{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:77A7ZWJZIWWHASS4LJCWRQPQWM","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":"4937f0ec789b8baf78bcadda5c6175e2170b536876ebb7a2af35d9c657935081","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2013-04-09T22:09:37Z","title_canon_sha256":"b323ffe5c3e16536232f598783c9bdb21a3ca3d4cb6aa624e8c567e878f1320e"},"schema_version":"1.0","source":{"id":"1304.2805","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.2805","created_at":"2026-05-18T03:28:28Z"},{"alias_kind":"arxiv_version","alias_value":"1304.2805v1","created_at":"2026-05-18T03:28:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.2805","created_at":"2026-05-18T03:28:28Z"},{"alias_kind":"pith_short_12","alias_value":"77A7ZWJZIWWH","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"77A7ZWJZIWWHASS4","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"77A7ZWJZ","created_at":"2026-05-18T12:27:36Z"}],"graph_snapshots":[{"event_id":"sha256:911660447f73c2a53f58fb8ac86438d96015ca824492923ad73565acb0d69bcc","target":"graph","created_at":"2026-05-18T03:28:28Z","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 show that a large class of limit-periodic Schr\\\"odinger operators has purely absolutely continuous spectrum in arbitrary dimensions. This result was previously known only in dimension one.\n  The proof proceeds through the non-perturbative construction of limit-periodic extended states. An essential step is a new estimate of the probability (in quasi-momentum) that the Floquet Bloch operators have only simple eigenvalues.","authors_text":"Helge Krueger","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2013-04-09T22:09:37Z","title":"Absolutely continuous spectrum for limit-periodic Schr\\\"odinger operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.2805","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":"sha256:9683dc71811ad0367a65cd857e8cb760ec117e31af2f8f7589832c83e5df385c","target":"record","created_at":"2026-05-18T03:28:28Z","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":"4937f0ec789b8baf78bcadda5c6175e2170b536876ebb7a2af35d9c657935081","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2013-04-09T22:09:37Z","title_canon_sha256":"b323ffe5c3e16536232f598783c9bdb21a3ca3d4cb6aa624e8c567e878f1320e"},"schema_version":"1.0","source":{"id":"1304.2805","kind":"arxiv","version":1}},"canonical_sha256":"ffc1fcd93945ac704a5c5a4568c1f0b314bb8b9415d3f514dddfd1ace0976f50","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ffc1fcd93945ac704a5c5a4568c1f0b314bb8b9415d3f514dddfd1ace0976f50","first_computed_at":"2026-05-18T03:28:28.187052Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:28:28.187052Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZX0aLnhmU5ZkRwZPy+/7NmipE8v8yHDbNM8XXYYRnZFc3jgiVeNkwTvCHoWMjiizhqLLOZNVUyHLG/Or7dWNCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:28:28.187781Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.2805","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9683dc71811ad0367a65cd857e8cb760ec117e31af2f8f7589832c83e5df385c","sha256:911660447f73c2a53f58fb8ac86438d96015ca824492923ad73565acb0d69bcc"],"state_sha256":"ea75eed50f5eebb8d6e2ff43350ec8e2234cd79f57f3d63166253d7860778eb9"}