{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:44UHDV4ACSRGHKVDFK2N6QJFKV","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":"ad270d223d24c6ab1104fba428a2081d1433b61cc61710333acc75af4a990bef","cross_cats_sorted":["cs.DS","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-12-06T17:38:48Z","title_canon_sha256":"eb5422ceeb503176892d8fd1bbf635c23da87fe0ca64038885979856f1894d82"},"schema_version":"1.0","source":{"id":"1712.02302","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.02302","created_at":"2026-05-18T00:28:38Z"},{"alias_kind":"arxiv_version","alias_value":"1712.02302v1","created_at":"2026-05-18T00:28:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.02302","created_at":"2026-05-18T00:28:38Z"},{"alias_kind":"pith_short_12","alias_value":"44UHDV4ACSRG","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"44UHDV4ACSRGHKVD","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"44UHDV4A","created_at":"2026-05-18T12:30:58Z"}],"graph_snapshots":[{"event_id":"sha256:8bb40b74fa67eea60a25f52993ac120d7bd77c2f4478d1ecde1ac8d85083f7f4","target":"graph","created_at":"2026-05-18T00:28:38Z","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":"The Cohn-Umans group-theoretic approach to matrix multiplication suggests embedding matrix multiplication into group algebra multiplication, and bounding $\\omega$ in terms of the representation theory of the host group. This framework is general enough to capture the best known upper bounds on $\\omega$ and is conjectured to be powerful enough to prove $\\omega = 2$, although finding a suitable group and constructing such an embedding has remained elusive. Recently it was shown, by a generalization of the proof of the Cap Set Conjecture, that abelian groups of bounded exponent cannot prove $\\ome","authors_text":"Chris Umans, Henry Cohn, Jonah Blasiak, Joshua A. Grochow, Thomas Church","cross_cats":["cs.DS","math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-12-06T17:38:48Z","title":"Which groups are amenable to proving exponent two for matrix multiplication?"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.02302","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:df5f065b72745c64a764a442621c40a1ef3891626639e7e493d7a15f4a92ba37","target":"record","created_at":"2026-05-18T00:28:38Z","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":"ad270d223d24c6ab1104fba428a2081d1433b61cc61710333acc75af4a990bef","cross_cats_sorted":["cs.DS","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-12-06T17:38:48Z","title_canon_sha256":"eb5422ceeb503176892d8fd1bbf635c23da87fe0ca64038885979856f1894d82"},"schema_version":"1.0","source":{"id":"1712.02302","kind":"arxiv","version":1}},"canonical_sha256":"e72871d78014a263aaa32ab4df41255558ab996671cc4ec908f7bc8e2d0b12e5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e72871d78014a263aaa32ab4df41255558ab996671cc4ec908f7bc8e2d0b12e5","first_computed_at":"2026-05-18T00:28:38.545517Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:28:38.545517Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"x+IePTZOSWSlMbvK7Jdd7BxR5jgWJTPOQ4C2QjlF41OZ4OEK9xAmIh1WVtjwwA9/A3maE/6LzT1xA/8WPgWCAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:28:38.546207Z","signed_message":"canonical_sha256_bytes"},"source_id":"1712.02302","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:df5f065b72745c64a764a442621c40a1ef3891626639e7e493d7a15f4a92ba37","sha256:8bb40b74fa67eea60a25f52993ac120d7bd77c2f4478d1ecde1ac8d85083f7f4"],"state_sha256":"dac4e97ff601479e2102f5bb97761c851efa64274767782a915e2fadfe9ed383"}