{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2006:PZYA5IIQ3UKMV5YD6F45NC2P7Y","short_pith_number":"pith:PZYA5IIQ","canonical_record":{"source":{"id":"math/0608193","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2006-08-08T08:24:26Z","cross_cats_sorted":[],"title_canon_sha256":"ac5802b8e2c99c665c9fbddb828f55132a441605e3713c51804c4485ebf1a54b","abstract_canon_sha256":"28948b1dde74578517d7fe0be44fc5d7c11f71717658189d617e223998b9e894"},"schema_version":"1.0"},"canonical_sha256":"7e700ea110dd14caf703f179d68b4ffe09b9be2341a353f881dae1480a568b18","source":{"kind":"arxiv","id":"math/0608193","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0608193","created_at":"2026-05-17T23:52:34Z"},{"alias_kind":"arxiv_version","alias_value":"math/0608193v3","created_at":"2026-05-17T23:52:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0608193","created_at":"2026-05-17T23:52:34Z"},{"alias_kind":"pith_short_12","alias_value":"PZYA5IIQ3UKM","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"PZYA5IIQ3UKMV5YD","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"PZYA5IIQ","created_at":"2026-05-18T12:25:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2006:PZYA5IIQ3UKMV5YD6F45NC2P7Y","target":"record","payload":{"canonical_record":{"source":{"id":"math/0608193","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2006-08-08T08:24:26Z","cross_cats_sorted":[],"title_canon_sha256":"ac5802b8e2c99c665c9fbddb828f55132a441605e3713c51804c4485ebf1a54b","abstract_canon_sha256":"28948b1dde74578517d7fe0be44fc5d7c11f71717658189d617e223998b9e894"},"schema_version":"1.0"},"canonical_sha256":"7e700ea110dd14caf703f179d68b4ffe09b9be2341a353f881dae1480a568b18","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:52:34.621133Z","signature_b64":"2KnOaQGE0O2qcJhG7NGwntnQsJtkN7B5QID19oHRGINj6SSUnm0RZviC9PUKG2qhZeZsnip9fahoQ9gFTiiVCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7e700ea110dd14caf703f179d68b4ffe09b9be2341a353f881dae1480a568b18","last_reissued_at":"2026-05-17T23:52:34.620761Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:52:34.620761Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0608193","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":"2026-05-17T23:52:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yhh5nH6qTwPehecnWI1el415y+PIBTray8K9Mf88czVwKIkOPlA6W1etAGBEZuGdwmGHgKRNw2Ep/NqyrNvEAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T07:55:36.660705Z"},"content_sha256":"bf4ee7d558fc8f3922962e5eff01b619ed2ef52b124f1aad634498f55bcee8ca","schema_version":"1.0","event_id":"sha256:bf4ee7d558fc8f3922962e5eff01b619ed2ef52b124f1aad634498f55bcee8ca"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2006:PZYA5IIQ3UKMV5YD6F45NC2P7Y","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Asymptotics of unitary and othogonal matrix integrals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Alice Guionnet, Benoit Collins, Edouard Maurel-Segala","submitted_at":"2006-08-08T08:24:26Z","abstract_excerpt":"In this paper, we prove that in small parameter regions, arbitrary unitary matrix integrals converge in the large $N$ limit and match their formal expansion. Secondly we give a combinatorial model for our matrix integral asymptotics and investigate examples related to free probability and the HCIZ integral. Our convergence result also leads us to new results of smoothness of microstates. We finally generalize our approach to integrals over the othogonal group."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0608193","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":""},"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":"2026-05-17T23:52:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nTE3dgiQlx5lA/FHYeas0HkUeAh/p1HwX7jCaBHw0iCrOqoPqmMw0xYhUfZg7GBVjTbYko8XPpAMDSX6c9uaDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T07:55:36.661051Z"},"content_sha256":"7b98c4e03eb5d71404233cc7b7598d2e6426b8b22c04405e22d147950f62d4a1","schema_version":"1.0","event_id":"sha256:7b98c4e03eb5d71404233cc7b7598d2e6426b8b22c04405e22d147950f62d4a1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PZYA5IIQ3UKMV5YD6F45NC2P7Y/bundle.json","state_url":"https://pith.science/pith/PZYA5IIQ3UKMV5YD6F45NC2P7Y/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PZYA5IIQ3UKMV5YD6F45NC2P7Y/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":"2026-05-28T07:55:36Z","links":{"resolver":"https://pith.science/pith/PZYA5IIQ3UKMV5YD6F45NC2P7Y","bundle":"https://pith.science/pith/PZYA5IIQ3UKMV5YD6F45NC2P7Y/bundle.json","state":"https://pith.science/pith/PZYA5IIQ3UKMV5YD6F45NC2P7Y/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PZYA5IIQ3UKMV5YD6F45NC2P7Y/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:PZYA5IIQ3UKMV5YD6F45NC2P7Y","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":"28948b1dde74578517d7fe0be44fc5d7c11f71717658189d617e223998b9e894","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2006-08-08T08:24:26Z","title_canon_sha256":"ac5802b8e2c99c665c9fbddb828f55132a441605e3713c51804c4485ebf1a54b"},"schema_version":"1.0","source":{"id":"math/0608193","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0608193","created_at":"2026-05-17T23:52:34Z"},{"alias_kind":"arxiv_version","alias_value":"math/0608193v3","created_at":"2026-05-17T23:52:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0608193","created_at":"2026-05-17T23:52:34Z"},{"alias_kind":"pith_short_12","alias_value":"PZYA5IIQ3UKM","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"PZYA5IIQ3UKMV5YD","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"PZYA5IIQ","created_at":"2026-05-18T12:25:54Z"}],"graph_snapshots":[{"event_id":"sha256:7b98c4e03eb5d71404233cc7b7598d2e6426b8b22c04405e22d147950f62d4a1","target":"graph","created_at":"2026-05-17T23:52:34Z","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":"In this paper, we prove that in small parameter regions, arbitrary unitary matrix integrals converge in the large $N$ limit and match their formal expansion. Secondly we give a combinatorial model for our matrix integral asymptotics and investigate examples related to free probability and the HCIZ integral. Our convergence result also leads us to new results of smoothness of microstates. We finally generalize our approach to integrals over the othogonal group.","authors_text":"Alice Guionnet, Benoit Collins, Edouard Maurel-Segala","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2006-08-08T08:24:26Z","title":"Asymptotics of unitary and othogonal matrix integrals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0608193","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:bf4ee7d558fc8f3922962e5eff01b619ed2ef52b124f1aad634498f55bcee8ca","target":"record","created_at":"2026-05-17T23:52:34Z","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":"28948b1dde74578517d7fe0be44fc5d7c11f71717658189d617e223998b9e894","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2006-08-08T08:24:26Z","title_canon_sha256":"ac5802b8e2c99c665c9fbddb828f55132a441605e3713c51804c4485ebf1a54b"},"schema_version":"1.0","source":{"id":"math/0608193","kind":"arxiv","version":3}},"canonical_sha256":"7e700ea110dd14caf703f179d68b4ffe09b9be2341a353f881dae1480a568b18","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7e700ea110dd14caf703f179d68b4ffe09b9be2341a353f881dae1480a568b18","first_computed_at":"2026-05-17T23:52:34.620761Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:52:34.620761Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2KnOaQGE0O2qcJhG7NGwntnQsJtkN7B5QID19oHRGINj6SSUnm0RZviC9PUKG2qhZeZsnip9fahoQ9gFTiiVCg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:52:34.621133Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0608193","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bf4ee7d558fc8f3922962e5eff01b619ed2ef52b124f1aad634498f55bcee8ca","sha256:7b98c4e03eb5d71404233cc7b7598d2e6426b8b22c04405e22d147950f62d4a1"],"state_sha256":"4eafd16cc1648dd6b1792734d6f4bb39bbec22bdbbd5eaed3c67326d2139f6a5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NUTVPSnAJFNbNRZNuTMOCjtF8FQmtTw5l8qQeRK3yjsfPob5Bn0lTR2UHruj7xex2Klrj5jpaSmYK48ByhheAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T07:55:36.663084Z","bundle_sha256":"600e85e1516eedd22ffd5e49b2f51456f169d9bfcc1a72ffcfbe166da75b2dd4"}}