{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2002:MM67T3AXDXIDKR7WXN7FG4623E","short_pith_number":"pith:MM67T3AX","canonical_record":{"source":{"id":"math-ph/0209019","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"2002-09-10T17:49:15Z","cross_cats_sorted":["cond-mat","hep-th","math.CO","math.MP"],"title_canon_sha256":"3752d9c45d0c322832413a2f7922785d726cd01b99823680e2c66759923854a0","abstract_canon_sha256":"b18df0e9f620fc95e4bedba0cb4bb048252513cbd950dc9d62f368bf015c7eec"},"schema_version":"1.0"},"canonical_sha256":"633df9ec171dd03547f6bb7e5373dad9117b65e0d914740399d87a19c50dc470","source":{"kind":"arxiv","id":"math-ph/0209019","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0209019","created_at":"2026-07-04T15:52:12Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0209019v3","created_at":"2026-07-04T15:52:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0209019","created_at":"2026-07-04T15:52:12Z"},{"alias_kind":"pith_short_12","alias_value":"MM67T3AXDXID","created_at":"2026-07-04T15:52:12Z"},{"alias_kind":"pith_short_16","alias_value":"MM67T3AXDXIDKR7W","created_at":"2026-07-04T15:52:12Z"},{"alias_kind":"pith_short_8","alias_value":"MM67T3AX","created_at":"2026-07-04T15:52:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2002:MM67T3AXDXIDKR7WXN7FG4623E","target":"record","payload":{"canonical_record":{"source":{"id":"math-ph/0209019","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"2002-09-10T17:49:15Z","cross_cats_sorted":["cond-mat","hep-th","math.CO","math.MP"],"title_canon_sha256":"3752d9c45d0c322832413a2f7922785d726cd01b99823680e2c66759923854a0","abstract_canon_sha256":"b18df0e9f620fc95e4bedba0cb4bb048252513cbd950dc9d62f368bf015c7eec"},"schema_version":"1.0"},"canonical_sha256":"633df9ec171dd03547f6bb7e5373dad9117b65e0d914740399d87a19c50dc470","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:52:12.560845Z","signature_b64":"ICZXHc1/hLID7qKJx24113AYrr+te4lvxgTTVITydMz8JrW1+RjZcvHCtdatKzHmGXXiRWJVBu6wxAZZh+W+AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"633df9ec171dd03547f6bb7e5373dad9117b65e0d914740399d87a19c50dc470","last_reissued_at":"2026-07-04T15:52:12.560492Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:52:12.560492Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math-ph/0209019","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T15:52:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6jlLNK8bSuealQzVCZCo+R3fSHatHxsq96xgrRssn1CF3OJzsKkEn3pqXY3a9o/yZXZcfPXDUUBYMyt3Lp1PBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T18:02:18.915956Z"},"content_sha256":"2563a4ef5ac3972dc021d190aad99064f868972f13313c4ea2b29eb9a6255d77","schema_version":"1.0","event_id":"sha256:2563a4ef5ac3972dc021d190aad99064f868972f13313c4ea2b29eb9a6255d77"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2002:MM67T3AXDXIDKR7WXN7FG4623E","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On some integrals over the U(N) unitary group and their large N limit","license":"","headline":"","cross_cats":["cond-mat","hep-th","math.CO","math.MP"],"primary_cat":"math-ph","authors_text":"J.-B. Zuber, P. Zinn-Justin","submitted_at":"2002-09-10T17:49:15Z","abstract_excerpt":"The integral over the U(N) unitary group $I=\\int DU \\exp\\Tr A U B U^\\dagger$ is reexamined. Various approaches and extensions are first reviewed. The second half of the paper deals with more recent developments: relation with integrable Toda lattice hierarchy, diagrammatic expansion and combinatorics, and on what they teach us on the large $N$ limit of $\\log I$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0209019","kind":"arxiv","version":3},"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/math-ph/0209019/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":"2026-07-04T15:52:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0P4FHppa6ZUjkzgdL/Kg6Nm6NiF1LdNymsdroCovkBAO0iZKaycu9NtlKpBxyWyyDduLw9i5NeMaFaEAoVOtAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T18:02:18.916501Z"},"content_sha256":"1253e53e943cf3cfc26751c8f27d9c94ac16912fa4cdc715f5be86e807a9707c","schema_version":"1.0","event_id":"sha256:1253e53e943cf3cfc26751c8f27d9c94ac16912fa4cdc715f5be86e807a9707c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MM67T3AXDXIDKR7WXN7FG4623E/bundle.json","state_url":"https://pith.science/pith/MM67T3AXDXIDKR7WXN7FG4623E/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MM67T3AXDXIDKR7WXN7FG4623E/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":"2026-08-08T18:02:18Z","links":{"resolver":"https://pith.science/pith/MM67T3AXDXIDKR7WXN7FG4623E","bundle":"https://pith.science/pith/MM67T3AXDXIDKR7WXN7FG4623E/bundle.json","state":"https://pith.science/pith/MM67T3AXDXIDKR7WXN7FG4623E/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MM67T3AXDXIDKR7WXN7FG4623E/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2002:MM67T3AXDXIDKR7WXN7FG4623E","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":"b18df0e9f620fc95e4bedba0cb4bb048252513cbd950dc9d62f368bf015c7eec","cross_cats_sorted":["cond-mat","hep-th","math.CO","math.MP"],"license":"","primary_cat":"math-ph","submitted_at":"2002-09-10T17:49:15Z","title_canon_sha256":"3752d9c45d0c322832413a2f7922785d726cd01b99823680e2c66759923854a0"},"schema_version":"1.0","source":{"id":"math-ph/0209019","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0209019","created_at":"2026-07-04T15:52:12Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0209019v3","created_at":"2026-07-04T15:52:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0209019","created_at":"2026-07-04T15:52:12Z"},{"alias_kind":"pith_short_12","alias_value":"MM67T3AXDXID","created_at":"2026-07-04T15:52:12Z"},{"alias_kind":"pith_short_16","alias_value":"MM67T3AXDXIDKR7W","created_at":"2026-07-04T15:52:12Z"},{"alias_kind":"pith_short_8","alias_value":"MM67T3AX","created_at":"2026-07-04T15:52:12Z"}],"graph_snapshots":[{"event_id":"sha256:1253e53e943cf3cfc26751c8f27d9c94ac16912fa4cdc715f5be86e807a9707c","target":"graph","created_at":"2026-07-04T15:52:12Z","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/math-ph/0209019/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The integral over the U(N) unitary group $I=\\int DU \\exp\\Tr A U B U^\\dagger$ is reexamined. Various approaches and extensions are first reviewed. The second half of the paper deals with more recent developments: relation with integrable Toda lattice hierarchy, diagrammatic expansion and combinatorics, and on what they teach us on the large $N$ limit of $\\log I$.","authors_text":"J.-B. Zuber, P. Zinn-Justin","cross_cats":["cond-mat","hep-th","math.CO","math.MP"],"headline":"","license":"","primary_cat":"math-ph","submitted_at":"2002-09-10T17:49:15Z","title":"On some integrals over the U(N) unitary group and their large N limit"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0209019","kind":"arxiv","version":3},"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":"sha256:2563a4ef5ac3972dc021d190aad99064f868972f13313c4ea2b29eb9a6255d77","target":"record","created_at":"2026-07-04T15:52:12Z","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":"b18df0e9f620fc95e4bedba0cb4bb048252513cbd950dc9d62f368bf015c7eec","cross_cats_sorted":["cond-mat","hep-th","math.CO","math.MP"],"license":"","primary_cat":"math-ph","submitted_at":"2002-09-10T17:49:15Z","title_canon_sha256":"3752d9c45d0c322832413a2f7922785d726cd01b99823680e2c66759923854a0"},"schema_version":"1.0","source":{"id":"math-ph/0209019","kind":"arxiv","version":3}},"canonical_sha256":"633df9ec171dd03547f6bb7e5373dad9117b65e0d914740399d87a19c50dc470","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"633df9ec171dd03547f6bb7e5373dad9117b65e0d914740399d87a19c50dc470","first_computed_at":"2026-07-04T15:52:12.560492Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:52:12.560492Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ICZXHc1/hLID7qKJx24113AYrr+te4lvxgTTVITydMz8JrW1+RjZcvHCtdatKzHmGXXiRWJVBu6wxAZZh+W+AA==","signature_status":"signed_v1","signed_at":"2026-07-04T15:52:12.560845Z","signed_message":"canonical_sha256_bytes"},"source_id":"math-ph/0209019","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2563a4ef5ac3972dc021d190aad99064f868972f13313c4ea2b29eb9a6255d77","sha256:1253e53e943cf3cfc26751c8f27d9c94ac16912fa4cdc715f5be86e807a9707c"],"state_sha256":"52fb23fd460b75b137b461afdd24536f02a60944431f71ad184407bca77c898a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gYytcFKlkmZwe1E2WapT5bLcsbyRYqf14geB90nOBZ6g3mDbaBp/8YfHPH8KzAyFBVgsY+LKdLfRnpQFTWdxCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T18:02:18.920890Z","bundle_sha256":"512d3936b94bbda79a93c61cf36c3cfb196c05e6f25286abd31c03d1de6a6194"}}