{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:WH7RBUQWEU4SI7IXPOPAPSVTUA","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":"843de84235b6c3874f2ff396b36a218ac29bfa3ee919ef2b6ecd8dbbbb6b8908","cross_cats_sorted":["math-ph","math.CO","math.GR","math.MP","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2024-10-17T15:03:41Z","title_canon_sha256":"5767af32543d025c3ef1ac307ed6d87b16fe1ca5c405ba9105ba30b67a364961"},"schema_version":"1.0","source":{"id":"2410.13631","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.13631","created_at":"2026-07-05T10:15:20Z"},{"alias_kind":"arxiv_version","alias_value":"2410.13631v2","created_at":"2026-07-05T10:15:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.13631","created_at":"2026-07-05T10:15:20Z"},{"alias_kind":"pith_short_12","alias_value":"WH7RBUQWEU4S","created_at":"2026-07-05T10:15:20Z"},{"alias_kind":"pith_short_16","alias_value":"WH7RBUQWEU4SI7IX","created_at":"2026-07-05T10:15:20Z"},{"alias_kind":"pith_short_8","alias_value":"WH7RBUQW","created_at":"2026-07-05T10:15:20Z"}],"graph_snapshots":[{"event_id":"sha256:4fef14badb85e74227d9669ff159d67e0aadec7b884e275162d1744b008b846b","target":"graph","created_at":"2026-07-05T10:15:20Z","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/2410.13631/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Multi-matrix invariants, and in particular the scalar multi-trace operators of $\\mathcal{N}=4$ SYM with $U(N)$ gauge symmetry, can be described using permutation centraliser algebras (PCA), which are generalisations of the symmetric group algebras and independent of $N$. Free-field two-point functions define an $N$-dependent inner product on the PCA, and bases of operators have been constructed which are orthogonal at finite $N$. Two such bases are well-known, the restricted Schur and covariant bases, and both definitions involve representation-theoretic quantities such as Young diagram labels","authors_text":"Adrian Padellaro, Ryo Suzuki, Sanjaye Ramgoolam","cross_cats":["math-ph","math.CO","math.GR","math.MP","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2024-10-17T15:03:41Z","title":"Eigenvalue systems for integer orthogonal bases of multi-matrix invariants at finite N"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.13631","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":"sha256:1d3ec19ec400bbe5299121b2c6ebde6c80d85d7af62adb8ce94a3f7722cb11fc","target":"record","created_at":"2026-07-05T10:15:20Z","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":"843de84235b6c3874f2ff396b36a218ac29bfa3ee919ef2b6ecd8dbbbb6b8908","cross_cats_sorted":["math-ph","math.CO","math.GR","math.MP","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2024-10-17T15:03:41Z","title_canon_sha256":"5767af32543d025c3ef1ac307ed6d87b16fe1ca5c405ba9105ba30b67a364961"},"schema_version":"1.0","source":{"id":"2410.13631","kind":"arxiv","version":2}},"canonical_sha256":"b1ff10d2162539247d177b9e07cab3a0046f904db022e244f997e21c51fb5055","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b1ff10d2162539247d177b9e07cab3a0046f904db022e244f997e21c51fb5055","first_computed_at":"2026-07-05T10:15:20.703564Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:15:20.703564Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"t61Bb+D6kmUXHWlMFvReHDzOL7o69ylMU75mJ/tWWEQ7MoBcCKmUl815tuW+wXT2L4q9XGoEY1k50CoN9VjbAw==","signature_status":"signed_v1","signed_at":"2026-07-05T10:15:20.704048Z","signed_message":"canonical_sha256_bytes"},"source_id":"2410.13631","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1d3ec19ec400bbe5299121b2c6ebde6c80d85d7af62adb8ce94a3f7722cb11fc","sha256:4fef14badb85e74227d9669ff159d67e0aadec7b884e275162d1744b008b846b"],"state_sha256":"0a354c74f4e6e42f06a9a0cea6600fa3648d3528ce7be916e0a5b51b4f30bd5d"}