{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:GXIB55E5PNFUEPXOM7U67TNKW5","short_pith_number":"pith:GXIB55E5","schema_version":"1.0","canonical_sha256":"35d01ef49d7b4b423eee67e9efcdaab756ffe8ed5ad1616f691be8d989a77657","source":{"kind":"arxiv","id":"1506.00450","version":1},"attestation_state":"computed","paper":{"title":"A multivariate generalization of Prony's method","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Stefan Kunis, Thomas Peter, Tim Roemer, Ulrich von der Ohe","submitted_at":"2015-06-01T11:23:54Z","abstract_excerpt":"Prony's method is a prototypical eigenvalue analysis based method for the reconstruction of a finitely supported complex measure on the unit circle from its moments up to a certain degree. In this note, we give a generalization of this method to the multivariate case and prove simple conditions under which the problem admits a unique solution. Provided the order of the moments is bounded from below by the number of points on which the measure is supported as well as by a small constant divided by the separation distance of these points, stable reconstruction is guaranteed. In its simplest form"},"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":"1506.00450","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-06-01T11:23:54Z","cross_cats_sorted":[],"title_canon_sha256":"ab7beb276e6b63fe8234294cf0871463ec5a9a3208f3205da6300c66564147d4","abstract_canon_sha256":"5c86a746f06636d146aa2ab37d473887c60f26c6bb8a68509740fc033e5893a4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:59:54.533037Z","signature_b64":"GQ2nuaf4yWLMYrP6Yp4VstpFFSPMgASzVrqlrg9K91IYvfvepsMFcCfQfDHguk8iFGZGUm7s2rbKlT3DNr0jBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"35d01ef49d7b4b423eee67e9efcdaab756ffe8ed5ad1616f691be8d989a77657","last_reissued_at":"2026-05-18T01:59:54.532443Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:59:54.532443Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A multivariate generalization of Prony's method","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Stefan Kunis, Thomas Peter, Tim Roemer, Ulrich von der Ohe","submitted_at":"2015-06-01T11:23:54Z","abstract_excerpt":"Prony's method is a prototypical eigenvalue analysis based method for the reconstruction of a finitely supported complex measure on the unit circle from its moments up to a certain degree. In this note, we give a generalization of this method to the multivariate case and prove simple conditions under which the problem admits a unique solution. Provided the order of the moments is bounded from below by the number of points on which the measure is supported as well as by a small constant divided by the separation distance of these points, stable reconstruction is guaranteed. In its simplest form"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.00450","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":"1506.00450","created_at":"2026-05-18T01:59:54.532532+00:00"},{"alias_kind":"arxiv_version","alias_value":"1506.00450v1","created_at":"2026-05-18T01:59:54.532532+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.00450","created_at":"2026-05-18T01:59:54.532532+00:00"},{"alias_kind":"pith_short_12","alias_value":"GXIB55E5PNFU","created_at":"2026-05-18T12:29:22.688609+00:00"},{"alias_kind":"pith_short_16","alias_value":"GXIB55E5PNFUEPXO","created_at":"2026-05-18T12:29:22.688609+00:00"},{"alias_kind":"pith_short_8","alias_value":"GXIB55E5","created_at":"2026-05-18T12:29:22.688609+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/GXIB55E5PNFUEPXOM7U67TNKW5","json":"https://pith.science/pith/GXIB55E5PNFUEPXOM7U67TNKW5.json","graph_json":"https://pith.science/api/pith-number/GXIB55E5PNFUEPXOM7U67TNKW5/graph.json","events_json":"https://pith.science/api/pith-number/GXIB55E5PNFUEPXOM7U67TNKW5/events.json","paper":"https://pith.science/paper/GXIB55E5"},"agent_actions":{"view_html":"https://pith.science/pith/GXIB55E5PNFUEPXOM7U67TNKW5","download_json":"https://pith.science/pith/GXIB55E5PNFUEPXOM7U67TNKW5.json","view_paper":"https://pith.science/paper/GXIB55E5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1506.00450&json=true","fetch_graph":"https://pith.science/api/pith-number/GXIB55E5PNFUEPXOM7U67TNKW5/graph.json","fetch_events":"https://pith.science/api/pith-number/GXIB55E5PNFUEPXOM7U67TNKW5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GXIB55E5PNFUEPXOM7U67TNKW5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GXIB55E5PNFUEPXOM7U67TNKW5/action/storage_attestation","attest_author":"https://pith.science/pith/GXIB55E5PNFUEPXOM7U67TNKW5/action/author_attestation","sign_citation":"https://pith.science/pith/GXIB55E5PNFUEPXOM7U67TNKW5/action/citation_signature","submit_replication":"https://pith.science/pith/GXIB55E5PNFUEPXOM7U67TNKW5/action/replication_record"}},"created_at":"2026-05-18T01:59:54.532532+00:00","updated_at":"2026-05-18T01:59:54.532532+00:00"}