{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:BQMJQ7MJFRV7W6DKCOEXH4UOXY","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":"a3e45ef7aa604c68bf804108c46aa64b239843e278513be1082f07dc404fef1d","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.SP","submitted_at":"2026-06-21T10:24:54Z","title_canon_sha256":"5c5acfe65264e8268b8290eba2c9a6a9d3338de7630db3966158172d161557f3"},"schema_version":"1.0","source":{"id":"2606.22426","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.22426","created_at":"2026-06-23T02:13:38Z"},{"alias_kind":"arxiv_version","alias_value":"2606.22426v1","created_at":"2026-06-23T02:13:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.22426","created_at":"2026-06-23T02:13:38Z"},{"alias_kind":"pith_short_12","alias_value":"BQMJQ7MJFRV7","created_at":"2026-06-23T02:13:38Z"},{"alias_kind":"pith_short_16","alias_value":"BQMJQ7MJFRV7W6DK","created_at":"2026-06-23T02:13:38Z"},{"alias_kind":"pith_short_8","alias_value":"BQMJQ7MJ","created_at":"2026-06-23T02:13:38Z"}],"graph_snapshots":[{"event_id":"sha256:007b7f739514958e48f459016a28daa66c65ddec5b09e73cef6f2390c54e3b11","target":"graph","created_at":"2026-06-23T02:13:38Z","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/2606.22426/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the one-dimensional Schr\\\"odinger operator on a fixed interval with Gaussian white-noise potential, \\[\n  H_\\omega=-\\frac{\\dd^2}{\\dd x^2}+\\rho\\dot B_x(\\omega), \\] under Dirichlet boundary conditions. The operator is defined pathwise through the quasi-derivative realization of Sturm--Liouville operators with distributional potentials. Let $\\lambda_n$ be the Dirichlet eigenvalues, $\\lambda_n^+=\\max\\{\\lambda_n,0\\}$, and $k_n=\\sqrt{\\lambda_n^+}$. For every finite $p$, we prove the high-energy expansion \\[\n  k_n=\\frac{n\\pi}{L}\n  +\\frac{\\rho}{n\\pi}\\int_0^L\n  \\sin^2\\left(\\frac{n\\pi s}{L}\\righ","authors_text":"Wenwen Jian, Xiaoping Yuan, Yingdu Dong","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.SP","submitted_at":"2026-06-21T10:24:54Z","title":"High-energy asymptotics for finite-interval Schr\\\"odinger operators with Gaussian white-noise potential"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.22426","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":"sha256:5fd2ec62be849585bc82d267fbd176201b50a703957307aa89676ab10992ee0c","target":"record","created_at":"2026-06-23T02:13:38Z","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":"a3e45ef7aa604c68bf804108c46aa64b239843e278513be1082f07dc404fef1d","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.SP","submitted_at":"2026-06-21T10:24:54Z","title_canon_sha256":"5c5acfe65264e8268b8290eba2c9a6a9d3338de7630db3966158172d161557f3"},"schema_version":"1.0","source":{"id":"2606.22426","kind":"arxiv","version":1}},"canonical_sha256":"0c18987d892c6bfb786a138973f28ebe1bfe8319abfc4a11385ae59643667bd9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0c18987d892c6bfb786a138973f28ebe1bfe8319abfc4a11385ae59643667bd9","first_computed_at":"2026-06-23T02:13:38.133117Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-23T02:13:38.133117Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"44ycVHOxGUIASoWpLq7rx6T3dCEAm/au/xs9yL0bXwjyX3P3E6wrYjcmeNZVcwLolqs/z6EiBKtq+tu5A5N6Ag==","signature_status":"signed_v1","signed_at":"2026-06-23T02:13:38.133535Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.22426","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5fd2ec62be849585bc82d267fbd176201b50a703957307aa89676ab10992ee0c","sha256:007b7f739514958e48f459016a28daa66c65ddec5b09e73cef6f2390c54e3b11"],"state_sha256":"fcfbb278ddd115ad769de424b81fb661bb9b482a9fcd0cf7f39077b26b6b1523"}