{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:YKO656CS25K5ZE2OAZY6OURZWR","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":"d718a57f6eaeffb97c6890b6a277208324577f5004225a97e84a811a5962fdfc","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2020-03-09T13:52:29Z","title_canon_sha256":"45e79beb9bb0b23cc709e4c6c96c93cee7e089a9b23e71bcb9b533f0e7f7aaa6"},"schema_version":"1.0","source":{"id":"2003.04152","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2003.04152","created_at":"2026-07-05T01:15:24Z"},{"alias_kind":"arxiv_version","alias_value":"2003.04152v2","created_at":"2026-07-05T01:15:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2003.04152","created_at":"2026-07-05T01:15:24Z"},{"alias_kind":"pith_short_12","alias_value":"YKO656CS25K5","created_at":"2026-07-05T01:15:24Z"},{"alias_kind":"pith_short_16","alias_value":"YKO656CS25K5ZE2O","created_at":"2026-07-05T01:15:24Z"},{"alias_kind":"pith_short_8","alias_value":"YKO656CS","created_at":"2026-07-05T01:15:24Z"}],"graph_snapshots":[{"event_id":"sha256:17d4ef76e21f611f8f68221ddc15254cade25a88aeab8720fcd5889d17a550c0","target":"graph","created_at":"2026-07-05T01:15:24Z","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/2003.04152/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We investigate the existence and properties of a double asymptotic expansion in $1/N^{2}$ and $1/\\sqrt{D}$ in $\\mathrm{U}(N)\\times\\mathrm{O}(D)$ invariant Hermitian multi-matrix models, where the $N\\times N$ matrices transform in the vector representation of $\\mathrm{O}(D)$. The crucial point is to prove the existence of an upper bound $\\eta(h)$ on the maximum power $D^{1+\\eta(h)}$ of $D$ that can appear for the contribution at a given order $N^{2-2h}$ in the large $N$ expansion. We conjecture that $\\eta(h)=h$ in a large class of models. In the case of traceless Hermitian matrices with the qua","authors_text":"Adrian Tanasa, Frank Ferrari, Guillaume Valette, Sylvain Carrozza","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2020-03-09T13:52:29Z","title":"On the large $D$ expansion of Hermitian multi-matrix models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2003.04152","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":"sha256:68fc4b59444e1d7b93afb1804bfe9862287fdbc2d6eded084a8250089b7168d9","target":"record","created_at":"2026-07-05T01:15:24Z","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":"d718a57f6eaeffb97c6890b6a277208324577f5004225a97e84a811a5962fdfc","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2020-03-09T13:52:29Z","title_canon_sha256":"45e79beb9bb0b23cc709e4c6c96c93cee7e089a9b23e71bcb9b533f0e7f7aaa6"},"schema_version":"1.0","source":{"id":"2003.04152","kind":"arxiv","version":2}},"canonical_sha256":"c29deef852d755dc934e0671e75239b4425c998159c2c123a8961750d68e195a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c29deef852d755dc934e0671e75239b4425c998159c2c123a8961750d68e195a","first_computed_at":"2026-07-05T01:15:24.879973Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:15:24.879973Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"b/OK/U67biyHfXyIGLSlsbhQbjrho02yjZjECL+qSb0+kI3Ydv2M7dX6ZwQN+wuZPrXGu+85Ws8rkaNeYYL7DA==","signature_status":"signed_v1","signed_at":"2026-07-05T01:15:24.880374Z","signed_message":"canonical_sha256_bytes"},"source_id":"2003.04152","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:68fc4b59444e1d7b93afb1804bfe9862287fdbc2d6eded084a8250089b7168d9","sha256:17d4ef76e21f611f8f68221ddc15254cade25a88aeab8720fcd5889d17a550c0"],"state_sha256":"be63cb75b115f0995d307870b74176a0e8f9c060e7fc218c7e75ebe60f00ec38"}