{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:BQFNTYR3HABVTVGBNNKYN2I6OL","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":"9041ddf7419a662bfea7c22ed855751beba239131bf0d7d011fe28b2e1d8caef","cross_cats_sorted":["math-ph","math.CO","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2017-08-11T12:45:35Z","title_canon_sha256":"f85153d746306b4a22643121c4675d67196a3ea0e5168a215c5ebd57b5bf0b35"},"schema_version":"1.0","source":{"id":"1708.03524","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.03524","created_at":"2026-07-05T00:57:47Z"},{"alias_kind":"arxiv_version","alias_value":"1708.03524v2","created_at":"2026-07-05T00:57:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.03524","created_at":"2026-07-05T00:57:47Z"},{"alias_kind":"pith_short_12","alias_value":"BQFNTYR3HABV","created_at":"2026-07-05T00:57:47Z"},{"alias_kind":"pith_short_16","alias_value":"BQFNTYR3HABVTVGB","created_at":"2026-07-05T00:57:47Z"},{"alias_kind":"pith_short_8","alias_value":"BQFNTYR3","created_at":"2026-07-05T00:57:47Z"}],"graph_snapshots":[{"event_id":"sha256:bb11af8c17691a905e123abc3d7f223000e71e3e9896f53d7f2376aaa3b0d043","target":"graph","created_at":"2026-07-05T00:57:47Z","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/1708.03524/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We show that the counting of observables and correlators for a 3-index tensor model are organized by the structure of a family of permutation centralizer algebras. These algebras are shown to be semi-simple and their Wedderburn-Artin decompositions into matrix blocks are given in terms of Clebsch-Gordan coefficients of symmetric groups. The matrix basis for the algebras also gives an orthogonal basis for the tensor observables which diagonalizes the Gaussian two-point functions. The centres of the algebras are associated with correlators which are expressible in terms of Kronecker coefficients","authors_text":"Joseph Ben Geloun, Sanjaye Ramgoolam","cross_cats":["math-ph","math.CO","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2017-08-11T12:45:35Z","title":"Tensor Models, Kronecker coefficients and Permutation Centralizer Algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.03524","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":"sha256:590c9e0faecbb91143c274ad7c77d285fe147efdd9920a8d6c4a7ae30cd49180","target":"record","created_at":"2026-07-05T00:57:47Z","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":"9041ddf7419a662bfea7c22ed855751beba239131bf0d7d011fe28b2e1d8caef","cross_cats_sorted":["math-ph","math.CO","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2017-08-11T12:45:35Z","title_canon_sha256":"f85153d746306b4a22643121c4675d67196a3ea0e5168a215c5ebd57b5bf0b35"},"schema_version":"1.0","source":{"id":"1708.03524","kind":"arxiv","version":2}},"canonical_sha256":"0c0ad9e23b380359d4c16b5586e91e72e86581acc3120d2bf29cc6fc0ab53d6c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0c0ad9e23b380359d4c16b5586e91e72e86581acc3120d2bf29cc6fc0ab53d6c","first_computed_at":"2026-07-05T00:57:47.895600Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:57:47.895600Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PT1VUos8lqlXRxIDs2fecSoSIw7KdgAGJiL3I0Y8N33h0KDn4olh4nR6SNWiro6nkwfkTjOzvHpm9YGLXdmbDA==","signature_status":"signed_v1","signed_at":"2026-07-05T00:57:47.896080Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.03524","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:590c9e0faecbb91143c274ad7c77d285fe147efdd9920a8d6c4a7ae30cd49180","sha256:bb11af8c17691a905e123abc3d7f223000e71e3e9896f53d7f2376aaa3b0d043"],"state_sha256":"57a81f12a63c6515fb15a069832b37d7e666b49ad5d1c38da764e7f8c5577ec1"}