{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:4TFY22O4H4ZRTUQZ3RFXALFMK2","short_pith_number":"pith:4TFY22O4","schema_version":"1.0","canonical_sha256":"e4cb8d69dc3f3319d219dc4b702cac569b04d6325ecf24d2211b7e34a6fb4890","source":{"kind":"arxiv","id":"1604.01601","version":3},"attestation_state":"computed","paper":{"title":"Inverse obstacle scattering with non-over-determined data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"A. G. Ramm","submitted_at":"2016-04-06T13:07:25Z","abstract_excerpt":"It is proved that the scattering amplitude $A(\\beta, \\alpha_0, k_0)$, known for all $\\beta\\in S^2$, where $S^2$ is the unit sphere in $\\mathbb{R}^3$, and fixed $\\alpha_0\\in S^2$ and $k_0>0$, determines uniquely the surface $S$ of the obstacle $D$ and the boundary condition on $S$. The boundary condition on $S$ is assumed to be the Dirichlet, or Neumann, or the impedance one. The uniqueness theorem for the solution of multidimensional inverse scattering problems with non-over-determined data was not known for many decades. Such a theorem is proved in this paper for inverse scattering by obstacl"},"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":"1604.01601","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-04-06T13:07:25Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"700807e7753dd67b94ac8b2ea113b308c558d701b0603b2b71fd57e04485da64","abstract_canon_sha256":"2f5b6b72b94e6535242ef11ef7403c137714ec5ea848d3ff361dbace431c0a65"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:43:35.856118Z","signature_b64":"PfTs3IStIltJ6/tV9U2LPX03gLq7Pckb0OFZz9eLUyiHplKlMEjHa7XtChAukWCGQwFoTpSDa67oQb5ONSR7Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e4cb8d69dc3f3319d219dc4b702cac569b04d6325ecf24d2211b7e34a6fb4890","last_reissued_at":"2026-05-18T00:43:35.855599Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:43:35.855599Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Inverse obstacle scattering with non-over-determined data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"A. G. Ramm","submitted_at":"2016-04-06T13:07:25Z","abstract_excerpt":"It is proved that the scattering amplitude $A(\\beta, \\alpha_0, k_0)$, known for all $\\beta\\in S^2$, where $S^2$ is the unit sphere in $\\mathbb{R}^3$, and fixed $\\alpha_0\\in S^2$ and $k_0>0$, determines uniquely the surface $S$ of the obstacle $D$ and the boundary condition on $S$. The boundary condition on $S$ is assumed to be the Dirichlet, or Neumann, or the impedance one. The uniqueness theorem for the solution of multidimensional inverse scattering problems with non-over-determined data was not known for many decades. Such a theorem is proved in this paper for inverse scattering by obstacl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.01601","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"1604.01601","created_at":"2026-05-18T00:43:35.855662+00:00"},{"alias_kind":"arxiv_version","alias_value":"1604.01601v3","created_at":"2026-05-18T00:43:35.855662+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.01601","created_at":"2026-05-18T00:43:35.855662+00:00"},{"alias_kind":"pith_short_12","alias_value":"4TFY22O4H4ZR","created_at":"2026-05-18T12:29:58.707656+00:00"},{"alias_kind":"pith_short_16","alias_value":"4TFY22O4H4ZRTUQZ","created_at":"2026-05-18T12:29:58.707656+00:00"},{"alias_kind":"pith_short_8","alias_value":"4TFY22O4","created_at":"2026-05-18T12:29:58.707656+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/4TFY22O4H4ZRTUQZ3RFXALFMK2","json":"https://pith.science/pith/4TFY22O4H4ZRTUQZ3RFXALFMK2.json","graph_json":"https://pith.science/api/pith-number/4TFY22O4H4ZRTUQZ3RFXALFMK2/graph.json","events_json":"https://pith.science/api/pith-number/4TFY22O4H4ZRTUQZ3RFXALFMK2/events.json","paper":"https://pith.science/paper/4TFY22O4"},"agent_actions":{"view_html":"https://pith.science/pith/4TFY22O4H4ZRTUQZ3RFXALFMK2","download_json":"https://pith.science/pith/4TFY22O4H4ZRTUQZ3RFXALFMK2.json","view_paper":"https://pith.science/paper/4TFY22O4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1604.01601&json=true","fetch_graph":"https://pith.science/api/pith-number/4TFY22O4H4ZRTUQZ3RFXALFMK2/graph.json","fetch_events":"https://pith.science/api/pith-number/4TFY22O4H4ZRTUQZ3RFXALFMK2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4TFY22O4H4ZRTUQZ3RFXALFMK2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4TFY22O4H4ZRTUQZ3RFXALFMK2/action/storage_attestation","attest_author":"https://pith.science/pith/4TFY22O4H4ZRTUQZ3RFXALFMK2/action/author_attestation","sign_citation":"https://pith.science/pith/4TFY22O4H4ZRTUQZ3RFXALFMK2/action/citation_signature","submit_replication":"https://pith.science/pith/4TFY22O4H4ZRTUQZ3RFXALFMK2/action/replication_record"}},"created_at":"2026-05-18T00:43:35.855662+00:00","updated_at":"2026-05-18T00:43:35.855662+00:00"}