{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1994:GTW5XPPR62KICTOMTFOSCJCZES","short_pith_number":"pith:GTW5XPPR","canonical_record":{"source":{"id":"hep-th/9404005","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"1994-04-01T23:08:30Z","cross_cats_sorted":[],"title_canon_sha256":"3cdccec69e6654f022e9d4cf084531f350a9c87cbfc4be3f70b928dddefd44a9","abstract_canon_sha256":"1d753d8a4682215e85dad2619489b693aeb9a4a2669068561ab6ef52e56fb433"},"schema_version":"1.0"},"canonical_sha256":"34eddbbdf1f694814dcc995d21245924b6b5fb0e78edd0fa708c9b54d0f81688","source":{"kind":"arxiv","id":"hep-th/9404005","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/9404005","created_at":"2026-07-04T15:57:43Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/9404005v2","created_at":"2026-07-04T15:57:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/9404005","created_at":"2026-07-04T15:57:43Z"},{"alias_kind":"pith_short_12","alias_value":"GTW5XPPR62KI","created_at":"2026-07-04T15:57:43Z"},{"alias_kind":"pith_short_16","alias_value":"GTW5XPPR62KICTOM","created_at":"2026-07-04T15:57:43Z"},{"alias_kind":"pith_short_8","alias_value":"GTW5XPPR","created_at":"2026-07-04T15:57:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1994:GTW5XPPR62KICTOMTFOSCJCZES","target":"record","payload":{"canonical_record":{"source":{"id":"hep-th/9404005","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"1994-04-01T23:08:30Z","cross_cats_sorted":[],"title_canon_sha256":"3cdccec69e6654f022e9d4cf084531f350a9c87cbfc4be3f70b928dddefd44a9","abstract_canon_sha256":"1d753d8a4682215e85dad2619489b693aeb9a4a2669068561ab6ef52e56fb433"},"schema_version":"1.0"},"canonical_sha256":"34eddbbdf1f694814dcc995d21245924b6b5fb0e78edd0fa708c9b54d0f81688","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:57:43.449482Z","signature_b64":"QtX6Mtb4OWYgTFgNg8NkaEmuELkKHHlafSqWLti6tcrw4x1xwrdSWsP6k9w1DXi/yLoMyfnIwMbGOIloWt7xAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"34eddbbdf1f694814dcc995d21245924b6b5fb0e78edd0fa708c9b54d0f81688","last_reissued_at":"2026-07-04T15:57:43.449138Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:57:43.449138Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"hep-th/9404005","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T15:57:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hh2MvJYyTZdmyUKqrA0C3RDtTmWK8Ce5wU5hLFVVEJ9r5rgRqnErRjlONU/pTxa40eYSONlrsWrlLn/lFwxKBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T00:40:38.425803Z"},"content_sha256":"4361fa8361f43a1ef4627c0bdb524a7ec4dc91d00eabc509fcd124151c70401c","schema_version":"1.0","event_id":"sha256:4361fa8361f43a1ef4627c0bdb524a7ec4dc91d00eabc509fcd124151c70401c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1994:GTW5XPPR62KICTOMTFOSCJCZES","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Unitary matrix integrals in the framework of Generalized Kontsevich Model. I. Brezin-Gross-Witten Model","license":"","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"A.Mironov, A.Morozov, G.Semenoff","submitted_at":"1994-04-01T23:08:30Z","abstract_excerpt":"We advocate a new approach to the study of unitary matrix models in external fields which emphasizes their relationship to Generalized Kontsevich Models (GKM) with non-polynomial potentials. For example, we show that the partition function of the Brezin-Gross-Witten Model (BGWM), which is defined as an integral over unitary $N\\times N$ matrices, $\\int [dU] e^{\\rm{Tr}(J^\\dagger U + JU^\\dagger)}$, can also be considered as a GKM with potential ${\\cal V}(X) = \\frac{1}{X}$. Moreover, it can be interpreted as the generating functional for correlators in the Penner model. The strong and weak couplin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/9404005","kind":"arxiv","version":2},"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/hep-th/9404005/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":"2026-07-04T15:57:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"A3ZzVl9o248X5N9TW2Zu9td262Mc4Ma+y9fHEwGcpEO+jmoK3vn0/zA1Z5kmmBXHqSdAnLaHMyyTegWBw+99Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T00:40:38.426305Z"},"content_sha256":"073c6ef7997f16bb18f3c9c4feaf1ad610b5138b9ba74cfd69e2a5d46a618f69","schema_version":"1.0","event_id":"sha256:073c6ef7997f16bb18f3c9c4feaf1ad610b5138b9ba74cfd69e2a5d46a618f69"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GTW5XPPR62KICTOMTFOSCJCZES/bundle.json","state_url":"https://pith.science/pith/GTW5XPPR62KICTOMTFOSCJCZES/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GTW5XPPR62KICTOMTFOSCJCZES/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":"2026-08-10T00:40:38Z","links":{"resolver":"https://pith.science/pith/GTW5XPPR62KICTOMTFOSCJCZES","bundle":"https://pith.science/pith/GTW5XPPR62KICTOMTFOSCJCZES/bundle.json","state":"https://pith.science/pith/GTW5XPPR62KICTOMTFOSCJCZES/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GTW5XPPR62KICTOMTFOSCJCZES/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1994:GTW5XPPR62KICTOMTFOSCJCZES","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":"1d753d8a4682215e85dad2619489b693aeb9a4a2669068561ab6ef52e56fb433","cross_cats_sorted":[],"license":"","primary_cat":"hep-th","submitted_at":"1994-04-01T23:08:30Z","title_canon_sha256":"3cdccec69e6654f022e9d4cf084531f350a9c87cbfc4be3f70b928dddefd44a9"},"schema_version":"1.0","source":{"id":"hep-th/9404005","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/9404005","created_at":"2026-07-04T15:57:43Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/9404005v2","created_at":"2026-07-04T15:57:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/9404005","created_at":"2026-07-04T15:57:43Z"},{"alias_kind":"pith_short_12","alias_value":"GTW5XPPR62KI","created_at":"2026-07-04T15:57:43Z"},{"alias_kind":"pith_short_16","alias_value":"GTW5XPPR62KICTOM","created_at":"2026-07-04T15:57:43Z"},{"alias_kind":"pith_short_8","alias_value":"GTW5XPPR","created_at":"2026-07-04T15:57:43Z"}],"graph_snapshots":[{"event_id":"sha256:073c6ef7997f16bb18f3c9c4feaf1ad610b5138b9ba74cfd69e2a5d46a618f69","target":"graph","created_at":"2026-07-04T15:57:43Z","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/hep-th/9404005/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We advocate a new approach to the study of unitary matrix models in external fields which emphasizes their relationship to Generalized Kontsevich Models (GKM) with non-polynomial potentials. For example, we show that the partition function of the Brezin-Gross-Witten Model (BGWM), which is defined as an integral over unitary $N\\times N$ matrices, $\\int [dU] e^{\\rm{Tr}(J^\\dagger U + JU^\\dagger)}$, can also be considered as a GKM with potential ${\\cal V}(X) = \\frac{1}{X}$. Moreover, it can be interpreted as the generating functional for correlators in the Penner model. The strong and weak couplin","authors_text":"A.Mironov, A.Morozov, G.Semenoff","cross_cats":[],"headline":"","license":"","primary_cat":"hep-th","submitted_at":"1994-04-01T23:08:30Z","title":"Unitary matrix integrals in the framework of Generalized Kontsevich Model. I. Brezin-Gross-Witten Model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/9404005","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":"sha256:4361fa8361f43a1ef4627c0bdb524a7ec4dc91d00eabc509fcd124151c70401c","target":"record","created_at":"2026-07-04T15:57:43Z","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":"1d753d8a4682215e85dad2619489b693aeb9a4a2669068561ab6ef52e56fb433","cross_cats_sorted":[],"license":"","primary_cat":"hep-th","submitted_at":"1994-04-01T23:08:30Z","title_canon_sha256":"3cdccec69e6654f022e9d4cf084531f350a9c87cbfc4be3f70b928dddefd44a9"},"schema_version":"1.0","source":{"id":"hep-th/9404005","kind":"arxiv","version":2}},"canonical_sha256":"34eddbbdf1f694814dcc995d21245924b6b5fb0e78edd0fa708c9b54d0f81688","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"34eddbbdf1f694814dcc995d21245924b6b5fb0e78edd0fa708c9b54d0f81688","first_computed_at":"2026-07-04T15:57:43.449138Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:57:43.449138Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QtX6Mtb4OWYgTFgNg8NkaEmuELkKHHlafSqWLti6tcrw4x1xwrdSWsP6k9w1DXi/yLoMyfnIwMbGOIloWt7xAg==","signature_status":"signed_v1","signed_at":"2026-07-04T15:57:43.449482Z","signed_message":"canonical_sha256_bytes"},"source_id":"hep-th/9404005","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4361fa8361f43a1ef4627c0bdb524a7ec4dc91d00eabc509fcd124151c70401c","sha256:073c6ef7997f16bb18f3c9c4feaf1ad610b5138b9ba74cfd69e2a5d46a618f69"],"state_sha256":"2c860d2c3eab1d92170dd7a13196d81278724a95704712bb9ce5568a66428a97"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8xU27ePyXzhgDzqMRaD/8kVy+tjJd1ofto4JkKhOMVr6GjLjbLsS5G3tHNq6/FNM4Rxoi5Hfm7uLVJf0RovQDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-10T00:40:38.430875Z","bundle_sha256":"2d67c5f5fac55803680a10b8be326931a45b348bbe44ae150637545d3114d8e9"}}