{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:4PX4INNGQEHGUZXV3URPUB3JKB","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":"dfdee1cbda5e8fe7c89ae3969f0b58f515d4a39ffacaaf7927e7a6e055293fbe","cross_cats_sorted":["math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2025-01-03T09:23:18Z","title_canon_sha256":"af5bf1b897143552b3e833b080fe181d0574b7b20023a2d1e1e35cfc78bbf287"},"schema_version":"1.0","source":{"id":"2501.01718","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.01718","created_at":"2026-07-05T11:06:26Z"},{"alias_kind":"arxiv_version","alias_value":"2501.01718v4","created_at":"2026-07-05T11:06:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.01718","created_at":"2026-07-05T11:06:26Z"},{"alias_kind":"pith_short_12","alias_value":"4PX4INNGQEHG","created_at":"2026-07-05T11:06:26Z"},{"alias_kind":"pith_short_16","alias_value":"4PX4INNGQEHGUZXV","created_at":"2026-07-05T11:06:26Z"},{"alias_kind":"pith_short_8","alias_value":"4PX4INNG","created_at":"2026-07-05T11:06:26Z"}],"graph_snapshots":[{"event_id":"sha256:7b63f81477c7541a4ab8b713c7b5fee898e87651b413f8c3517484c0ae6fcbf3","target":"graph","created_at":"2026-07-05T11:06:26Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2501.01718/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Consider an $ N \\times N$ Hermitian one-dimensional random band matrix with band width $W > N^{1 / 2 + \\frak c} $ for any $ {\\frak c} > 0$. In the bulk of the spectrum and in the large $ N $ limit, we obtain the following results: (i) The semicircle law holds up to the scale $ N^{-1 + \\varepsilon} $ for any $ \\varepsilon > 0 $. (ii) All $ L^2 $- normalized eigenvectors are delocalized, meaning their $ L^\\infty$ norms are simultaneously bounded by $ N^{-\\frac{1}{2} + \\varepsilon} $ with overwhelming probability, for any $ \\varepsilon > 0 $. (iii) Quantum unique ergodicity holds in the sense tha","authors_text":"Horng-Tzer Yau, Jun Yin","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2025-01-03T09:23:18Z","title":"Delocalization of One-Dimensional Random Band Matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.01718","kind":"arxiv","version":4},"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":"sha256:7742abe64f29f5d36114fe4122a9420cdbf2d0d157cf1fcfeac5029a2363b088","target":"record","created_at":"2026-07-05T11:06:26Z","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":"dfdee1cbda5e8fe7c89ae3969f0b58f515d4a39ffacaaf7927e7a6e055293fbe","cross_cats_sorted":["math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2025-01-03T09:23:18Z","title_canon_sha256":"af5bf1b897143552b3e833b080fe181d0574b7b20023a2d1e1e35cfc78bbf287"},"schema_version":"1.0","source":{"id":"2501.01718","kind":"arxiv","version":4}},"canonical_sha256":"e3efc435a6810e6a66f5dd22fa0769506c3db945e29881b436d9ef479dce4942","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e3efc435a6810e6a66f5dd22fa0769506c3db945e29881b436d9ef479dce4942","first_computed_at":"2026-07-05T11:06:26.477425Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:06:26.477425Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fG6bzCoIwTI6rouRcWs8TD8AIySPkRNgYbeoXNLfAZQbPWxpUQRs89UNBLwj+ngcwYYzDxIl3v6BFaN1zIL2AA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:06:26.477918Z","signed_message":"canonical_sha256_bytes"},"source_id":"2501.01718","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7742abe64f29f5d36114fe4122a9420cdbf2d0d157cf1fcfeac5029a2363b088","sha256:7b63f81477c7541a4ab8b713c7b5fee898e87651b413f8c3517484c0ae6fcbf3"],"state_sha256":"77eb905d03b46c552c433f02e91949cb787d44812ec554c45c707b46768982c3"}