{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:PQ5YPIUHRVXBGEP6YOV7H74NED","short_pith_number":"pith:PQ5YPIUH","schema_version":"1.0","canonical_sha256":"7c3b87a2878d6e1311fec3abf3ff8d20e8bb46925efab7a6640c136a15c7077f","source":{"kind":"arxiv","id":"2607.22079","version":1},"attestation_state":"computed","paper":{"title":"An Inverse Obstacle Problem for the Fractional Schr\\\"odinger Equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Gunter Uhlmann, Philipp Zimmermann","submitted_at":"2026-07-24T08:23:51Z","abstract_excerpt":"We study an inverse obstacle problem for the fractional Schr\\\"odinger operator $(-\\Delta)^s+q$, $0<s<1$. For each exterior datum, the state is constrained by a prescribed obstacle in a bounded domain and satisfies the fractional Schr\\\"odinger equation only in the associated noncontact set. This set is unknown and depends on the coefficient, so the exterior Dirichlet-to-Neumann map is nonlinear. We show that the nonlocal character of the equation gives a direct way around this moving-free-boundary difficulty. Equality of one obstacle measurement on an exterior open set forces equality of the tw"},"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":"2607.22079","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-07-24T08:23:51Z","cross_cats_sorted":[],"title_canon_sha256":"9a9318fa58818f4f13c5b5b45683d4261aa449a5c842b9bf9aa383f55db6bef0","abstract_canon_sha256":"bea506dfac907ab74a2f9df6622ee2b7ec4f7c57e9e6b4cb8838a5db6b2df42e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-27T01:20:46.957938Z","signature_b64":"sdKfW7pMN0LPj0UEd+9df0W8Qv8v2yUplZU4e6tm8ZHSnLFXE/mIAif7cEp9MmX6XbMSqQn5SVIgsKRcNDn3CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7c3b87a2878d6e1311fec3abf3ff8d20e8bb46925efab7a6640c136a15c7077f","last_reissued_at":"2026-07-27T01:20:46.957077Z","signature_status":"signed_v1","first_computed_at":"2026-07-27T01:20:46.957077Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An Inverse Obstacle Problem for the Fractional Schr\\\"odinger Equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Gunter Uhlmann, Philipp Zimmermann","submitted_at":"2026-07-24T08:23:51Z","abstract_excerpt":"We study an inverse obstacle problem for the fractional Schr\\\"odinger operator $(-\\Delta)^s+q$, $0<s<1$. For each exterior datum, the state is constrained by a prescribed obstacle in a bounded domain and satisfies the fractional Schr\\\"odinger equation only in the associated noncontact set. This set is unknown and depends on the coefficient, so the exterior Dirichlet-to-Neumann map is nonlinear. We show that the nonlocal character of the equation gives a direct way around this moving-free-boundary difficulty. Equality of one obstacle measurement on an exterior open set forces equality of the tw"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.22079","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/2607.22079/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":"2607.22079","created_at":"2026-07-27T01:20:46.957532+00:00"},{"alias_kind":"arxiv_version","alias_value":"2607.22079v1","created_at":"2026-07-27T01:20:46.957532+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.22079","created_at":"2026-07-27T01:20:46.957532+00:00"},{"alias_kind":"pith_short_12","alias_value":"PQ5YPIUHRVXB","created_at":"2026-07-27T01:20:46.957532+00:00"},{"alias_kind":"pith_short_16","alias_value":"PQ5YPIUHRVXBGEP6","created_at":"2026-07-27T01:20:46.957532+00:00"},{"alias_kind":"pith_short_8","alias_value":"PQ5YPIUH","created_at":"2026-07-27T01:20:46.957532+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/PQ5YPIUHRVXBGEP6YOV7H74NED","json":"https://pith.science/pith/PQ5YPIUHRVXBGEP6YOV7H74NED.json","graph_json":"https://pith.science/api/pith-number/PQ5YPIUHRVXBGEP6YOV7H74NED/graph.json","events_json":"https://pith.science/api/pith-number/PQ5YPIUHRVXBGEP6YOV7H74NED/events.json","paper":"https://pith.science/paper/PQ5YPIUH"},"agent_actions":{"view_html":"https://pith.science/pith/PQ5YPIUHRVXBGEP6YOV7H74NED","download_json":"https://pith.science/pith/PQ5YPIUHRVXBGEP6YOV7H74NED.json","view_paper":"https://pith.science/paper/PQ5YPIUH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2607.22079&json=true","fetch_graph":"https://pith.science/api/pith-number/PQ5YPIUHRVXBGEP6YOV7H74NED/graph.json","fetch_events":"https://pith.science/api/pith-number/PQ5YPIUHRVXBGEP6YOV7H74NED/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PQ5YPIUHRVXBGEP6YOV7H74NED/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PQ5YPIUHRVXBGEP6YOV7H74NED/action/storage_attestation","attest_author":"https://pith.science/pith/PQ5YPIUHRVXBGEP6YOV7H74NED/action/author_attestation","sign_citation":"https://pith.science/pith/PQ5YPIUHRVXBGEP6YOV7H74NED/action/citation_signature","submit_replication":"https://pith.science/pith/PQ5YPIUHRVXBGEP6YOV7H74NED/action/replication_record"}},"created_at":"2026-07-27T01:20:46.957532+00:00","updated_at":"2026-07-27T01:20:46.957532+00:00"}