{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:N74N6NDUYDCB52UISBUJE26IOE","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":"227daea32bcf3130aafccac57a9630fe5dde4d694e190186ee5024253d1b7b90","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2015-02-19T02:06:40Z","title_canon_sha256":"3dc8e1c3876a0171cdc81d88d93ed5e450f854e3a677d0d937783d3b1c2129f2"},"schema_version":"1.0","source":{"id":"1502.05454","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.05454","created_at":"2026-05-18T01:37:11Z"},{"alias_kind":"arxiv_version","alias_value":"1502.05454v2","created_at":"2026-05-18T01:37:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.05454","created_at":"2026-05-18T01:37:11Z"},{"alias_kind":"pith_short_12","alias_value":"N74N6NDUYDCB","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"N74N6NDUYDCB52UI","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"N74N6NDU","created_at":"2026-05-18T12:29:32Z"}],"graph_snapshots":[{"event_id":"sha256:568dd4f8b75972f502da54d3592fdb2739085265aa35b632442f19bca1b34738","target":"graph","created_at":"2026-05-18T01:37:11Z","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 prove that the spectrum of a limit-periodic Schr\\\"odinger operator is homogeneous in the sense of Carleson whenever the potential obeys the Pastur--Tkachenko condition. This implies that a dense set of limit-periodic Schr\\\"odinger operators have purely absolutely continuous spectrum supported on a homogeneous Cantor set. When combined with work of Gesztesy--Yuditskii, this also implies that the spectrum of a Pastur--Tkachenko potential has infinite gap length whenever the potential fails to be uniformly almost periodic.","authors_text":"Jake Fillman, Milivoje Lukic","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2015-02-19T02:06:40Z","title":"Spectral Homogeneity of Limit-Periodic Schr\\\"odinger Operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.05454","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":"sha256:122e7e4dd024874da75b9126a1927ac65a94cb1c2d5b4d08806898dc85ab0c5a","target":"record","created_at":"2026-05-18T01:37:11Z","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":"227daea32bcf3130aafccac57a9630fe5dde4d694e190186ee5024253d1b7b90","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2015-02-19T02:06:40Z","title_canon_sha256":"3dc8e1c3876a0171cdc81d88d93ed5e450f854e3a677d0d937783d3b1c2129f2"},"schema_version":"1.0","source":{"id":"1502.05454","kind":"arxiv","version":2}},"canonical_sha256":"6ff8df3474c0c41eea889068926bc8712897424f5f3bdd6ba82b594496c254c4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6ff8df3474c0c41eea889068926bc8712897424f5f3bdd6ba82b594496c254c4","first_computed_at":"2026-05-18T01:37:11.021777Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:37:11.021777Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bXOqA3d1t/8Kdxi2atGMxPFP4Mz7Auq+pIq+haV/3uTKME7OdCYqJZ+14A+oXIUWugwfvDOm0PzRZGtGWSSnDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:37:11.022201Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.05454","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:122e7e4dd024874da75b9126a1927ac65a94cb1c2d5b4d08806898dc85ab0c5a","sha256:568dd4f8b75972f502da54d3592fdb2739085265aa35b632442f19bca1b34738"],"state_sha256":"59061969693e9f17f31ffa1338a62b78949f2c1a06835dfbd8528d572e5f1c11"}