{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:L5PBFCXWWGL44EV4HOSFFQKDXA","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":"a0ddc53543bcaa46e68eea8eef4ff6d3332ffe96d1bd9246eb55e01bf3208aab","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2024-11-22T09:02:37Z","title_canon_sha256":"7125aa5d565e46061d4d49eb56a646fb06dfbb2199dee845bfd17143420217ff"},"schema_version":"1.0","source":{"id":"2411.17730","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.17730","created_at":"2026-07-05T09:42:15Z"},{"alias_kind":"arxiv_version","alias_value":"2411.17730v2","created_at":"2026-07-05T09:42:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.17730","created_at":"2026-07-05T09:42:15Z"},{"alias_kind":"pith_short_12","alias_value":"L5PBFCXWWGL4","created_at":"2026-07-05T09:42:15Z"},{"alias_kind":"pith_short_16","alias_value":"L5PBFCXWWGL44EV4","created_at":"2026-07-05T09:42:15Z"},{"alias_kind":"pith_short_8","alias_value":"L5PBFCXW","created_at":"2026-07-05T09:42:15Z"}],"graph_snapshots":[{"event_id":"sha256:e6f81bbe9bf708894c298cb93a190804d76c4626c2ac0f1db7642b41609a5b01","target":"graph","created_at":"2026-07-05T09:42:15Z","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/2411.17730/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we study the almost sure well-posedness theory and orbital stability for the nonlinear Schr\\\"odinger equation with potential \\begin{equation*}\n  \\left\\{\\begin{array}{l} i \\partial_t u+\\Delta u-V(x)u+|u|^{2}u=0,\\ (x, t) \\in \\mathbb{R}^4 \\times \\mathbb{R}, \\\\ \\left.u\\right|_{t=0}=f \\in H ^s(\\mathbb{R}^4), \\end{array}\\right. \\end{equation*} where $\\frac{1}{3}<s<1$ and $V(x):\\mathbb{R}^4\\rightarrow \\mathbb{R}$ satisfies appropriate conditions. The main idea in the proofs is based on Strichartz spaces as well as variants of local smoothing, inhomogeneous local smoothing and maximal f","authors_text":"Jun Wang, Zhaoyang Yin","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2024-11-22T09:02:37Z","title":"Almost sure well-posedness and orbital stability for Schr\\\"odinger equation with potential"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.17730","kind":"arxiv","version":2},"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":"sha256:351907c4b8f23b3301981c07b32dbf2526e16d27b73f6f5e2583d919c8f49a99","target":"record","created_at":"2026-07-05T09:42:15Z","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":"a0ddc53543bcaa46e68eea8eef4ff6d3332ffe96d1bd9246eb55e01bf3208aab","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2024-11-22T09:02:37Z","title_canon_sha256":"7125aa5d565e46061d4d49eb56a646fb06dfbb2199dee845bfd17143420217ff"},"schema_version":"1.0","source":{"id":"2411.17730","kind":"arxiv","version":2}},"canonical_sha256":"5f5e128af6b197ce12bc3ba452c143b834a0657e2418bd1982519e1abbad2c4c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5f5e128af6b197ce12bc3ba452c143b834a0657e2418bd1982519e1abbad2c4c","first_computed_at":"2026-07-05T09:42:15.351969Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:42:15.351969Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1Gn0OmmRfO47nRiO8Khm51EUncH6Z7yJkRa01mUxcIrClchmUogCQz7cYK1HxP7gjUshulkZV8jATrJXhSX7Ag==","signature_status":"signed_v1","signed_at":"2026-07-05T09:42:15.352577Z","signed_message":"canonical_sha256_bytes"},"source_id":"2411.17730","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:351907c4b8f23b3301981c07b32dbf2526e16d27b73f6f5e2583d919c8f49a99","sha256:e6f81bbe9bf708894c298cb93a190804d76c4626c2ac0f1db7642b41609a5b01"],"state_sha256":"fa0106ae264613075d0faa83a5d2496489cc5a1d77b59e3c3c0ce7bd3bb46847"}