{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:TSDLQ2VJ4EOWISRTUGI6BJXCSG","short_pith_number":"pith:TSDLQ2VJ","schema_version":"1.0","canonical_sha256":"9c86b86aa9e11d644a33a191e0a6e2918eaf21d5cc0fb5b492b5ce0138379a7f","source":{"kind":"arxiv","id":"1304.2297","version":2},"attestation_state":"computed","paper":{"title":"A solution to the Pompeiu problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"A.G.Ramm","submitted_at":"2013-04-08T18:29:34Z","abstract_excerpt":"Let $f \\in L_{loc}^1 (\\R^n)\\cap \\mathcal{S}$, where $\\mathcal{S}$ is the Schwartz class of distributions, and $$\\int_{\\sigma (D)} f(x) dx = 0 \\quad \\forall \\sigma \\in G, \\qquad (*)$$ where $D\\subset \\R^n$ is a bounded domain, the closure $\\bar{D}$ of which is diffeomorphic to a closed ball, and $S$ is its boundary. Then the comp$ is connected and path connected. By $G$ the group of all rigid motions of $\\R^n$ is denoted. This group consists of all translations and rotations. A proof of the following theorem is given.\n  Theorem 1. {\\it Assume that $n=2$, $f\\not\\equiv 0$, and (*) holds. Then $D$"},"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":"1304.2297","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-04-08T18:29:34Z","cross_cats_sorted":[],"title_canon_sha256":"5c76c021c97565eb20b8b1fa5439105d7b5e508acfc78080c94df99736f00919","abstract_canon_sha256":"45066bfaaece0eafcd306eefd2da4fbbf014afe518d459bf990eee1ae95eb746"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:28:04.653579Z","signature_b64":"QIUAs2dTKKIjwWekPaL7hK3kuQt+A9u8J8IhX/MTjtRYEZXK0VlwM+616NiBRxSVQiERm3e2YfVy1tL+5y1hAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9c86b86aa9e11d644a33a191e0a6e2918eaf21d5cc0fb5b492b5ce0138379a7f","last_reissued_at":"2026-05-18T03:28:04.652788Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:28:04.652788Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A solution to the Pompeiu problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"A.G.Ramm","submitted_at":"2013-04-08T18:29:34Z","abstract_excerpt":"Let $f \\in L_{loc}^1 (\\R^n)\\cap \\mathcal{S}$, where $\\mathcal{S}$ is the Schwartz class of distributions, and $$\\int_{\\sigma (D)} f(x) dx = 0 \\quad \\forall \\sigma \\in G, \\qquad (*)$$ where $D\\subset \\R^n$ is a bounded domain, the closure $\\bar{D}$ of which is diffeomorphic to a closed ball, and $S$ is its boundary. Then the comp$ is connected and path connected. By $G$ the group of all rigid motions of $\\R^n$ is denoted. This group consists of all translations and rotations. A proof of the following theorem is given.\n  Theorem 1. {\\it Assume that $n=2$, $f\\not\\equiv 0$, and (*) holds. Then $D$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.2297","kind":"arxiv","version":2},"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":"1304.2297","created_at":"2026-05-18T03:28:04.652934+00:00"},{"alias_kind":"arxiv_version","alias_value":"1304.2297v2","created_at":"2026-05-18T03:28:04.652934+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.2297","created_at":"2026-05-18T03:28:04.652934+00:00"},{"alias_kind":"pith_short_12","alias_value":"TSDLQ2VJ4EOW","created_at":"2026-05-18T12:28:02.375192+00:00"},{"alias_kind":"pith_short_16","alias_value":"TSDLQ2VJ4EOWISRT","created_at":"2026-05-18T12:28:02.375192+00:00"},{"alias_kind":"pith_short_8","alias_value":"TSDLQ2VJ","created_at":"2026-05-18T12:28:02.375192+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/TSDLQ2VJ4EOWISRTUGI6BJXCSG","json":"https://pith.science/pith/TSDLQ2VJ4EOWISRTUGI6BJXCSG.json","graph_json":"https://pith.science/api/pith-number/TSDLQ2VJ4EOWISRTUGI6BJXCSG/graph.json","events_json":"https://pith.science/api/pith-number/TSDLQ2VJ4EOWISRTUGI6BJXCSG/events.json","paper":"https://pith.science/paper/TSDLQ2VJ"},"agent_actions":{"view_html":"https://pith.science/pith/TSDLQ2VJ4EOWISRTUGI6BJXCSG","download_json":"https://pith.science/pith/TSDLQ2VJ4EOWISRTUGI6BJXCSG.json","view_paper":"https://pith.science/paper/TSDLQ2VJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1304.2297&json=true","fetch_graph":"https://pith.science/api/pith-number/TSDLQ2VJ4EOWISRTUGI6BJXCSG/graph.json","fetch_events":"https://pith.science/api/pith-number/TSDLQ2VJ4EOWISRTUGI6BJXCSG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TSDLQ2VJ4EOWISRTUGI6BJXCSG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TSDLQ2VJ4EOWISRTUGI6BJXCSG/action/storage_attestation","attest_author":"https://pith.science/pith/TSDLQ2VJ4EOWISRTUGI6BJXCSG/action/author_attestation","sign_citation":"https://pith.science/pith/TSDLQ2VJ4EOWISRTUGI6BJXCSG/action/citation_signature","submit_replication":"https://pith.science/pith/TSDLQ2VJ4EOWISRTUGI6BJXCSG/action/replication_record"}},"created_at":"2026-05-18T03:28:04.652934+00:00","updated_at":"2026-05-18T03:28:04.652934+00:00"}