{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:KI2ZR3B5SWTNTEA2HSVTRKCNGX","short_pith_number":"pith:KI2ZR3B5","schema_version":"1.0","canonical_sha256":"523598ec3d95a6d9901a3cab38a84d35c019662a83d2b90bb7592d268ba667a3","source":{"kind":"arxiv","id":"2502.02566","version":1},"attestation_state":"computed","paper":{"title":"Tail bounds for the Dyson series of random Schr\\\"odinger equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.MP","math.PR"],"primary_cat":"math-ph","authors_text":"Adam Black, Felipe Hern\\'andez, Reuben Drogin","submitted_at":"2025-02-04T18:40:33Z","abstract_excerpt":"We study Schr\\\"odinger equations on $\\mathbb{Z}^d$ and $\\mathbb{R}^d$, $d\\geq 2$ with random potentials of strength $\\lambda$. Our main result gives tail bounds for the terms of the Dyson series that are effective at time scales on the order of $\\lambda^{-2+\\varepsilon}$. As corollaries, we obtain estimates on the frequency localization and spatial delocalization of approximate eigenfunctions in the spirit of works by Schlag-Shubin-Wolff and T. Chen. These estimates also apply to Floquet states associated to time-periodic potentials. Our proof is elementary in that we use neither sophisticated"},"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":"2502.02566","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2025-02-04T18:40:33Z","cross_cats_sorted":["math.AP","math.MP","math.PR"],"title_canon_sha256":"532440cb1edadfcdaa7631fec30aa752206c3a0706dea34241280e18e6279505","abstract_canon_sha256":"40c4031bad7fc2ee9d1474607f5d795957a1c7e58d73d1689e31eed4add5b78b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:09:30.333260Z","signature_b64":"Jn9Zx3CssMcunEY4ZdIjXejFm8E820hOQ2KDJ9Icf4tg9JkhparNCZv97+/geYSdTioGKIEJMaQoKvHpab5MDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"523598ec3d95a6d9901a3cab38a84d35c019662a83d2b90bb7592d268ba667a3","last_reissued_at":"2026-07-05T10:09:30.332813Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:09:30.332813Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Tail bounds for the Dyson series of random Schr\\\"odinger equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.MP","math.PR"],"primary_cat":"math-ph","authors_text":"Adam Black, Felipe Hern\\'andez, Reuben Drogin","submitted_at":"2025-02-04T18:40:33Z","abstract_excerpt":"We study Schr\\\"odinger equations on $\\mathbb{Z}^d$ and $\\mathbb{R}^d$, $d\\geq 2$ with random potentials of strength $\\lambda$. Our main result gives tail bounds for the terms of the Dyson series that are effective at time scales on the order of $\\lambda^{-2+\\varepsilon}$. As corollaries, we obtain estimates on the frequency localization and spatial delocalization of approximate eigenfunctions in the spirit of works by Schlag-Shubin-Wolff and T. Chen. These estimates also apply to Floquet states associated to time-periodic potentials. Our proof is elementary in that we use neither sophisticated"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.02566","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/2502.02566/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":"2502.02566","created_at":"2026-07-05T10:09:30.332872+00:00"},{"alias_kind":"arxiv_version","alias_value":"2502.02566v1","created_at":"2026-07-05T10:09:30.332872+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.02566","created_at":"2026-07-05T10:09:30.332872+00:00"},{"alias_kind":"pith_short_12","alias_value":"KI2ZR3B5SWTN","created_at":"2026-07-05T10:09:30.332872+00:00"},{"alias_kind":"pith_short_16","alias_value":"KI2ZR3B5SWTNTEA2","created_at":"2026-07-05T10:09:30.332872+00:00"},{"alias_kind":"pith_short_8","alias_value":"KI2ZR3B5","created_at":"2026-07-05T10:09:30.332872+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/KI2ZR3B5SWTNTEA2HSVTRKCNGX","json":"https://pith.science/pith/KI2ZR3B5SWTNTEA2HSVTRKCNGX.json","graph_json":"https://pith.science/api/pith-number/KI2ZR3B5SWTNTEA2HSVTRKCNGX/graph.json","events_json":"https://pith.science/api/pith-number/KI2ZR3B5SWTNTEA2HSVTRKCNGX/events.json","paper":"https://pith.science/paper/KI2ZR3B5"},"agent_actions":{"view_html":"https://pith.science/pith/KI2ZR3B5SWTNTEA2HSVTRKCNGX","download_json":"https://pith.science/pith/KI2ZR3B5SWTNTEA2HSVTRKCNGX.json","view_paper":"https://pith.science/paper/KI2ZR3B5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2502.02566&json=true","fetch_graph":"https://pith.science/api/pith-number/KI2ZR3B5SWTNTEA2HSVTRKCNGX/graph.json","fetch_events":"https://pith.science/api/pith-number/KI2ZR3B5SWTNTEA2HSVTRKCNGX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KI2ZR3B5SWTNTEA2HSVTRKCNGX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KI2ZR3B5SWTNTEA2HSVTRKCNGX/action/storage_attestation","attest_author":"https://pith.science/pith/KI2ZR3B5SWTNTEA2HSVTRKCNGX/action/author_attestation","sign_citation":"https://pith.science/pith/KI2ZR3B5SWTNTEA2HSVTRKCNGX/action/citation_signature","submit_replication":"https://pith.science/pith/KI2ZR3B5SWTNTEA2HSVTRKCNGX/action/replication_record"}},"created_at":"2026-07-05T10:09:30.332872+00:00","updated_at":"2026-07-05T10:09:30.332872+00:00"}