{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:46S4YUKRBRRWENGWIIS6565LXZ","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":"145c09a41fa02a7f341462875fe257c95fee372345f88e4abcd5b367b7f8d364","cross_cats_sorted":["math.CO","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2016-05-03T11:28:54Z","title_canon_sha256":"a3f4ed2633b1b67a0fa70f7cdc65fd55c985d6f62dfafe38540a62a6de4d54b8"},"schema_version":"1.0","source":{"id":"1605.00843","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.00843","created_at":"2026-05-18T01:15:47Z"},{"alias_kind":"arxiv_version","alias_value":"1605.00843v1","created_at":"2026-05-18T01:15:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.00843","created_at":"2026-05-18T01:15:47Z"},{"alias_kind":"pith_short_12","alias_value":"46S4YUKRBRRW","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"46S4YUKRBRRWENGW","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"46S4YUKR","created_at":"2026-05-18T12:29:58Z"}],"graph_snapshots":[{"event_id":"sha256:54550bcb3fc0cdba9c453080dc32b3e556d4b780b8786094a5996c731620c963","target":"graph","created_at":"2026-05-18T01:15:47Z","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"},"paper":{"abstract_excerpt":"Group algebras of permutations have proved highly useful in solving a number of problems in large N gauge theories. I review the use of permutations in classifying gauge invariants in one-matrix and multi-matrix models and computing their correlators. These methods are also applicable to tensor models and have revealed a link between tensor models and the counting of branched covers. The key idea is to parametrize $U(N)$ gauge invariants using permutations, subject to equivalences. Correlators are related to group theoretic properties of these equivalence classes. Fourier transformation on sym","authors_text":"Sanjaye Ramgoolam","cross_cats":["math.CO","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2016-05-03T11:28:54Z","title":"Permutations and the combinatorics of gauge invariants for general N"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.00843","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":"sha256:3ac3269ac2559a7745831f5483a77d4677acdd40ff51e1df48580e1f4af4a553","target":"record","created_at":"2026-05-18T01:15:47Z","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":"145c09a41fa02a7f341462875fe257c95fee372345f88e4abcd5b367b7f8d364","cross_cats_sorted":["math.CO","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2016-05-03T11:28:54Z","title_canon_sha256":"a3f4ed2633b1b67a0fa70f7cdc65fd55c985d6f62dfafe38540a62a6de4d54b8"},"schema_version":"1.0","source":{"id":"1605.00843","kind":"arxiv","version":1}},"canonical_sha256":"e7a5cc51510c636234d64225eefbabbe493e869a87478a0aa45aaa3cef44e9e0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e7a5cc51510c636234d64225eefbabbe493e869a87478a0aa45aaa3cef44e9e0","first_computed_at":"2026-05-18T01:15:47.887498Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:15:47.887498Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/0ovdQ/HT00WOoLDx6NJ/IAoOpbDr1pzRtVVzwC267B9SGaMQewzIoHhGAjNQvLUFzZF27s2GPN2uzwnlNhpAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:15:47.888179Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.00843","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3ac3269ac2559a7745831f5483a77d4677acdd40ff51e1df48580e1f4af4a553","sha256:54550bcb3fc0cdba9c453080dc32b3e556d4b780b8786094a5996c731620c963"],"state_sha256":"334ce8a1bf06da691150e915f956512aeb70aaec8431e13521c8233fd06d8e22"}