{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:S4JL7GGUDHBR2OIBXPD5BCIOPE","merge_version":"pith-open-graph-merge-v1","event_count":4,"valid_event_count":4,"invalid_event_count":0,"equivocation_count":1,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"2d06521a8a68aa83a2af994ce49fc5ad437c92182ebb298df55b0d386f46c00f","cross_cats_sorted":["math-ph","math.MP","math.PR","math.SP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CA","submitted_at":"2026-08-01T17:39:04Z","title_canon_sha256":"51f02b8288f8481e0e2634c9586600b38f2afa69181d505183f8bf5f426b32fc"},"schema_version":"1.0","source":{"id":"2608.00788","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.00788","created_at":"2026-08-04T01:55:09Z"},{"alias_kind":"arxiv_version","alias_value":"2608.00788v1","created_at":"2026-08-04T01:55:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.00788","created_at":"2026-08-04T01:55:09Z"},{"alias_kind":"pith_short_12","alias_value":"S4JL7GGUDHBR","created_at":"2026-08-04T01:55:09Z"},{"alias_kind":"pith_short_16","alias_value":"S4JL7GGUDHBR2OIB","created_at":"2026-08-04T01:55:09Z"},{"alias_kind":"pith_short_8","alias_value":"S4JL7GGU","created_at":"2026-08-04T01:55:09Z"}],"graph_snapshots":[{"event_id":"sha256:83f32eb82c0fa905b64d271a707ad2d008d8c803b653338f8d25668e6872fa26","target":"graph","created_at":"2026-08-04T01:55:09Z","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/2608.00788/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"An ordered positive bidiagonal factorization (PBF) is used to develop a spectral and probabilistic theory for Markov transition matrices of arbitrary finite bandwidth. The factors determine two families of mixed-type multiple orthogonal polynomials, an entrywise positive $q\\times p$ matrix of measures, and a sequence of elementary death-or-stay and birth-or-stay transitions. This yields Karlin-McGregor formulas for transition probabilities, Green kernels, resolvents, potentials, and first-passage transforms without reversibility or block symmetrizability. Rational stochastic PBFs are character","authors_text":"Manuel Ma\\~nas","cross_cats":["math-ph","math.MP","math.PR","math.SP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CA","submitted_at":"2026-08-01T17:39:04Z","title":"Positive Bidiagonal Factorizations for Banded Markov Processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.00788","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":"sha256:39210ec69d790f1be237511ea0500679611c5c86a17493c5554740aec5613666","target":"record","created_at":"2026-08-04T01:55:09Z","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":"2d06521a8a68aa83a2af994ce49fc5ad437c92182ebb298df55b0d386f46c00f","cross_cats_sorted":["math-ph","math.MP","math.PR","math.SP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CA","submitted_at":"2026-08-01T17:39:04Z","title_canon_sha256":"51f02b8288f8481e0e2634c9586600b38f2afa69181d505183f8bf5f426b32fc"},"schema_version":"1.0","source":{"id":"2608.00788","kind":"arxiv","version":1}},"canonical_sha256":"9712bf98d419c31d3901bbc7d0890e7912543354755c8ef6953d5c744276508f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9712bf98d419c31d3901bbc7d0890e7912543354755c8ef6953d5c744276508f","first_computed_at":"2026-08-04T01:55:09.096826Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-04T01:55:09.096826Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KVMJ8X7PVfggXx16VUUoqzi1b97uKwhSz1VgewnvRkphhqt6WA/kTc3p2NSk6Lf7z7yeqSRdwzg/lWrpmOaKAw==","signature_status":"signed_v1","signed_at":"2026-08-04T01:55:09.098225Z","signed_message":"canonical_sha256_bytes"},"source_id":"2608.00788","source_kind":"arxiv","source_version":1}}},"equivocations":[{"signer_id":"pith.science","event_type":"integrity_finding","target":"integrity","event_ids":["sha256:091d8de0e7555c517fb9e6b179191ace8db13ea3ce18a134e054420211c10221","sha256:1c5cbd5961811a8372f088c0e7528acc56b3edbd260240c523df00518e7386a2"]}],"invalid_events":[],"applied_event_ids":["sha256:39210ec69d790f1be237511ea0500679611c5c86a17493c5554740aec5613666","sha256:83f32eb82c0fa905b64d271a707ad2d008d8c803b653338f8d25668e6872fa26"],"state_sha256":"8e4d9a2c5234085ac7669823ec009dda160264aa1e5a6bf36e70069627ac6155"}