_8","alias_value":"O6SW4PHF","created_at":"2026-07-04T14:46:40Z"}],"graph_snapshots":[{"event_id":"sha256:31711a879cb246fd59b9ff5ed4564f39b20866dfbf05e1412b7142b1f674d293","target":"graph","created_at":"2026-07-04T14:46:40Z","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/quant-ph/0409035/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We present a quantum algorithm that verifies a product of two n*n matrices over any field with bounded error in worst-case time n^{5/3} and expected time n^{5/3} / min(w,sqrt(n))^{1/3}, where w is the number of wrong entries. This improves the previous best algorithm that runs in time n^{7/4}. We also present a quantum matrix multiplication algorithm that is efficient when the result has few nonzero entries.","authors_text":"Harry Buhrman, Robert Spalek (CWI, U of Amsterdam)","cross_cats":[],"headline":"","license":"","primary_cat":"quant-ph","submitted_at":"2004-09-06T13:37:37Z","title":"Quantum Verification of Matrix Products"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/0409035","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":"sha256:3b9d49b5b73f7c2e6f65437a251ea92d338ceb96c48debc5203aeb20429977d9","target":"record","created_at":"2026-07-04T14:46:40Z","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":"6c46f32f0301362b97fa22ffcd937d61d6526babaf4bb986163313d4009fcb34","cross_cats_sorted":[],"license":"","primary_cat":"quant-ph","submitted_at":"2004-09-06T13:37:37Z","title_canon_sha256":"78f254c4f8615112da1a849a9d36dbacda9acfe49bf77005d58cc7e01d083c77"},"schema_version":"1.0","source":{"id":"quant-ph/0409035","kind":"arxiv","version":2}},"canonical_sha256":"77a56e3ce5d9d2373b8c53867e0617a5a8d3a179335d8abd122dbf846a34e7a1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"77a56e3ce5d9d2373b8c53867e0617a5a8d3a179335d8abd122dbf846a34e7a1","first_computed_at":"2026-07-04T14:46:40.707872Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:46:40.707872Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UIuImC6D6nv7e3k6yJ4LsBUruUH1OSej3lAS6mOGZGmOyYQZfuAIalkOkZTz/hfeHqEc3SJOCkdGHbeYax9CCA==","signature_status":"signed_v1","signed_at":"2026-07-04T14:46:40.708247Z","signed_message":"canonical_sha256_bytes"},"source_id":"quant-ph/0409035","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3b9d49b5b73f7c2e6f65437a251ea92d338ceb96c48debc5203aeb20429977d9","sha256:31711a879cb246fd59b9ff5ed4564f39b20866dfbf05e1412b7142b1f674d293"],"state_sha256":"d46d71636144834b4541ab47bab1cc5b577ad2903f4c3584ed745cdeb1fcd8b1"}