{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:XZFIFPJELC3PAZI6G4IMDANALX","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":"12c59ffd13533e963b6494d0c22974c95405f7f06b415fcd9729e72a000df662","cross_cats_sorted":["math-ph","math.MP"],"license":"","primary_cat":"math.SP","submitted_at":"2007-12-14T11:32:08Z","title_canon_sha256":"6434048704e1e17449e03ea02f05eeb5e3c493f840ff2d64a037d466202d66d4"},"schema_version":"1.0","source":{"id":"0712.2323","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0712.2323","created_at":"2026-05-18T03:06:05Z"},{"alias_kind":"arxiv_version","alias_value":"0712.2323v2","created_at":"2026-05-18T03:06:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0712.2323","created_at":"2026-05-18T03:06:05Z"},{"alias_kind":"pith_short_12","alias_value":"XZFIFPJELC3P","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"XZFIFPJELC3PAZI6","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"XZFIFPJE","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:7556a4f548fa09d60279abdb899612793f29f67d201317530c425ff611fa8cbc","target":"graph","created_at":"2026-05-18T03:06:05Z","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 consider standard subordinacy theory for general Sturm--Liouville operators and give criteria when boundedness of solutions implies that no subordinate solutions exist. As applications, we prove a Weidmann-type result for general Sturm--Liouville operators and investigate the absolutely continuous spectrum of radially symmetric quantum trees.","authors_text":"Gerald Teschl, Michael Schmied, Robert Sims","cross_cats":["math-ph","math.MP"],"headline":"","license":"","primary_cat":"math.SP","submitted_at":"2007-12-14T11:32:08Z","title":"On the Absolutely Continuous Spectrum of Sturm-Liouville Operators with Applications to Radial Quantum Trees"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0712.2323","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":"sha256:63e8a15b23c4b7d2d1a29a777b63598982c1999ecf3b3a2ad9cbedb939c6d2cb","target":"record","created_at":"2026-05-18T03:06:05Z","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":"12c59ffd13533e963b6494d0c22974c95405f7f06b415fcd9729e72a000df662","cross_cats_sorted":["math-ph","math.MP"],"license":"","primary_cat":"math.SP","submitted_at":"2007-12-14T11:32:08Z","title_canon_sha256":"6434048704e1e17449e03ea02f05eeb5e3c493f840ff2d64a037d466202d66d4"},"schema_version":"1.0","source":{"id":"0712.2323","kind":"arxiv","version":2}},"canonical_sha256":"be4a82bd2458b6f0651e3710c181a05df8543fd1477638345b6e5ebf1e8dab2b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"be4a82bd2458b6f0651e3710c181a05df8543fd1477638345b6e5ebf1e8dab2b","first_computed_at":"2026-05-18T03:06:05.770723Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:06:05.770723Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yhVfACob/SsIHCGdTwTIkNFN/KDAQ7CSDkMxQMJTyMUpKqna7QSfjZPN3tnPovegZ3Fov7prkTf2n6FB8fouCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:06:05.771056Z","signed_message":"canonical_sha256_bytes"},"source_id":"0712.2323","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:63e8a15b23c4b7d2d1a29a777b63598982c1999ecf3b3a2ad9cbedb939c6d2cb","sha256:7556a4f548fa09d60279abdb899612793f29f67d201317530c425ff611fa8cbc"],"state_sha256":"af9eb7ef269595c6583e11ab1cf9d92e0799baf6da6aab87e2de8a9eff10fe12"}