{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:OVC4L6IZEBPQQYQSVA4BEONDF2","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":"a53ba99de7ae6c65776ebbf60051943466b061669170cf912c8ffd32656d7090","cross_cats_sorted":["cs.CC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-10-02T08:27:06Z","title_canon_sha256":"c978fb14f5eaef2ff7339b81c56a96834693e305dbabff26122fb1b568332927"},"schema_version":"1.0","source":{"id":"1710.00528","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.00528","created_at":"2026-05-18T00:19:03Z"},{"alias_kind":"arxiv_version","alias_value":"1710.00528v3","created_at":"2026-05-18T00:19:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.00528","created_at":"2026-05-18T00:19:03Z"},{"alias_kind":"pith_short_12","alias_value":"OVC4L6IZEBPQ","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_16","alias_value":"OVC4L6IZEBPQQYQS","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_8","alias_value":"OVC4L6IZ","created_at":"2026-05-18T12:31:34Z"}],"graph_snapshots":[{"event_id":"sha256:bd2e7ae4c5b6f43e50e7d570fe699d51ca988bd745f0115905b72726358e6448","target":"graph","created_at":"2026-05-18T00:19:03Z","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":"Motivated by the symmetric version of matrix multiplication we study the plethysm $S^k(\\mathfrak{sl}_n)$ of the adjoint representation $\\mathfrak{sl}_n$ of the Lie group $SL_n$. In particular, we describe the decomposition of this representation into irreducible components for $k=3$, and find highest weight vectors for all irreducible components. Relations to fast matrix multiplication, in particular the Coppersmith-Winograd tensor are presented.","authors_text":"Tim Seynnaeve","cross_cats":["cs.CC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-10-02T08:27:06Z","title":"Plethysm and fast matrix multiplication"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.00528","kind":"arxiv","version":3},"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:dcff63a15bebf7be3a14431ef454a6d46448b8a62e8b5447c819e49e6e5b0397","target":"record","created_at":"2026-05-18T00:19:03Z","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":"a53ba99de7ae6c65776ebbf60051943466b061669170cf912c8ffd32656d7090","cross_cats_sorted":["cs.CC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-10-02T08:27:06Z","title_canon_sha256":"c978fb14f5eaef2ff7339b81c56a96834693e305dbabff26122fb1b568332927"},"schema_version":"1.0","source":{"id":"1710.00528","kind":"arxiv","version":3}},"canonical_sha256":"7545c5f919205f086212a8381239a32ea9daedcf0918b697a1c8f22ede08fd65","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7545c5f919205f086212a8381239a32ea9daedcf0918b697a1c8f22ede08fd65","first_computed_at":"2026-05-18T00:19:03.459234Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:19:03.459234Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ntTT1aMj/LSfYr2v+g6BQtJth7JsjQV1cgl8s9mg+2u61185ucv1DM8ao46IKq5Rd2uyX9KPbtZkqvZmfgt3Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:19:03.460022Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.00528","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dcff63a15bebf7be3a14431ef454a6d46448b8a62e8b5447c819e49e6e5b0397","sha256:bd2e7ae4c5b6f43e50e7d570fe699d51ca988bd745f0115905b72726358e6448"],"state_sha256":"649bfd1be5acae1e1358a40f01bb1f2daec2cdef6aedde2482a08eee66ea35d0"}