{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:DE2WVYZSZ67GJXGO4B5ONS6UOV","short_pith_number":"pith:DE2WVYZS","canonical_record":{"source":{"id":"2209.02026","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2022-09-05T15:57:31Z","cross_cats_sorted":["math-ph","math.CO","math.MP"],"title_canon_sha256":"65adb30477de5bf85ea80911391cfe7b55e8a6bbe3f7d60cc38f7096426324ac","abstract_canon_sha256":"a9c0ad41b6f528453880be6ac30c47f77ca17850c93431c6577cb6caa17551ed"},"schema_version":"1.0"},"canonical_sha256":"19356ae332cfbe64dccee07ae6cbd4754d2c68fb598cd91981329cdfb60d52e6","source":{"kind":"arxiv","id":"2209.02026","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2209.02026","created_at":"2026-07-05T05:46:22Z"},{"alias_kind":"arxiv_version","alias_value":"2209.02026v1","created_at":"2026-07-05T05:46:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2209.02026","created_at":"2026-07-05T05:46:22Z"},{"alias_kind":"pith_short_12","alias_value":"DE2WVYZSZ67G","created_at":"2026-07-05T05:46:22Z"},{"alias_kind":"pith_short_16","alias_value":"DE2WVYZSZ67GJXGO","created_at":"2026-07-05T05:46:22Z"},{"alias_kind":"pith_short_8","alias_value":"DE2WVYZS","created_at":"2026-07-05T05:46:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:DE2WVYZSZ67GJXGO4B5ONS6UOV","target":"record","payload":{"canonical_record":{"source":{"id":"2209.02026","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2022-09-05T15:57:31Z","cross_cats_sorted":["math-ph","math.CO","math.MP"],"title_canon_sha256":"65adb30477de5bf85ea80911391cfe7b55e8a6bbe3f7d60cc38f7096426324ac","abstract_canon_sha256":"a9c0ad41b6f528453880be6ac30c47f77ca17850c93431c6577cb6caa17551ed"},"schema_version":"1.0"},"canonical_sha256":"19356ae332cfbe64dccee07ae6cbd4754d2c68fb598cd91981329cdfb60d52e6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:46:22.134406Z","signature_b64":"VDIZc+pO5YxhPchEXGg5YuNnsBTcq6ZQqo+W6yVLu5w1ISWmWiXLKUEBU48vroenS/8BR61vdraSYgmI6lwEBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"19356ae332cfbe64dccee07ae6cbd4754d2c68fb598cd91981329cdfb60d52e6","last_reissued_at":"2026-07-05T05:46:22.134020Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:46:22.134020Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2209.02026","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T05:46:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pjzvB8dLxRCRdYgg0EeBhVYHdc4ChyhP4AhD6Muaqv/PLXleoyAeTqSAlRqnyRTeyTJE2NW9c3/YY399IwxXBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T11:57:58.667112Z"},"content_sha256":"78bef52ed023f9aec69afa068cde691f4661539f0fdf82975977baa435d57c38","schema_version":"1.0","event_id":"sha256:78bef52ed023f9aec69afa068cde691f4661539f0fdf82975977baa435d57c38"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:DE2WVYZSZ67GJXGO4B5ONS6UOV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Double scaling limit of multi-matrix models at large $D$","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.CO","math.MP"],"primary_cat":"hep-th","authors_text":"Adrian Tanasa, Valentin Bonzom, Victor Nador","submitted_at":"2022-09-05T15:57:31Z","abstract_excerpt":"In this paper, we study a double scaling limit of two multi-matrix models: the $U(N)^2 \\times O(D)$-invariant model with all quartic interactions and the bipartite $U(N) \\times O(D)$-invariant model with tetrahedral interaction ($D$ being here the number of matrices and $N$ being the size of each matrix). Those models admit a double, large $N$ and large $D$ expansion. While $N$ tracks the genus of the Feynman graphs, $D$ tracks another quantity called the grade. In both models, we rewrite the sum over Feynman graphs at fixed genus and grade as a finite sum over combinatorial objects called sch"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2209.02026","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2209.02026/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T05:46:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UIKkYWWT2zmDY6cPS1xexCkfDFu88E7FdDU5dwNXFhgK1dRW2HjCjZ83ByTvz/DJZ1Y0PTeI+Z+es6SAY5WnDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T11:57:58.667637Z"},"content_sha256":"f598b415b606a31d43098ebb8aacf580a5499ac46d52898853c559e143ce4744","schema_version":"1.0","event_id":"sha256:f598b415b606a31d43098ebb8aacf580a5499ac46d52898853c559e143ce4744"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DE2WVYZSZ67GJXGO4B5ONS6UOV/bundle.json","state_url":"https://pith.science/pith/DE2WVYZSZ67GJXGO4B5ONS6UOV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DE2WVYZSZ67GJXGO4B5ONS6UOV/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-15T11:57:58Z","links":{"resolver":"https://pith.science/pith/DE2WVYZSZ67GJXGO4B5ONS6UOV","bundle":"https://pith.science/pith/DE2WVYZSZ67GJXGO4B5ONS6UOV/bundle.json","state":"https://pith.science/pith/DE2WVYZSZ67GJXGO4B5ONS6UOV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DE2WVYZSZ67GJXGO4B5ONS6UOV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:DE2WVYZSZ67GJXGO4B5ONS6UOV","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":"a9c0ad41b6f528453880be6ac30c47f77ca17850c93431c6577cb6caa17551ed","cross_cats_sorted":["math-ph","math.CO","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2022-09-05T15:57:31Z","title_canon_sha256":"65adb30477de5bf85ea80911391cfe7b55e8a6bbe3f7d60cc38f7096426324ac"},"schema_version":"1.0","source":{"id":"2209.02026","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2209.02026","created_at":"2026-07-05T05:46:22Z"},{"alias_kind":"arxiv_version","alias_value":"2209.02026v1","created_at":"2026-07-05T05:46:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2209.02026","created_at":"2026-07-05T05:46:22Z"},{"alias_kind":"pith_short_12","alias_value":"DE2WVYZSZ67G","created_at":"2026-07-05T05:46:22Z"},{"alias_kind":"pith_short_16","alias_value":"DE2WVYZSZ67GJXGO","created_at":"2026-07-05T05:46:22Z"},{"alias_kind":"pith_short_8","alias_value":"DE2WVYZS","created_at":"2026-07-05T05:46:22Z"}],"graph_snapshots":[{"event_id":"sha256:f598b415b606a31d43098ebb8aacf580a5499ac46d52898853c559e143ce4744","target":"graph","created_at":"2026-07-05T05:46:22Z","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/2209.02026/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we study a double scaling limit of two multi-matrix models: the $U(N)^2 \\times O(D)$-invariant model with all quartic interactions and the bipartite $U(N) \\times O(D)$-invariant model with tetrahedral interaction ($D$ being here the number of matrices and $N$ being the size of each matrix). Those models admit a double, large $N$ and large $D$ expansion. While $N$ tracks the genus of the Feynman graphs, $D$ tracks another quantity called the grade. In both models, we rewrite the sum over Feynman graphs at fixed genus and grade as a finite sum over combinatorial objects called sch","authors_text":"Adrian Tanasa, Valentin Bonzom, Victor Nador","cross_cats":["math-ph","math.CO","math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2022-09-05T15:57:31Z","title":"Double scaling limit of multi-matrix models at large $D$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2209.02026","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":"sha256:78bef52ed023f9aec69afa068cde691f4661539f0fdf82975977baa435d57c38","target":"record","created_at":"2026-07-05T05:46:22Z","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":"a9c0ad41b6f528453880be6ac30c47f77ca17850c93431c6577cb6caa17551ed","cross_cats_sorted":["math-ph","math.CO","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2022-09-05T15:57:31Z","title_canon_sha256":"65adb30477de5bf85ea80911391cfe7b55e8a6bbe3f7d60cc38f7096426324ac"},"schema_version":"1.0","source":{"id":"2209.02026","kind":"arxiv","version":1}},"canonical_sha256":"19356ae332cfbe64dccee07ae6cbd4754d2c68fb598cd91981329cdfb60d52e6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"19356ae332cfbe64dccee07ae6cbd4754d2c68fb598cd91981329cdfb60d52e6","first_computed_at":"2026-07-05T05:46:22.134020Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:46:22.134020Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VDIZc+pO5YxhPchEXGg5YuNnsBTcq6ZQqo+W6yVLu5w1ISWmWiXLKUEBU48vroenS/8BR61vdraSYgmI6lwEBg==","signature_status":"signed_v1","signed_at":"2026-07-05T05:46:22.134406Z","signed_message":"canonical_sha256_bytes"},"source_id":"2209.02026","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:78bef52ed023f9aec69afa068cde691f4661539f0fdf82975977baa435d57c38","sha256:f598b415b606a31d43098ebb8aacf580a5499ac46d52898853c559e143ce4744"],"state_sha256":"fd103802c6c6dfdf0e7143352ba15dc79521107d3fce79bf14be863e8c95f5f4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J+CFQrkM+LzjR5aT+jT9y1FpdDx0f3b5BFSwJIPsLRLuolTvQ4GFEJ8pMETVBO8wvR4Mvq3JWPoETUWwwDw2Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-15T11:57:58.671470Z","bundle_sha256":"932cc9bf5960ece361a712aefada99ce3d807f94f355113707ed8b99124dd731"}}