{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:RIGWE2MVSU25QWSCTKPXFMMCGA","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":"96670cc175b899d08b02cd5820d28fbba3faebd78fb22df4651d35b5979fd898","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2015-12-23T21:22:39Z","title_canon_sha256":"b51509e54fa11ddf561743874a5bbff6ba1e3bb4fa44794cfc2f9a3dcfb18891"},"schema_version":"1.0","source":{"id":"1512.07641","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.07641","created_at":"2026-05-18T00:49:47Z"},{"alias_kind":"arxiv_version","alias_value":"1512.07641v1","created_at":"2026-05-18T00:49:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.07641","created_at":"2026-05-18T00:49:47Z"},{"alias_kind":"pith_short_12","alias_value":"RIGWE2MVSU25","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"RIGWE2MVSU25QWSC","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"RIGWE2MV","created_at":"2026-05-18T12:29:39Z"}],"graph_snapshots":[{"event_id":"sha256:003671ae77013b2c0ff1a31ab04983aa9c904179bd6e17af9d06301b187e5c20","target":"graph","created_at":"2026-05-18T00:49:47Z","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 spectral characteristics of a one-dimensional quantum walk whose coins are distributed quasi-periodically. The unitary update rule of this quantum walk shares many spectral characteristics with the critical Almost-Mathieu Operator; however, it possesses a feature not present in the Almost-Mathieu Operator, namely singularity of the associated cocycles (this feature is, however, present in the so-called Extended Harper's Model). We show that this operator has empty absolutely continuous spectrum and that the Lyapunov exponent vanishes on the spectrum; hence, this model exhibits Canto","authors_text":"Darren C. Ong, Jake Fillman, Zhenghe Zhang","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2015-12-23T21:22:39Z","title":"Spectral Characteristics of the Unitary Critical Almost-Mathieu Operator"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.07641","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":"sha256:98acc129241c254b33845f594f0f72f1522f3f0e95d24754e1003d3e82f8a06b","target":"record","created_at":"2026-05-18T00:49:47Z","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":"96670cc175b899d08b02cd5820d28fbba3faebd78fb22df4651d35b5979fd898","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2015-12-23T21:22:39Z","title_canon_sha256":"b51509e54fa11ddf561743874a5bbff6ba1e3bb4fa44794cfc2f9a3dcfb18891"},"schema_version":"1.0","source":{"id":"1512.07641","kind":"arxiv","version":1}},"canonical_sha256":"8a0d6269959535d85a429a9f72b1823016d9e823251368dafe96f068a1e92a64","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8a0d6269959535d85a429a9f72b1823016d9e823251368dafe96f068a1e92a64","first_computed_at":"2026-05-18T00:49:47.185288Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:49:47.185288Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7v8fwYaTSN6041XlDtlU4zFlfH92XOlsLJQsve4hgDVV9hQq5ReIftnbpxGuTYM8hIQ9C/Gz3mPUKEzr8ANBAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:49:47.185973Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.07641","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:98acc129241c254b33845f594f0f72f1522f3f0e95d24754e1003d3e82f8a06b","sha256:003671ae77013b2c0ff1a31ab04983aa9c904179bd6e17af9d06301b187e5c20"],"state_sha256":"7561e6b6a1ad0d9ec627f26a716cd5e67ffd3b607e06ec8a1fa9f88131d4e321"}