{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:HNOMLOY3KPXW4JSTDYZAUSSBCR","short_pith_number":"pith:HNOMLOY3","schema_version":"1.0","canonical_sha256":"3b5cc5bb1b53ef6e26531e320a4a411449d37790f956dbc3ae5fb839275691e3","source":{"kind":"arxiv","id":"1302.5000","version":1},"attestation_state":"computed","paper":{"title":"Inverse scattering with the data at fixed energy and fixed incident direction","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":"2013-02-02T16:00:30Z","abstract_excerpt":"Consider the Schr\\\"odinger operator $-\\nabla^2+q$ $ $q$, $q=q(x), x \\in \\mathbf{R}^3$. Let $A(\\beta,\\alpha, k)$ be the corresponding scattering amplitude, $k^2$ be the energy, $\\alpha \\in S^2$ be the incident direction, $\\beta \\in S^2$ be the direction of scattered wave, $S^2$ be the unit sphere in $\\mathbf{R}^3$. Assume that $k=k_0 >0$ is fixed, and $\\alpha=\\alpha_0$ is fixed. Then the scattering data are $A(\\beta)= A(\\beta,\\alpha_0, k_0)=A_q(\\beta)$ is a function on $S^2$. The following invers$ \\textit{IP: Given an arbitrary $f \\in L^2(S^2)$ and an arbitrary small number $$ $q \\in C_0^{\\inft"},"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":"1302.5000","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-02-02T16:00:30Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"451b104e087e20d6028170e702318a22969484bcf74c4bf3ec58b6048bb0d423","abstract_canon_sha256":"4a8a76f4bcae30ef384f37b70afda8719e63a92b666ebcc5e07cb72179c7e1ca"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:33:00.459789Z","signature_b64":"iMVRwALSHfOmqQuEuBBXMlPfpaqAgAfUuHwKl2ZHGabkTOyoEtMQBhxhmPVVF/F61oAqDo0RIpHKc13qySuHAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3b5cc5bb1b53ef6e26531e320a4a411449d37790f956dbc3ae5fb839275691e3","last_reissued_at":"2026-05-18T03:33:00.458936Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:33:00.458936Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Inverse scattering with the data at fixed energy and fixed incident direction","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":"2013-02-02T16:00:30Z","abstract_excerpt":"Consider the Schr\\\"odinger operator $-\\nabla^2+q$ $ $q$, $q=q(x), x \\in \\mathbf{R}^3$. Let $A(\\beta,\\alpha, k)$ be the corresponding scattering amplitude, $k^2$ be the energy, $\\alpha \\in S^2$ be the incident direction, $\\beta \\in S^2$ be the direction of scattered wave, $S^2$ be the unit sphere in $\\mathbf{R}^3$. Assume that $k=k_0 >0$ is fixed, and $\\alpha=\\alpha_0$ is fixed. Then the scattering data are $A(\\beta)= A(\\beta,\\alpha_0, k_0)=A_q(\\beta)$ is a function on $S^2$. The following invers$ \\textit{IP: Given an arbitrary $f \\in L^2(S^2)$ and an arbitrary small number $$ $q \\in C_0^{\\inft"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.5000","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":""},"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":"1302.5000","created_at":"2026-05-18T03:33:00.459074+00:00"},{"alias_kind":"arxiv_version","alias_value":"1302.5000v1","created_at":"2026-05-18T03:33:00.459074+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.5000","created_at":"2026-05-18T03:33:00.459074+00:00"},{"alias_kind":"pith_short_12","alias_value":"HNOMLOY3KPXW","created_at":"2026-05-18T12:27:46.883200+00:00"},{"alias_kind":"pith_short_16","alias_value":"HNOMLOY3KPXW4JST","created_at":"2026-05-18T12:27:46.883200+00:00"},{"alias_kind":"pith_short_8","alias_value":"HNOMLOY3","created_at":"2026-05-18T12:27:46.883200+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/HNOMLOY3KPXW4JSTDYZAUSSBCR","json":"https://pith.science/pith/HNOMLOY3KPXW4JSTDYZAUSSBCR.json","graph_json":"https://pith.science/api/pith-number/HNOMLOY3KPXW4JSTDYZAUSSBCR/graph.json","events_json":"https://pith.science/api/pith-number/HNOMLOY3KPXW4JSTDYZAUSSBCR/events.json","paper":"https://pith.science/paper/HNOMLOY3"},"agent_actions":{"view_html":"https://pith.science/pith/HNOMLOY3KPXW4JSTDYZAUSSBCR","download_json":"https://pith.science/pith/HNOMLOY3KPXW4JSTDYZAUSSBCR.json","view_paper":"https://pith.science/paper/HNOMLOY3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1302.5000&json=true","fetch_graph":"https://pith.science/api/pith-number/HNOMLOY3KPXW4JSTDYZAUSSBCR/graph.json","fetch_events":"https://pith.science/api/pith-number/HNOMLOY3KPXW4JSTDYZAUSSBCR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HNOMLOY3KPXW4JSTDYZAUSSBCR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HNOMLOY3KPXW4JSTDYZAUSSBCR/action/storage_attestation","attest_author":"https://pith.science/pith/HNOMLOY3KPXW4JSTDYZAUSSBCR/action/author_attestation","sign_citation":"https://pith.science/pith/HNOMLOY3KPXW4JSTDYZAUSSBCR/action/citation_signature","submit_replication":"https://pith.science/pith/HNOMLOY3KPXW4JSTDYZAUSSBCR/action/replication_record"}},"created_at":"2026-05-18T03:33:00.459074+00:00","updated_at":"2026-05-18T03:33:00.459074+00:00"}