{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2002:CKYCC4VN74ZXEWL3RXFRONJDCP","short_pith_number":"pith:CKYCC4VN","canonical_record":{"source":{"id":"math-ph/0208007","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"2002-08-02T16:53:09Z","cross_cats_sorted":["math.MP","math.NT"],"title_canon_sha256":"bcdc841b8542690c33a3dcbd7e1ff65f7e33adba0ba4fbd1a67cfd00244637e6","abstract_canon_sha256":"b28ab2c95ee237f7ea3efa62d9ab8cb8e7d5dd9cfe29da274157f020baeb5901"},"schema_version":"1.0"},"canonical_sha256":"12b02172adff3372597b8dcb17352313e443735d79c481da383274a71cc48238","source":{"kind":"arxiv","id":"math-ph/0208007","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0208007","created_at":"2026-05-18T01:05:31Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0208007v2","created_at":"2026-05-18T01:05:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0208007","created_at":"2026-05-18T01:05:31Z"},{"alias_kind":"pith_short_12","alias_value":"CKYCC4VN74ZX","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"CKYCC4VN74ZXEWL3","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"CKYCC4VN","created_at":"2026-05-18T12:25:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2002:CKYCC4VN74ZXEWL3RXFRONJDCP","target":"record","payload":{"canonical_record":{"source":{"id":"math-ph/0208007","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"2002-08-02T16:53:09Z","cross_cats_sorted":["math.MP","math.NT"],"title_canon_sha256":"bcdc841b8542690c33a3dcbd7e1ff65f7e33adba0ba4fbd1a67cfd00244637e6","abstract_canon_sha256":"b28ab2c95ee237f7ea3efa62d9ab8cb8e7d5dd9cfe29da274157f020baeb5901"},"schema_version":"1.0"},"canonical_sha256":"12b02172adff3372597b8dcb17352313e443735d79c481da383274a71cc48238","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:31.932850Z","signature_b64":"TPElmfaFudk3Ol1OkxZ7SuKixKZgLswUz08zAiaJ1E7UE3mzfgaKCiZQESfIGmFWCZ/CwnSoWWWYIMH2pSqTAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"12b02172adff3372597b8dcb17352313e443735d79c481da383274a71cc48238","last_reissued_at":"2026-05-18T01:05:31.932187Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:31.932187Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math-ph/0208007","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":"2026-05-18T01:05:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cUXKK2z1ID3fj+tIHks62nlXUZHoYco+fYEJJecPB+bw2YuCotFhujZrS+8vy9th/9l4/3pA5Ij9iCLil0GwDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T22:47:19.622829Z"},"content_sha256":"131481bc50ebd1ef9f4d2d4d33bc664feb0f65d7118cf0d12a035ad5b73f9e2d","schema_version":"1.0","event_id":"sha256:131481bc50ebd1ef9f4d2d4d33bc664feb0f65d7118cf0d12a035ad5b73f9e2d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2002:CKYCC4VN74ZXEWL3RXFRONJDCP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Autocorrelation of Random Matrix Polynomials","license":"","headline":"","cross_cats":["math.MP","math.NT"],"primary_cat":"math-ph","authors_text":"D.W. Farmer, J.B. Conrey, J.P. Keating, M.O. Rubinstein, N.C. Snaith","submitted_at":"2002-08-02T16:53:09Z","abstract_excerpt":"We calculate the autocorrelation functions (or shifted moments) of the characteristic polynomials of matrices drawn uniformly with respect to Haar measure from the groups U(N), O(2N) and USp(2N). In each case the result can be expressed in three equivalent forms: as a determinant sum (and hence in terms of symmetric polynomials), as a combinatorial sum, and as a multiple contour integral. These formulae are analogous to those previously obtained for the Gaussian ensembles of Random Matrix Theory, but in this case are identities for any size of matrix, rather than large-matrix asymptotic approx"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0208007","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":""},"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":"2026-05-18T01:05:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"o5yusdue4Kd5DmEElkw0FRrDQNMBdsP0eJ0GOQkMS1ktj/BGyA3CC/LAluzoFf9pmojvjRp3pAf5z1GHuAaDCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T22:47:19.623551Z"},"content_sha256":"ff3e6eec5c1fa70bfb9fb5951b0aa4594585886fd12b6744c4c5d2bf1facc847","schema_version":"1.0","event_id":"sha256:ff3e6eec5c1fa70bfb9fb5951b0aa4594585886fd12b6744c4c5d2bf1facc847"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CKYCC4VN74ZXEWL3RXFRONJDCP/bundle.json","state_url":"https://pith.science/pith/CKYCC4VN74ZXEWL3RXFRONJDCP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CKYCC4VN74ZXEWL3RXFRONJDCP/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":"2026-06-09T22:47:19Z","links":{"resolver":"https://pith.science/pith/CKYCC4VN74ZXEWL3RXFRONJDCP","bundle":"https://pith.science/pith/CKYCC4VN74ZXEWL3RXFRONJDCP/bundle.json","state":"https://pith.science/pith/CKYCC4VN74ZXEWL3RXFRONJDCP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CKYCC4VN74ZXEWL3RXFRONJDCP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2002:CKYCC4VN74ZXEWL3RXFRONJDCP","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":"b28ab2c95ee237f7ea3efa62d9ab8cb8e7d5dd9cfe29da274157f020baeb5901","cross_cats_sorted":["math.MP","math.NT"],"license":"","primary_cat":"math-ph","submitted_at":"2002-08-02T16:53:09Z","title_canon_sha256":"bcdc841b8542690c33a3dcbd7e1ff65f7e33adba0ba4fbd1a67cfd00244637e6"},"schema_version":"1.0","source":{"id":"math-ph/0208007","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0208007","created_at":"2026-05-18T01:05:31Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0208007v2","created_at":"2026-05-18T01:05:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0208007","created_at":"2026-05-18T01:05:31Z"},{"alias_kind":"pith_short_12","alias_value":"CKYCC4VN74ZX","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"CKYCC4VN74ZXEWL3","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"CKYCC4VN","created_at":"2026-05-18T12:25:50Z"}],"graph_snapshots":[{"event_id":"sha256:ff3e6eec5c1fa70bfb9fb5951b0aa4594585886fd12b6744c4c5d2bf1facc847","target":"graph","created_at":"2026-05-18T01:05:31Z","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 calculate the autocorrelation functions (or shifted moments) of the characteristic polynomials of matrices drawn uniformly with respect to Haar measure from the groups U(N), O(2N) and USp(2N). In each case the result can be expressed in three equivalent forms: as a determinant sum (and hence in terms of symmetric polynomials), as a combinatorial sum, and as a multiple contour integral. These formulae are analogous to those previously obtained for the Gaussian ensembles of Random Matrix Theory, but in this case are identities for any size of matrix, rather than large-matrix asymptotic approx","authors_text":"D.W. Farmer, J.B. Conrey, J.P. Keating, M.O. Rubinstein, N.C. Snaith","cross_cats":["math.MP","math.NT"],"headline":"","license":"","primary_cat":"math-ph","submitted_at":"2002-08-02T16:53:09Z","title":"Autocorrelation of Random Matrix Polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0208007","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":"sha256:131481bc50ebd1ef9f4d2d4d33bc664feb0f65d7118cf0d12a035ad5b73f9e2d","target":"record","created_at":"2026-05-18T01:05:31Z","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":"b28ab2c95ee237f7ea3efa62d9ab8cb8e7d5dd9cfe29da274157f020baeb5901","cross_cats_sorted":["math.MP","math.NT"],"license":"","primary_cat":"math-ph","submitted_at":"2002-08-02T16:53:09Z","title_canon_sha256":"bcdc841b8542690c33a3dcbd7e1ff65f7e33adba0ba4fbd1a67cfd00244637e6"},"schema_version":"1.0","source":{"id":"math-ph/0208007","kind":"arxiv","version":2}},"canonical_sha256":"12b02172adff3372597b8dcb17352313e443735d79c481da383274a71cc48238","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"12b02172adff3372597b8dcb17352313e443735d79c481da383274a71cc48238","first_computed_at":"2026-05-18T01:05:31.932187Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:31.932187Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TPElmfaFudk3Ol1OkxZ7SuKixKZgLswUz08zAiaJ1E7UE3mzfgaKCiZQESfIGmFWCZ/CwnSoWWWYIMH2pSqTAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:31.932850Z","signed_message":"canonical_sha256_bytes"},"source_id":"math-ph/0208007","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:131481bc50ebd1ef9f4d2d4d33bc664feb0f65d7118cf0d12a035ad5b73f9e2d","sha256:ff3e6eec5c1fa70bfb9fb5951b0aa4594585886fd12b6744c4c5d2bf1facc847"],"state_sha256":"2471d61808d2fdcf6198c76487f77197dcf9731bb041d564e3d27b551d8c0c5e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ED19R+r/8Y9pvi9t35r9AmKn56T1RiaODHTv5CZsTpzdFlaG6QgLVh1YPLLTJvygRejZ4falNRkfiXDISncvCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T22:47:19.627299Z","bundle_sha256":"0f78673376a039ad825fc9da54114c0321f0dbd7a200c6c992e49a9255e8380b"}}