{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:FP5OZEVTCM4KE7RWUXMYYHUMNF","short_pith_number":"pith:FP5OZEVT","canonical_record":{"source":{"id":"2507.10193","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2025-07-14T12:00:12Z","cross_cats_sorted":["cond-mat.dis-nn","hep-th","math.MP","math.PR"],"title_canon_sha256":"2a4867572f432acb3ada2ff5e599e31a4b25ad15aa82f28d585b5a4d3734d946","abstract_canon_sha256":"c49d02528a88f1cd86acfc6f6d8e03d58730f2a57f10e1b408f17290b054c4fb"},"schema_version":"1.0"},"canonical_sha256":"2bfaec92b31338a27e36a5d98c1e8c69594f9a7f4ca83a21598fe779e6110715","source":{"kind":"arxiv","id":"2507.10193","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.10193","created_at":"2026-07-05T11:43:33Z"},{"alias_kind":"arxiv_version","alias_value":"2507.10193v1","created_at":"2026-07-05T11:43:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.10193","created_at":"2026-07-05T11:43:33Z"},{"alias_kind":"pith_short_12","alias_value":"FP5OZEVTCM4K","created_at":"2026-07-05T11:43:33Z"},{"alias_kind":"pith_short_16","alias_value":"FP5OZEVTCM4KE7RW","created_at":"2026-07-05T11:43:33Z"},{"alias_kind":"pith_short_8","alias_value":"FP5OZEVT","created_at":"2026-07-05T11:43:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:FP5OZEVTCM4KE7RWUXMYYHUMNF","target":"record","payload":{"canonical_record":{"source":{"id":"2507.10193","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2025-07-14T12:00:12Z","cross_cats_sorted":["cond-mat.dis-nn","hep-th","math.MP","math.PR"],"title_canon_sha256":"2a4867572f432acb3ada2ff5e599e31a4b25ad15aa82f28d585b5a4d3734d946","abstract_canon_sha256":"c49d02528a88f1cd86acfc6f6d8e03d58730f2a57f10e1b408f17290b054c4fb"},"schema_version":"1.0"},"canonical_sha256":"2bfaec92b31338a27e36a5d98c1e8c69594f9a7f4ca83a21598fe779e6110715","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:43:33.611916Z","signature_b64":"zF4npbUyDEuOixHUpYuR2Fg+jfA0Hp8AbmT8mNRo7TGlTl/OFCJFBbVs9x/9qdDiOWB4Eb6/N68hR//ALEj7Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2bfaec92b31338a27e36a5d98c1e8c69594f9a7f4ca83a21598fe779e6110715","last_reissued_at":"2026-07-05T11:43:33.611462Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:43:33.611462Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2507.10193","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":"2026-07-05T11:43:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+wZYP6KxZylNqY2SXc2jtcOT/jfD+JXLkYWYDL8+KYotz76E5e9J5677lmQlYTZ6pokz7XdZXg1dZH4fC9iuDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T15:37:05.455057Z"},"content_sha256":"a62cb6accb692946aa3389e46a23b5f8ed400d9bf9e44e38414ccc1717ec8a31","schema_version":"1.0","event_id":"sha256:a62cb6accb692946aa3389e46a23b5f8ed400d9bf9e44e38414ccc1717ec8a31"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:FP5OZEVTCM4KE7RWUXMYYHUMNF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Distributions of consecutive level spacings of circular unitary ensemble and their ratio: finite-size corrections and Riemann $\\zeta$ zeros","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cond-mat.dis-nn","hep-th","math.MP","math.PR"],"primary_cat":"math-ph","authors_text":"Shinsuke M. Nishigaki","submitted_at":"2025-07-14T12:00:12Z","abstract_excerpt":"We compute the joint distribution of two consecutive eigenphase spacings and their ratio for Haar-distributed $\\mathrm{U}(N)$ matrices (the circular unitary ensemble) using our framework for J\\'{a}nossy densities in random matrix theory, formulated via the Tracy-Widom system of nonlinear PDEs. Our result shows that the leading finite-$N$ correction in the gap-ratio distribution relative to the universal sine-kernel limit is of $\\mathcal{O}(N^{-4})$, reflecting a nontrivial cancellation of the $\\mathcal{O}(N^{-2})$ part present in the joint distributions of consecutive spacings. This finding su"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.10193","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2507.10193/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":"2026-07-05T11:43:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9Zk9D6etKyu7Fv1OWxOoV3TAMchZS+LO1myzHEmOFW/eEJG0OBJ2FmXWwfE45FXiRQAZd/YXmNUOrAW6toMkAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T15:37:05.456371Z"},"content_sha256":"5afe62a2f5b8e3fe64dfc64f39a5435f805bddfb13bb065d277c84ee00e01ed9","schema_version":"1.0","event_id":"sha256:5afe62a2f5b8e3fe64dfc64f39a5435f805bddfb13bb065d277c84ee00e01ed9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FP5OZEVTCM4KE7RWUXMYYHUMNF/bundle.json","state_url":"https://pith.science/pith/FP5OZEVTCM4KE7RWUXMYYHUMNF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FP5OZEVTCM4KE7RWUXMYYHUMNF/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":"2026-08-17T15:37:05Z","links":{"resolver":"https://pith.science/pith/FP5OZEVTCM4KE7RWUXMYYHUMNF","bundle":"https://pith.science/pith/FP5OZEVTCM4KE7RWUXMYYHUMNF/bundle.json","state":"https://pith.science/pith/FP5OZEVTCM4KE7RWUXMYYHUMNF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FP5OZEVTCM4KE7RWUXMYYHUMNF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:FP5OZEVTCM4KE7RWUXMYYHUMNF","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":"c49d02528a88f1cd86acfc6f6d8e03d58730f2a57f10e1b408f17290b054c4fb","cross_cats_sorted":["cond-mat.dis-nn","hep-th","math.MP","math.PR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2025-07-14T12:00:12Z","title_canon_sha256":"2a4867572f432acb3ada2ff5e599e31a4b25ad15aa82f28d585b5a4d3734d946"},"schema_version":"1.0","source":{"id":"2507.10193","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.10193","created_at":"2026-07-05T11:43:33Z"},{"alias_kind":"arxiv_version","alias_value":"2507.10193v1","created_at":"2026-07-05T11:43:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.10193","created_at":"2026-07-05T11:43:33Z"},{"alias_kind":"pith_short_12","alias_value":"FP5OZEVTCM4K","created_at":"2026-07-05T11:43:33Z"},{"alias_kind":"pith_short_16","alias_value":"FP5OZEVTCM4KE7RW","created_at":"2026-07-05T11:43:33Z"},{"alias_kind":"pith_short_8","alias_value":"FP5OZEVT","created_at":"2026-07-05T11:43:33Z"}],"graph_snapshots":[{"event_id":"sha256:5afe62a2f5b8e3fe64dfc64f39a5435f805bddfb13bb065d277c84ee00e01ed9","target":"graph","created_at":"2026-07-05T11:43:33Z","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/2507.10193/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We compute the joint distribution of two consecutive eigenphase spacings and their ratio for Haar-distributed $\\mathrm{U}(N)$ matrices (the circular unitary ensemble) using our framework for J\\'{a}nossy densities in random matrix theory, formulated via the Tracy-Widom system of nonlinear PDEs. Our result shows that the leading finite-$N$ correction in the gap-ratio distribution relative to the universal sine-kernel limit is of $\\mathcal{O}(N^{-4})$, reflecting a nontrivial cancellation of the $\\mathcal{O}(N^{-2})$ part present in the joint distributions of consecutive spacings. This finding su","authors_text":"Shinsuke M. Nishigaki","cross_cats":["cond-mat.dis-nn","hep-th","math.MP","math.PR"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2025-07-14T12:00:12Z","title":"Distributions of consecutive level spacings of circular unitary ensemble and their ratio: finite-size corrections and Riemann $\\zeta$ zeros"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.10193","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:a62cb6accb692946aa3389e46a23b5f8ed400d9bf9e44e38414ccc1717ec8a31","target":"record","created_at":"2026-07-05T11:43:33Z","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":"c49d02528a88f1cd86acfc6f6d8e03d58730f2a57f10e1b408f17290b054c4fb","cross_cats_sorted":["cond-mat.dis-nn","hep-th","math.MP","math.PR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2025-07-14T12:00:12Z","title_canon_sha256":"2a4867572f432acb3ada2ff5e599e31a4b25ad15aa82f28d585b5a4d3734d946"},"schema_version":"1.0","source":{"id":"2507.10193","kind":"arxiv","version":1}},"canonical_sha256":"2bfaec92b31338a27e36a5d98c1e8c69594f9a7f4ca83a21598fe779e6110715","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2bfaec92b31338a27e36a5d98c1e8c69594f9a7f4ca83a21598fe779e6110715","first_computed_at":"2026-07-05T11:43:33.611462Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:43:33.611462Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zF4npbUyDEuOixHUpYuR2Fg+jfA0Hp8AbmT8mNRo7TGlTl/OFCJFBbVs9x/9qdDiOWB4Eb6/N68hR//ALEj7Cw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:43:33.611916Z","signed_message":"canonical_sha256_bytes"},"source_id":"2507.10193","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a62cb6accb692946aa3389e46a23b5f8ed400d9bf9e44e38414ccc1717ec8a31","sha256:5afe62a2f5b8e3fe64dfc64f39a5435f805bddfb13bb065d277c84ee00e01ed9"],"state_sha256":"a52ab3ae5f13cf7b6f61d05c7bcd991f84b9f941b42be5fd19ea8c99d18c80af"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LhWgfRc2x7mnK/OJLqivfLCJm7fwQBc3ar5AQeA5j+PJJz5KXns782UMNT7aa5HWL4brxvxEevteXs40MTQ+AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-17T15:37:05.493806Z","bundle_sha256":"06a8746dbf16a09ac1c4a60ba4f6e3e44d95c3255c9cc311a4eaa31eabacfeae"}}