{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2002:NXLQFXQC3NO5UKW5MKH3FGVDMU","short_pith_number":"pith:NXLQFXQC","canonical_record":{"source":{"id":"math-ph/0204001","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"2002-04-01T19:34:19Z","cross_cats_sorted":["cond-mat","hep-th","math.CA","math.MP","nlin.SI"],"title_canon_sha256":"28ad42e9f3f5c6f938bb72e7c63fb756034092296b04f5616fc33492dd5c56ae","abstract_canon_sha256":"fdc0b89abc3ec78fd74260a7d65199851733f89ddf335e0e004d5957ecad6130"},"schema_version":"1.0"},"canonical_sha256":"6dd702de02db5dda2add628fb29aa3651aedf4467025d617f3fc40eb8649aa48","source":{"kind":"arxiv","id":"math-ph/0204001","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0204001","created_at":"2026-07-04T16:35:02Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0204001v1","created_at":"2026-07-04T16:35:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0204001","created_at":"2026-07-04T16:35:02Z"},{"alias_kind":"pith_short_12","alias_value":"NXLQFXQC3NO5","created_at":"2026-07-04T16:35:02Z"},{"alias_kind":"pith_short_16","alias_value":"NXLQFXQC3NO5UKW5","created_at":"2026-07-04T16:35:02Z"},{"alias_kind":"pith_short_8","alias_value":"NXLQFXQC","created_at":"2026-07-04T16:35:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2002:NXLQFXQC3NO5UKW5MKH3FGVDMU","target":"record","payload":{"canonical_record":{"source":{"id":"math-ph/0204001","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"2002-04-01T19:34:19Z","cross_cats_sorted":["cond-mat","hep-th","math.CA","math.MP","nlin.SI"],"title_canon_sha256":"28ad42e9f3f5c6f938bb72e7c63fb756034092296b04f5616fc33492dd5c56ae","abstract_canon_sha256":"fdc0b89abc3ec78fd74260a7d65199851733f89ddf335e0e004d5957ecad6130"},"schema_version":"1.0"},"canonical_sha256":"6dd702de02db5dda2add628fb29aa3651aedf4467025d617f3fc40eb8649aa48","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T16:35:02.586705Z","signature_b64":"nXgzDejnj6uOTZjSbdetO1Pd/h1eYPtsJGKjVyjDMQHsCdj4d/im+eIHbYaQPyFEqV3achUrPBrapeMmCmm/AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6dd702de02db5dda2add628fb29aa3651aedf4467025d617f3fc40eb8649aa48","last_reissued_at":"2026-07-04T16:35:02.586266Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T16:35:02.586266Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math-ph/0204001","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":"2026-07-04T16:35:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"V1nzuI8R81JmjD4veHe/BqLPQ0GSO4VDB/dNY6u4W41FB0w/YIRTb6Et5pPzGuyTe3FiQU9e3nKs+7+MkK2BCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T19:38:07.039154Z"},"content_sha256":"0d07f8f529833aadeaf7d46ababd7fa16b886a9c6d7549dd1165785e886b82f2","schema_version":"1.0","event_id":"sha256:0d07f8f529833aadeaf7d46ababd7fa16b886a9c6d7549dd1165785e886b82f2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2002:NXLQFXQC3NO5UKW5MKH3FGVDMU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Distribution of the first particle in discrete orthogonal polynomial ensembles","license":"","headline":"","cross_cats":["cond-mat","hep-th","math.CA","math.MP","nlin.SI"],"primary_cat":"math-ph","authors_text":"Alexei Borodin, Dmitriy Boyarchenko","submitted_at":"2002-04-01T19:34:19Z","abstract_excerpt":"We show that the distribution function of the first particle in a discrete orthogonal polynomial ensemble can be obtained through a certain recurrence procedure, if the (difference or q-) log-derivative of the weight function is rational. In a number of classical special cases the recurrence procedure is equivalent to the difference and q-Painleve equations of chao-dyn/9507010, [Sakai].\n  Our approach is based on the formalism of discrete integrable operators and discrete Riemann--Hilbert problems developed in math.CO/9912093, math-ph/0111008."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0204001","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/math-ph/0204001/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":"2026-07-04T16:35:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mKEDUNYoUMP/KqPFqfvgJ3dO0hOVN6EYog87KnpIYaFOVwQXLKT9uv7GvC8U738fqBOdqiS0ohJqPbZ56QtCBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T19:38:07.040077Z"},"content_sha256":"8f422e8f118af6388804d72ff4df5a01ad201c8e6e1735ba79d7323f59eb488c","schema_version":"1.0","event_id":"sha256:8f422e8f118af6388804d72ff4df5a01ad201c8e6e1735ba79d7323f59eb488c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NXLQFXQC3NO5UKW5MKH3FGVDMU/bundle.json","state_url":"https://pith.science/pith/NXLQFXQC3NO5UKW5MKH3FGVDMU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NXLQFXQC3NO5UKW5MKH3FGVDMU/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":"2026-08-17T19:38:07Z","links":{"resolver":"https://pith.science/pith/NXLQFXQC3NO5UKW5MKH3FGVDMU","bundle":"https://pith.science/pith/NXLQFXQC3NO5UKW5MKH3FGVDMU/bundle.json","state":"https://pith.science/pith/NXLQFXQC3NO5UKW5MKH3FGVDMU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NXLQFXQC3NO5UKW5MKH3FGVDMU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2002:NXLQFXQC3NO5UKW5MKH3FGVDMU","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":"fdc0b89abc3ec78fd74260a7d65199851733f89ddf335e0e004d5957ecad6130","cross_cats_sorted":["cond-mat","hep-th","math.CA","math.MP","nlin.SI"],"license":"","primary_cat":"math-ph","submitted_at":"2002-04-01T19:34:19Z","title_canon_sha256":"28ad42e9f3f5c6f938bb72e7c63fb756034092296b04f5616fc33492dd5c56ae"},"schema_version":"1.0","source":{"id":"math-ph/0204001","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0204001","created_at":"2026-07-04T16:35:02Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0204001v1","created_at":"2026-07-04T16:35:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0204001","created_at":"2026-07-04T16:35:02Z"},{"alias_kind":"pith_short_12","alias_value":"NXLQFXQC3NO5","created_at":"2026-07-04T16:35:02Z"},{"alias_kind":"pith_short_16","alias_value":"NXLQFXQC3NO5UKW5","created_at":"2026-07-04T16:35:02Z"},{"alias_kind":"pith_short_8","alias_value":"NXLQFXQC","created_at":"2026-07-04T16:35:02Z"}],"graph_snapshots":[{"event_id":"sha256:8f422e8f118af6388804d72ff4df5a01ad201c8e6e1735ba79d7323f59eb488c","target":"graph","created_at":"2026-07-04T16:35:02Z","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/0204001/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We show that the distribution function of the first particle in a discrete orthogonal polynomial ensemble can be obtained through a certain recurrence procedure, if the (difference or q-) log-derivative of the weight function is rational. In a number of classical special cases the recurrence procedure is equivalent to the difference and q-Painleve equations of chao-dyn/9507010, [Sakai].\n  Our approach is based on the formalism of discrete integrable operators and discrete Riemann--Hilbert problems developed in math.CO/9912093, math-ph/0111008.","authors_text":"Alexei Borodin, Dmitriy Boyarchenko","cross_cats":["cond-mat","hep-th","math.CA","math.MP","nlin.SI"],"headline":"","license":"","primary_cat":"math-ph","submitted_at":"2002-04-01T19:34:19Z","title":"Distribution of the first particle in discrete orthogonal polynomial ensembles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0204001","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":"sha256:0d07f8f529833aadeaf7d46ababd7fa16b886a9c6d7549dd1165785e886b82f2","target":"record","created_at":"2026-07-04T16:35:02Z","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":"fdc0b89abc3ec78fd74260a7d65199851733f89ddf335e0e004d5957ecad6130","cross_cats_sorted":["cond-mat","hep-th","math.CA","math.MP","nlin.SI"],"license":"","primary_cat":"math-ph","submitted_at":"2002-04-01T19:34:19Z","title_canon_sha256":"28ad42e9f3f5c6f938bb72e7c63fb756034092296b04f5616fc33492dd5c56ae"},"schema_version":"1.0","source":{"id":"math-ph/0204001","kind":"arxiv","version":1}},"canonical_sha256":"6dd702de02db5dda2add628fb29aa3651aedf4467025d617f3fc40eb8649aa48","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6dd702de02db5dda2add628fb29aa3651aedf4467025d617f3fc40eb8649aa48","first_computed_at":"2026-07-04T16:35:02.586266Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T16:35:02.586266Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nXgzDejnj6uOTZjSbdetO1Pd/h1eYPtsJGKjVyjDMQHsCdj4d/im+eIHbYaQPyFEqV3achUrPBrapeMmCmm/AA==","signature_status":"signed_v1","signed_at":"2026-07-04T16:35:02.586705Z","signed_message":"canonical_sha256_bytes"},"source_id":"math-ph/0204001","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0d07f8f529833aadeaf7d46ababd7fa16b886a9c6d7549dd1165785e886b82f2","sha256:8f422e8f118af6388804d72ff4df5a01ad201c8e6e1735ba79d7323f59eb488c"],"state_sha256":"5a6bde7b30243f706a1c20aefe47efacce110414112dc43beab388a4b8fc41db"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"l+XGcbnWr2oyfJ6BLCgUhO88L4lphJS1bB0ZG2R5FtR+8XtIqCRI62TpkoQj7pQQFoyLmgLIqk5AB0ax2szOBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-17T19:38:07.047697Z","bundle_sha256":"51caa78bac1eac4d86f050e04ec284129347c5c9e2bfc263839d54007ab5cdb8"}}