{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:CU5RZYJN5ZQR65OSDM3OV3T5OM","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":"2bc01f0622c1343f3c04143bddccd622219b42666c16574d57022404ebd8807f","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2014-11-20T01:07:08Z","title_canon_sha256":"84c4cdf19950ab2eb261f50d5bf7c8df3774392bc2e7651c93f364c7fa9da8cc"},"schema_version":"1.0","source":{"id":"1411.5414","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.5414","created_at":"2026-07-05T03:19:36Z"},{"alias_kind":"arxiv_version","alias_value":"1411.5414v1","created_at":"2026-07-05T03:19:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.5414","created_at":"2026-07-05T03:19:36Z"},{"alias_kind":"pith_short_12","alias_value":"CU5RZYJN5ZQR","created_at":"2026-07-05T03:19:36Z"},{"alias_kind":"pith_short_16","alias_value":"CU5RZYJN5ZQR65OS","created_at":"2026-07-05T03:19:36Z"},{"alias_kind":"pith_short_8","alias_value":"CU5RZYJN","created_at":"2026-07-05T03:19:36Z"}],"graph_snapshots":[{"event_id":"sha256:29dd4799d9b5bc7fc645144fad55c2bd32b6790adf7d3ed800af84256a2b948a","target":"graph","created_at":"2026-07-05T03:19:36Z","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/1411.5414/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Until a few years ago, the fastest known matrix multiplication algorithm, due to Coppersmith and Winograd (1990), ran in time $O(n^{2.3755})$. Recently, a surge of activity by Stothers, Vassilevska-Williams, and Le Gall has led to an improved algorithm running in time $O(n^{2.3729})$. These algorithms are obtained by analyzing higher and higher tensor powers of a certain identity of Coppersmith and Winograd. We show that this exact approach cannot result in an algorithm with running time $O(n^{2.3725})$, and identify a wide class of variants of this approach which cannot result in an algorithm","authors_text":"Andris Ambainis, Fran\\c{c}ois Le Gall, Yuval Filmus","cross_cats":["cs.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2014-11-20T01:07:08Z","title":"Fast Matrix Multiplication: Limitations of the Laser Method"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.5414","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":"sha256:8d9b058f26900b5d243ed11d86039ec14e8163fe7e39b2d2953908db6d153b7a","target":"record","created_at":"2026-07-05T03:19:36Z","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":"2bc01f0622c1343f3c04143bddccd622219b42666c16574d57022404ebd8807f","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2014-11-20T01:07:08Z","title_canon_sha256":"84c4cdf19950ab2eb261f50d5bf7c8df3774392bc2e7651c93f364c7fa9da8cc"},"schema_version":"1.0","source":{"id":"1411.5414","kind":"arxiv","version":1}},"canonical_sha256":"153b1ce12dee611f75d21b36eaee7d73270718154acf398fe751ff215f0df354","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"153b1ce12dee611f75d21b36eaee7d73270718154acf398fe751ff215f0df354","first_computed_at":"2026-07-05T03:19:36.785224Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:19:36.785224Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9Q5h9w24eam6QDakq0jCZFQAV8x8DBOmvFzwVCG7PdwHexQGKAOqdYHhJQgxEkXl+R/8Jxw6/xV/w/TVmbq0Cg==","signature_status":"signed_v1","signed_at":"2026-07-05T03:19:36.785716Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.5414","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8d9b058f26900b5d243ed11d86039ec14e8163fe7e39b2d2953908db6d153b7a","sha256:29dd4799d9b5bc7fc645144fad55c2bd32b6790adf7d3ed800af84256a2b948a"],"state_sha256":"0786d9509e73d97ad1d14dbc5729a7956b908ad781811bfab76f90990dda80a6"}