{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:OFDK7QLHWOZHWDMESM4NOFTTUQ","short_pith_number":"pith:OFDK7QLH","schema_version":"1.0","canonical_sha256":"7146afc167b3b27b0d849338d71673a41ceca0841fc84e1ad25cf1559bc27501","source":{"kind":"arxiv","id":"1201.0314","version":1},"attestation_state":"computed","paper":{"title":"Spherical mean transform from the pde point of view","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Linh V. Nguyen","submitted_at":"2011-12-31T23:37:57Z","abstract_excerpt":"We study the spherical mean transform on $\\rN^n$. The transform is characterized by the Euler-Poisson-Darboux equation. By looking at the spherical harmonic expansions, we obtain a system of 1+1-dimension hyperbolic equations, which provide a good machinery to attack problems of spherical mean transform.\n  As showcases, we discuss two known problems. The first one is a local uniqueness problem investigated by M. Agranovsky and P. Kuchment, [{\\em Memoirs on Differential Equations and Mathematical Physics}, 52:1--16, 2011]. We present a simple proof which works even under a weaker condition. The"},"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":"1201.0314","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-12-31T23:37:57Z","cross_cats_sorted":[],"title_canon_sha256":"33e47afd33830aab8ec74b0481eddc3205798d415275de8278f6a6eae3137be0","abstract_canon_sha256":"b17bdb4e8365b19d82563817e181b13603f7e8d7458390d2ced1f5fd30419210"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:05:25.510452Z","signature_b64":"PT9Na91pse7fGiNBVRHcLvoht0+jiiajz9R8NPHho3kuQQDb90o8lgGQC/gnPao/6uLjuvH34K6lpqi3x/VJDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7146afc167b3b27b0d849338d71673a41ceca0841fc84e1ad25cf1559bc27501","last_reissued_at":"2026-05-18T04:05:25.509918Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:05:25.509918Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Spherical mean transform from the pde point of view","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Linh V. Nguyen","submitted_at":"2011-12-31T23:37:57Z","abstract_excerpt":"We study the spherical mean transform on $\\rN^n$. The transform is characterized by the Euler-Poisson-Darboux equation. By looking at the spherical harmonic expansions, we obtain a system of 1+1-dimension hyperbolic equations, which provide a good machinery to attack problems of spherical mean transform.\n  As showcases, we discuss two known problems. The first one is a local uniqueness problem investigated by M. Agranovsky and P. Kuchment, [{\\em Memoirs on Differential Equations and Mathematical Physics}, 52:1--16, 2011]. We present a simple proof which works even under a weaker condition. The"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.0314","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":"1201.0314","created_at":"2026-05-18T04:05:25.509995+00:00"},{"alias_kind":"arxiv_version","alias_value":"1201.0314v1","created_at":"2026-05-18T04:05:25.509995+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.0314","created_at":"2026-05-18T04:05:25.509995+00:00"},{"alias_kind":"pith_short_12","alias_value":"OFDK7QLHWOZH","created_at":"2026-05-18T12:26:37.096874+00:00"},{"alias_kind":"pith_short_16","alias_value":"OFDK7QLHWOZHWDME","created_at":"2026-05-18T12:26:37.096874+00:00"},{"alias_kind":"pith_short_8","alias_value":"OFDK7QLH","created_at":"2026-05-18T12:26:37.096874+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/OFDK7QLHWOZHWDMESM4NOFTTUQ","json":"https://pith.science/pith/OFDK7QLHWOZHWDMESM4NOFTTUQ.json","graph_json":"https://pith.science/api/pith-number/OFDK7QLHWOZHWDMESM4NOFTTUQ/graph.json","events_json":"https://pith.science/api/pith-number/OFDK7QLHWOZHWDMESM4NOFTTUQ/events.json","paper":"https://pith.science/paper/OFDK7QLH"},"agent_actions":{"view_html":"https://pith.science/pith/OFDK7QLHWOZHWDMESM4NOFTTUQ","download_json":"https://pith.science/pith/OFDK7QLHWOZHWDMESM4NOFTTUQ.json","view_paper":"https://pith.science/paper/OFDK7QLH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1201.0314&json=true","fetch_graph":"https://pith.science/api/pith-number/OFDK7QLHWOZHWDMESM4NOFTTUQ/graph.json","fetch_events":"https://pith.science/api/pith-number/OFDK7QLHWOZHWDMESM4NOFTTUQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OFDK7QLHWOZHWDMESM4NOFTTUQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OFDK7QLHWOZHWDMESM4NOFTTUQ/action/storage_attestation","attest_author":"https://pith.science/pith/OFDK7QLHWOZHWDMESM4NOFTTUQ/action/author_attestation","sign_citation":"https://pith.science/pith/OFDK7QLHWOZHWDMESM4NOFTTUQ/action/citation_signature","submit_replication":"https://pith.science/pith/OFDK7QLHWOZHWDMESM4NOFTTUQ/action/replication_record"}},"created_at":"2026-05-18T04:05:25.509995+00:00","updated_at":"2026-05-18T04:05:25.509995+00:00"}