{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:ZXGQXJ3ZADKXGSMIUWGJGB3VEW","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":"93acda5aedbfc9c936268fa340c3accb54194c7253d149cc91cd082fdd1d2afe","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2012-07-20T23:36:13Z","title_canon_sha256":"e0b223315fbcce43b8241f8457c53f8b11d60dde85dcc643333bea8d136c958d"},"schema_version":"1.0","source":{"id":"1207.5077","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.5077","created_at":"2026-05-18T01:56:15Z"},{"alias_kind":"arxiv_version","alias_value":"1207.5077v1","created_at":"2026-05-18T01:56:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.5077","created_at":"2026-05-18T01:56:15Z"},{"alias_kind":"pith_short_12","alias_value":"ZXGQXJ3ZADKX","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"ZXGQXJ3ZADKXGSMI","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"ZXGQXJ3Z","created_at":"2026-05-18T12:27:30Z"}],"graph_snapshots":[{"event_id":"sha256:6ece37d730477c70f5085ab09fc614913c18d00394dc36b1f859dd7d1964a6cf","target":"graph","created_at":"2026-05-18T01:56:15Z","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 discuss Schr\\\"odinger operators on a half-line with decaying oscillatory potentials, such as products of an almost periodic function and a decaying function. We provide sufficient conditions for preservation of absolutely continuous spectrum and give bounds on the Hausdorff dimension of the singular part of the spectral measure. We also discuss the analogs for orthogonal polynomials on the real line and unit circle.","authors_text":"Milivoje Lukic","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2012-07-20T23:36:13Z","title":"A class of Schrodinger operators with decaying oscillatory potentials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.5077","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":"sha256:31cee9f6e7f42549f38f4f7f42d1f8015f55f9ab5ef13263d2fe51ee0310fc8d","target":"record","created_at":"2026-05-18T01:56:15Z","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":"93acda5aedbfc9c936268fa340c3accb54194c7253d149cc91cd082fdd1d2afe","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2012-07-20T23:36:13Z","title_canon_sha256":"e0b223315fbcce43b8241f8457c53f8b11d60dde85dcc643333bea8d136c958d"},"schema_version":"1.0","source":{"id":"1207.5077","kind":"arxiv","version":1}},"canonical_sha256":"cdcd0ba77900d5734988a58c93077525902498f328616be69e3858f1ff7ee2f5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cdcd0ba77900d5734988a58c93077525902498f328616be69e3858f1ff7ee2f5","first_computed_at":"2026-05-18T01:56:15.486245Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:56:15.486245Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bAhRcB27bsyfirbc0Ru1BRqHP1pxOsorFd/sYrdsQYlmi9GAmVujbTcErjmUGFbywUhDJB+ArHowuHgPEZ6sCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:56:15.486739Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.5077","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:31cee9f6e7f42549f38f4f7f42d1f8015f55f9ab5ef13263d2fe51ee0310fc8d","sha256:6ece37d730477c70f5085ab09fc614913c18d00394dc36b1f859dd7d1964a6cf"],"state_sha256":"332f9e0e50ed2cccd1eb1dfa4f1573dd42b15a8493942f279c5d6f5d9ad0da3a"}