{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:WCPEDYTIGB7ZQNJK3IQW45MSID","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":"feed1049767c9b67054d8b7e5b22eab8705649df4b627f95d5c92286256c31a8","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2018-09-08T00:00:52Z","title_canon_sha256":"4f45f957be40e9ee69d9b48ba5dabd1e2d18338d98e581d4f03c91cb0cc25b9e"},"schema_version":"1.0","source":{"id":"1809.02720","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.02720","created_at":"2026-05-17T23:47:20Z"},{"alias_kind":"arxiv_version","alias_value":"1809.02720v1","created_at":"2026-05-17T23:47:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.02720","created_at":"2026-05-17T23:47:20Z"},{"alias_kind":"pith_short_12","alias_value":"WCPEDYTIGB7Z","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"WCPEDYTIGB7ZQNJK","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"WCPEDYTI","created_at":"2026-05-18T12:32:59Z"}],"graph_snapshots":[{"event_id":"sha256:90062056f315383840b8737e923614ab28502e8c103e9d6cf09bbcd5be11ec7e","target":"graph","created_at":"2026-05-17T23:47:20Z","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 construct multidimensional almost-periodic Schr\\\"odinger operators whose spectrum has zero lower box counting dimension. In particular, the spectrum in these cases is a generalized Cantor set of zero Lebesgue measure.","authors_text":"Anton Gorodetski (UC Irvine), David Damanik (Rice University), Jake Fillman (Virginia Tech)","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2018-09-08T00:00:52Z","title":"Multidimensional Almost-Periodic Schr\\\"odinger Operators with Cantor Spectrum"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.02720","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":"sha256:9e969bfa7c0322e188dbeb7a5dc8999bc7a3011ab0bc90e025bf603beb7a942e","target":"record","created_at":"2026-05-17T23:47:20Z","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":"feed1049767c9b67054d8b7e5b22eab8705649df4b627f95d5c92286256c31a8","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2018-09-08T00:00:52Z","title_canon_sha256":"4f45f957be40e9ee69d9b48ba5dabd1e2d18338d98e581d4f03c91cb0cc25b9e"},"schema_version":"1.0","source":{"id":"1809.02720","kind":"arxiv","version":1}},"canonical_sha256":"b09e41e268307f98352ada216e759240edc2cf017c7cf824d84e0f0749a657ce","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b09e41e268307f98352ada216e759240edc2cf017c7cf824d84e0f0749a657ce","first_computed_at":"2026-05-17T23:47:20.487149Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:47:20.487149Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SgyurKkfzNwq/G7fJiZ891uQtkull2AaWCrKjX5SgJxRwttn+Ovgy0vSuQ9EnDnIj8aVOVzU1sQFVbr+dA7AAw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:47:20.487749Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.02720","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9e969bfa7c0322e188dbeb7a5dc8999bc7a3011ab0bc90e025bf603beb7a942e","sha256:90062056f315383840b8737e923614ab28502e8c103e9d6cf09bbcd5be11ec7e"],"state_sha256":"854ee947a147b076a4d439edea872f97bcf45cf065586f911658b09d2bcc984c"}