{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:7VQULFC3QWQL3CCGUJHT4OLTX5","short_pith_number":"pith:7VQULFC3","schema_version":"1.0","canonical_sha256":"fd6145945b85a0bd8846a24f3e3973bf410d15eac2f9fe1e1e0049b63062311a","source":{"kind":"arxiv","id":"2307.10909","version":1},"attestation_state":"computed","paper":{"title":"Exact mobility edges for almost-periodic CMV matrices via gauge symmetries","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.FA","math.MP","quant-ph"],"primary_cat":"math.SP","authors_text":"Christopher Cedzich, Darren Ong, Jake Fillman, Long Li, Qi Zhou","submitted_at":"2023-07-20T14:31:14Z","abstract_excerpt":"We investigate the symmetries of so-called generalized extended CMV matrices. It is well-documented that problems involving reflection symmetries of standard extended CMV matrices can be subtle. We show how to deal with this in an elegant fashion by passing to the class of generalized extended CMV matrices via explicit diagonal unitaries in the spirit of Cantero-Gr\\\"unbaum-Moral-Vel\\'azquez. As an application of these ideas, we construct an explicit family of almost-periodic CMV matrices, which we call the mosaic unitary almost-Mathieu operator, and prove the occurrence of exact mobility edges"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2307.10909","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2023-07-20T14:31:14Z","cross_cats_sorted":["math-ph","math.FA","math.MP","quant-ph"],"title_canon_sha256":"50fe3c3e9b2355aebd0d2c6ed466ec0170b52e9e8546612ddf3f763579215722","abstract_canon_sha256":"a92794faa8b27a17297a72a4749943e0747d8e8cf3a88502797e9bb4d5e321aa"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:16:44.308398Z","signature_b64":"Uji5oNDu22+tadCw/g0LN5MByFRkVeSOHaKPpmHl2z6NzGzLVCT3xZOUc7nzhIrSCkOirYkbL1Am2Ibfsm2/AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fd6145945b85a0bd8846a24f3e3973bf410d15eac2f9fe1e1e0049b63062311a","last_reissued_at":"2026-07-05T09:16:44.307861Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:16:44.307861Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Exact mobility edges for almost-periodic CMV matrices via gauge symmetries","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.FA","math.MP","quant-ph"],"primary_cat":"math.SP","authors_text":"Christopher Cedzich, Darren Ong, Jake Fillman, Long Li, Qi Zhou","submitted_at":"2023-07-20T14:31:14Z","abstract_excerpt":"We investigate the symmetries of so-called generalized extended CMV matrices. It is well-documented that problems involving reflection symmetries of standard extended CMV matrices can be subtle. We show how to deal with this in an elegant fashion by passing to the class of generalized extended CMV matrices via explicit diagonal unitaries in the spirit of Cantero-Gr\\\"unbaum-Moral-Vel\\'azquez. As an application of these ideas, we construct an explicit family of almost-periodic CMV matrices, which we call the mosaic unitary almost-Mathieu operator, and prove the occurrence of exact mobility edges"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2307.10909","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2307.10909/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2307.10909","created_at":"2026-07-05T09:16:44.307928+00:00"},{"alias_kind":"arxiv_version","alias_value":"2307.10909v1","created_at":"2026-07-05T09:16:44.307928+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2307.10909","created_at":"2026-07-05T09:16:44.307928+00:00"},{"alias_kind":"pith_short_12","alias_value":"7VQULFC3QWQL","created_at":"2026-07-05T09:16:44.307928+00:00"},{"alias_kind":"pith_short_16","alias_value":"7VQULFC3QWQL3CCG","created_at":"2026-07-05T09:16:44.307928+00:00"},{"alias_kind":"pith_short_8","alias_value":"7VQULFC3","created_at":"2026-07-05T09:16:44.307928+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":3,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.27740","citing_title":"Bottleneck Effects and Harmonic-Type Velocity Bounds for Periodic Quantum Walks","ref_index":17,"is_internal_anchor":false},{"citing_arxiv_id":"2411.16843","citing_title":"Mobility edges in pseudo-unitary quasiperiodic quantum walks","ref_index":25,"is_internal_anchor":false},{"citing_arxiv_id":"2604.20654","citing_title":"Absence of Ballistic Transport in Quantum Walks with Asymptotically Reflecting Sites","ref_index":15,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/7VQULFC3QWQL3CCGUJHT4OLTX5","json":"https://pith.science/pith/7VQULFC3QWQL3CCGUJHT4OLTX5.json","graph_json":"https://pith.science/api/pith-number/7VQULFC3QWQL3CCGUJHT4OLTX5/graph.json","events_json":"https://pith.science/api/pith-number/7VQULFC3QWQL3CCGUJHT4OLTX5/events.json","paper":"https://pith.science/paper/7VQULFC3"},"agent_actions":{"view_html":"https://pith.science/pith/7VQULFC3QWQL3CCGUJHT4OLTX5","download_json":"https://pith.science/pith/7VQULFC3QWQL3CCGUJHT4OLTX5.json","view_paper":"https://pith.science/paper/7VQULFC3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2307.10909&json=true","fetch_graph":"https://pith.science/api/pith-number/7VQULFC3QWQL3CCGUJHT4OLTX5/graph.json","fetch_events":"https://pith.science/api/pith-number/7VQULFC3QWQL3CCGUJHT4OLTX5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7VQULFC3QWQL3CCGUJHT4OLTX5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7VQULFC3QWQL3CCGUJHT4OLTX5/action/storage_attestation","attest_author":"https://pith.science/pith/7VQULFC3QWQL3CCGUJHT4OLTX5/action/author_attestation","sign_citation":"https://pith.science/pith/7VQULFC3QWQL3CCGUJHT4OLTX5/action/citation_signature","submit_replication":"https://pith.science/pith/7VQULFC3QWQL3CCGUJHT4OLTX5/action/replication_record"}},"created_at":"2026-07-05T09:16:44.307928+00:00","updated_at":"2026-07-05T09:16:44.307928+00:00"}