{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:BGEYQHCD7KE4CMXVRS4QJGYGA7","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":"5514451e3eb6672922a8f6db196e6f8c45d42997d5d1e9be1d2341c535339acb","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2007-02-13T19:07:18Z","title_canon_sha256":"9e52f74dc5475a48d17e129d1f81f45aea62481db72085ac0540511be14ecca0"},"schema_version":"1.0","source":{"id":"math/0702388","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0702388","created_at":"2026-05-18T02:30:23Z"},{"alias_kind":"arxiv_version","alias_value":"math/0702388v2","created_at":"2026-05-18T02:30:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0702388","created_at":"2026-05-18T02:30:23Z"},{"alias_kind":"pith_short_12","alias_value":"BGEYQHCD7KE4","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"BGEYQHCD7KE4CMXV","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"BGEYQHCD","created_at":"2026-05-18T12:25:55Z"}],"graph_snapshots":[{"event_id":"sha256:c988a6c44f9440670b949cfaf4eda0fd763588467852a27436a3e586581af6cc","target":"graph","created_at":"2026-05-18T02:30:23Z","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 extend the results of Denisov-Rakhmanov, Szego-Shohat-Nevai, and Killip-Simon from asymptotically constant orthogonal polynomials on the real line (OPRL) and unit circle (OPUC) to asymptotically periodic OPRL and OPUC. The key tool is a characterization of the isospectral torus that is well adapted to the study of perturbations.","authors_text":"Barry Simon (Caltech), David Damanik (Rice), Rowan Killip (UCLA)","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2007-02-13T19:07:18Z","title":"Perturbations of Orthogonal Polynomials With Periodic Recursion Coefficients"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0702388","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":"sha256:8fcfd6ada92e66fd7d5ad93caa408ad5159c844c0e80234341fb81271d610d5f","target":"record","created_at":"2026-05-18T02:30:23Z","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":"5514451e3eb6672922a8f6db196e6f8c45d42997d5d1e9be1d2341c535339acb","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2007-02-13T19:07:18Z","title_canon_sha256":"9e52f74dc5475a48d17e129d1f81f45aea62481db72085ac0540511be14ecca0"},"schema_version":"1.0","source":{"id":"math/0702388","kind":"arxiv","version":2}},"canonical_sha256":"0989881c43fa89c132f58cb9049b0607caf3e0585c18a0eb1271152bd603e71a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0989881c43fa89c132f58cb9049b0607caf3e0585c18a0eb1271152bd603e71a","first_computed_at":"2026-05-18T02:30:23.103558Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:30:23.103558Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9cFo6uyUfAj+SxABp2Cylhf+3PdsjGKabo9tdXyX1McyyXJ+5pBgSvsvNwT8OOCPYAnKL9PQHkDn8QVEzuuRDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:30:23.103971Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0702388","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8fcfd6ada92e66fd7d5ad93caa408ad5159c844c0e80234341fb81271d610d5f","sha256:c988a6c44f9440670b949cfaf4eda0fd763588467852a27436a3e586581af6cc"],"state_sha256":"86df8adbcb90afaa6157bb2f7d05217bc58ffa236e3c49b48a2be38e4e572109"}