{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:6GVPOIAIGU436DGD66LZ2U7WMP","short_pith_number":"pith:6GVPOIAI","schema_version":"1.0","canonical_sha256":"f1aaf720083539bf0cc3f7979d53f663ceb3eaf8c324a43a363cae4ba4dfedb5","source":{"kind":"arxiv","id":"1610.09553","version":1},"attestation_state":"computed","paper":{"title":"Recovering Finite Parametric Distributions and Functions Using the Spherical Mean Transform","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Yehonatan Salman","submitted_at":"2016-10-29T18:18:17Z","abstract_excerpt":"The aim of the article is to recover a certain type of finite parametric distributions and functions using their spherical mean transform which is given on a certain family of spheres whose centers belong to a finite set $\\Gamma$. For this, we show how the problem of reconstruction can be converted to a Prony's type system of equations whose regularity is guaranteed by the assumption that the points in the set $\\Gamma$ are in general position. By solving the corresponding Prony's system we can extract the set of parameters which define the corresponding function or distribution."},"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":"1610.09553","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-10-29T18:18:17Z","cross_cats_sorted":[],"title_canon_sha256":"61ac3defea8b90fc6aec3710c66555f16acdb35e98e74e36a788d9eda3cac748","abstract_canon_sha256":"e1785b291a347328080fe1b6b53ff32e88ae8dd1082e566831c52f2d10b4e612"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:00:51.681307Z","signature_b64":"PrKwozbNS1V2taAvpXmF25RodnIVab36RqG4MaSIqaqsWV5KjtXzeAfJ94kp+t+aisWJ+h9AddjEXEJDXxUDAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f1aaf720083539bf0cc3f7979d53f663ceb3eaf8c324a43a363cae4ba4dfedb5","last_reissued_at":"2026-05-18T01:00:51.680684Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:00:51.680684Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Recovering Finite Parametric Distributions and Functions Using the Spherical Mean Transform","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Yehonatan Salman","submitted_at":"2016-10-29T18:18:17Z","abstract_excerpt":"The aim of the article is to recover a certain type of finite parametric distributions and functions using their spherical mean transform which is given on a certain family of spheres whose centers belong to a finite set $\\Gamma$. For this, we show how the problem of reconstruction can be converted to a Prony's type system of equations whose regularity is guaranteed by the assumption that the points in the set $\\Gamma$ are in general position. By solving the corresponding Prony's system we can extract the set of parameters which define the corresponding function or distribution."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.09553","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":"1610.09553","created_at":"2026-05-18T01:00:51.680784+00:00"},{"alias_kind":"arxiv_version","alias_value":"1610.09553v1","created_at":"2026-05-18T01:00:51.680784+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.09553","created_at":"2026-05-18T01:00:51.680784+00:00"},{"alias_kind":"pith_short_12","alias_value":"6GVPOIAIGU43","created_at":"2026-05-18T12:30:01.593930+00:00"},{"alias_kind":"pith_short_16","alias_value":"6GVPOIAIGU436DGD","created_at":"2026-05-18T12:30:01.593930+00:00"},{"alias_kind":"pith_short_8","alias_value":"6GVPOIAI","created_at":"2026-05-18T12:30:01.593930+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/6GVPOIAIGU436DGD66LZ2U7WMP","json":"https://pith.science/pith/6GVPOIAIGU436DGD66LZ2U7WMP.json","graph_json":"https://pith.science/api/pith-number/6GVPOIAIGU436DGD66LZ2U7WMP/graph.json","events_json":"https://pith.science/api/pith-number/6GVPOIAIGU436DGD66LZ2U7WMP/events.json","paper":"https://pith.science/paper/6GVPOIAI"},"agent_actions":{"view_html":"https://pith.science/pith/6GVPOIAIGU436DGD66LZ2U7WMP","download_json":"https://pith.science/pith/6GVPOIAIGU436DGD66LZ2U7WMP.json","view_paper":"https://pith.science/paper/6GVPOIAI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1610.09553&json=true","fetch_graph":"https://pith.science/api/pith-number/6GVPOIAIGU436DGD66LZ2U7WMP/graph.json","fetch_events":"https://pith.science/api/pith-number/6GVPOIAIGU436DGD66LZ2U7WMP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6GVPOIAIGU436DGD66LZ2U7WMP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6GVPOIAIGU436DGD66LZ2U7WMP/action/storage_attestation","attest_author":"https://pith.science/pith/6GVPOIAIGU436DGD66LZ2U7WMP/action/author_attestation","sign_citation":"https://pith.science/pith/6GVPOIAIGU436DGD66LZ2U7WMP/action/citation_signature","submit_replication":"https://pith.science/pith/6GVPOIAIGU436DGD66LZ2U7WMP/action/replication_record"}},"created_at":"2026-05-18T01:00:51.680784+00:00","updated_at":"2026-05-18T01:00:51.680784+00:00"}