{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1992:VBCBVSDJ5P4WWRXMGNHLC5Q3KU","short_pith_number":"pith:VBCBVSDJ","canonical_record":{"source":{"id":"hep-th/9206090","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"1992-06-24T11:18:03Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"b0f622a1a01010bece278f4c217ac8a980164b85f66fb05c6d5078c5cdb1063d","abstract_canon_sha256":"528edda404692795f3bc94c71da16f179f39c866076b0062f6915d026618bb3d"},"schema_version":"1.0"},"canonical_sha256":"a8441ac869ebf96b46ec334eb1761b55046d7ec11d84a203b399a5e095dcf73f","source":{"kind":"arxiv","id":"hep-th/9206090","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/9206090","created_at":"2026-05-18T01:38:44Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/9206090v1","created_at":"2026-05-18T01:38:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/9206090","created_at":"2026-05-18T01:38:44Z"},{"alias_kind":"pith_short_12","alias_value":"VBCBVSDJ5P4W","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_16","alias_value":"VBCBVSDJ5P4WWRXM","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_8","alias_value":"VBCBVSDJ","created_at":"2026-05-18T12:25:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1992:VBCBVSDJ5P4WWRXMGNHLC5Q3KU","target":"record","payload":{"canonical_record":{"source":{"id":"hep-th/9206090","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"1992-06-24T11:18:03Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"b0f622a1a01010bece278f4c217ac8a980164b85f66fb05c6d5078c5cdb1063d","abstract_canon_sha256":"528edda404692795f3bc94c71da16f179f39c866076b0062f6915d026618bb3d"},"schema_version":"1.0"},"canonical_sha256":"a8441ac869ebf96b46ec334eb1761b55046d7ec11d84a203b399a5e095dcf73f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:38:44.698871Z","signature_b64":"BVTVSYGdZvDzOyAVKbYaRO+qUlfK8GnfsJJO8ESBYSx2rK/tIZA/fSEyhFhKLM7X5v0Y+5zoI1pySMpBUCHXCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a8441ac869ebf96b46ec334eb1761b55046d7ec11d84a203b399a5e095dcf73f","last_reissued_at":"2026-05-18T01:38:44.698485Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:38:44.698485Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"hep-th/9206090","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":"2026-05-18T01:38:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gUDfY3NrXf9xGYYdPTRWYiYSitZx2EW4Dz1VXyDi3zDZXgvKJNhyl6N3Kcx+DFM4LkWc8PIjil6ufPNcmmP/AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T16:32:46.806168Z"},"content_sha256":"b6e0e41bc1b4ab06f0fa7b6be77d2b85609767eec82d63ab9db942358db9ff4a","schema_version":"1.0","event_id":"sha256:b6e0e41bc1b4ab06f0fa7b6be77d2b85609767eec82d63ab9db942358db9ff4a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1992:VBCBVSDJ5P4WWRXMGNHLC5Q3KU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Polynomial averages in the Kontsevich model","license":"","headline":"","cross_cats":["math.QA"],"primary_cat":"hep-th","authors_text":"C. Itzykson, J.-B. Zuber, P. Di Francesco","submitted_at":"1992-06-24T11:18:03Z","abstract_excerpt":"We obtain in closed form averages of polynomials, taken over hermitian matrices with the Gaussian measure involved in the Kontsevich integral, and prove a conjecture of Witten enabling one to express analogous averages with the full (cubic potential) measure, as derivatives of the partition function with respect to traces of inverse odd powers of the external argument. The proofs are based on elementary algebraic identities involving a new set of invariant polynomials of the linear group, closely related to the general Schur functions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/9206090","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":""},"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":"2026-05-18T01:38:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2XIvhLNt16OyBhqPBB1T9l1NTassBKQfBSdTYsgsKgcHR9nlur0vYRctH8Z3A1PjzvQkYmy/JESGihRv0lW1BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T16:32:46.806850Z"},"content_sha256":"67c3150b77f555ac1110cc1f6e81df54a76521dd0364e32e339876695ab57525","schema_version":"1.0","event_id":"sha256:67c3150b77f555ac1110cc1f6e81df54a76521dd0364e32e339876695ab57525"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VBCBVSDJ5P4WWRXMGNHLC5Q3KU/bundle.json","state_url":"https://pith.science/pith/VBCBVSDJ5P4WWRXMGNHLC5Q3KU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VBCBVSDJ5P4WWRXMGNHLC5Q3KU/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":"2026-05-26T16:32:46Z","links":{"resolver":"https://pith.science/pith/VBCBVSDJ5P4WWRXMGNHLC5Q3KU","bundle":"https://pith.science/pith/VBCBVSDJ5P4WWRXMGNHLC5Q3KU/bundle.json","state":"https://pith.science/pith/VBCBVSDJ5P4WWRXMGNHLC5Q3KU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VBCBVSDJ5P4WWRXMGNHLC5Q3KU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1992:VBCBVSDJ5P4WWRXMGNHLC5Q3KU","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":"528edda404692795f3bc94c71da16f179f39c866076b0062f6915d026618bb3d","cross_cats_sorted":["math.QA"],"license":"","primary_cat":"hep-th","submitted_at":"1992-06-24T11:18:03Z","title_canon_sha256":"b0f622a1a01010bece278f4c217ac8a980164b85f66fb05c6d5078c5cdb1063d"},"schema_version":"1.0","source":{"id":"hep-th/9206090","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/9206090","created_at":"2026-05-18T01:38:44Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/9206090v1","created_at":"2026-05-18T01:38:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/9206090","created_at":"2026-05-18T01:38:44Z"},{"alias_kind":"pith_short_12","alias_value":"VBCBVSDJ5P4W","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_16","alias_value":"VBCBVSDJ5P4WWRXM","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_8","alias_value":"VBCBVSDJ","created_at":"2026-05-18T12:25:47Z"}],"graph_snapshots":[{"event_id":"sha256:67c3150b77f555ac1110cc1f6e81df54a76521dd0364e32e339876695ab57525","target":"graph","created_at":"2026-05-18T01:38:44Z","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":"We obtain in closed form averages of polynomials, taken over hermitian matrices with the Gaussian measure involved in the Kontsevich integral, and prove a conjecture of Witten enabling one to express analogous averages with the full (cubic potential) measure, as derivatives of the partition function with respect to traces of inverse odd powers of the external argument. The proofs are based on elementary algebraic identities involving a new set of invariant polynomials of the linear group, closely related to the general Schur functions.","authors_text":"C. Itzykson, J.-B. Zuber, P. Di Francesco","cross_cats":["math.QA"],"headline":"","license":"","primary_cat":"hep-th","submitted_at":"1992-06-24T11:18:03Z","title":"Polynomial averages in the Kontsevich model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/9206090","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:b6e0e41bc1b4ab06f0fa7b6be77d2b85609767eec82d63ab9db942358db9ff4a","target":"record","created_at":"2026-05-18T01:38:44Z","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":"528edda404692795f3bc94c71da16f179f39c866076b0062f6915d026618bb3d","cross_cats_sorted":["math.QA"],"license":"","primary_cat":"hep-th","submitted_at":"1992-06-24T11:18:03Z","title_canon_sha256":"b0f622a1a01010bece278f4c217ac8a980164b85f66fb05c6d5078c5cdb1063d"},"schema_version":"1.0","source":{"id":"hep-th/9206090","kind":"arxiv","version":1}},"canonical_sha256":"a8441ac869ebf96b46ec334eb1761b55046d7ec11d84a203b399a5e095dcf73f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a8441ac869ebf96b46ec334eb1761b55046d7ec11d84a203b399a5e095dcf73f","first_computed_at":"2026-05-18T01:38:44.698485Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:38:44.698485Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BVTVSYGdZvDzOyAVKbYaRO+qUlfK8GnfsJJO8ESBYSx2rK/tIZA/fSEyhFhKLM7X5v0Y+5zoI1pySMpBUCHXCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:38:44.698871Z","signed_message":"canonical_sha256_bytes"},"source_id":"hep-th/9206090","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b6e0e41bc1b4ab06f0fa7b6be77d2b85609767eec82d63ab9db942358db9ff4a","sha256:67c3150b77f555ac1110cc1f6e81df54a76521dd0364e32e339876695ab57525"],"state_sha256":"9aa3ddb80ccaac1a848c62718c4aac1ff9f23ecb84c9fa83f9f9a4590dd30262"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4wWs8aeampYtS0mNLH4DUIPQh8CYQeUANjhKJB8qJHxoFSF77EHkP6jrzQB7knX1q9x8FiM020rhVcsT6iDrAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T16:32:46.810396Z","bundle_sha256":"bebb79dfa30fea2dc19db00f5a5cee136af616472935df275692cc0a48ae3d26"}}