{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2006:3M2UVNI46NHY3YKVLXCDGXR7F5","short_pith_number":"pith:3M2UVNI4","schema_version":"1.0","canonical_sha256":"db354ab51cf34f8de1555dc4335e3f2f4cc8d37e26c4d8fbf135a4317e590b1b","source":{"kind":"arxiv","id":"math-ph/0612046","version":2},"attestation_state":"computed","paper":{"title":"Sampling Theorem and Discrete Fourier Transform on the Riemann Sphere","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Juan Carlos S\\'anchez-Monreal, Julio Guerrero, Manuel Calixto","submitted_at":"2006-12-15T11:57:44Z","abstract_excerpt":"Using coherent-state techniques, we prove a sampling theorem for Majorana's (holomorphic) functions on the Riemann sphere and we provide an exact reconstruction formula as a convolution product of $N$ samples and a given reconstruction kernel (a sinc-type function). We also discuss the effect of over- and under-sampling. Sample points are roots of unity, a fact which allows explicit inversion formulas for resolution and overlapping kernel operators through the theory of Circulant Matrices and Rectangular Fourier Matrices. The case of band-limited functions on the Riemann sphere, with spins up "},"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":"math-ph/0612046","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2006-12-15T11:57:44Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"e692c8e349e392c78670a13c255d4901a712252386797f599298bd7731390fed","abstract_canon_sha256":"d4dfc74494c01f9dce97f93c980ed931f9fb77804c65b00130704035cb7773f0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:13:27.298856Z","signature_b64":"uQ4QeOofQn8uyE/DFFpXOU/z5kBbTRuLylDqc4ipVHQNl0FBnowJyJ9ZeLkHYRSwFa5vmXs/uXNtjGbNyv2gBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"db354ab51cf34f8de1555dc4335e3f2f4cc8d37e26c4d8fbf135a4317e590b1b","last_reissued_at":"2026-05-18T04:13:27.298270Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:13:27.298270Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sampling Theorem and Discrete Fourier Transform on the Riemann Sphere","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Juan Carlos S\\'anchez-Monreal, Julio Guerrero, Manuel Calixto","submitted_at":"2006-12-15T11:57:44Z","abstract_excerpt":"Using coherent-state techniques, we prove a sampling theorem for Majorana's (holomorphic) functions on the Riemann sphere and we provide an exact reconstruction formula as a convolution product of $N$ samples and a given reconstruction kernel (a sinc-type function). We also discuss the effect of over- and under-sampling. Sample points are roots of unity, a fact which allows explicit inversion formulas for resolution and overlapping kernel operators through the theory of Circulant Matrices and Rectangular Fourier Matrices. The case of band-limited functions on the Riemann sphere, with spins up "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0612046","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":"math-ph/0612046","created_at":"2026-05-18T04:13:27.298372+00:00"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0612046v2","created_at":"2026-05-18T04:13:27.298372+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0612046","created_at":"2026-05-18T04:13:27.298372+00:00"},{"alias_kind":"pith_short_12","alias_value":"3M2UVNI46NHY","created_at":"2026-05-18T12:25:53.939244+00:00"},{"alias_kind":"pith_short_16","alias_value":"3M2UVNI46NHY3YKV","created_at":"2026-05-18T12:25:53.939244+00:00"},{"alias_kind":"pith_short_8","alias_value":"3M2UVNI4","created_at":"2026-05-18T12:25:53.939244+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/3M2UVNI46NHY3YKVLXCDGXR7F5","json":"https://pith.science/pith/3M2UVNI46NHY3YKVLXCDGXR7F5.json","graph_json":"https://pith.science/api/pith-number/3M2UVNI46NHY3YKVLXCDGXR7F5/graph.json","events_json":"https://pith.science/api/pith-number/3M2UVNI46NHY3YKVLXCDGXR7F5/events.json","paper":"https://pith.science/paper/3M2UVNI4"},"agent_actions":{"view_html":"https://pith.science/pith/3M2UVNI46NHY3YKVLXCDGXR7F5","download_json":"https://pith.science/pith/3M2UVNI46NHY3YKVLXCDGXR7F5.json","view_paper":"https://pith.science/paper/3M2UVNI4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math-ph/0612046&json=true","fetch_graph":"https://pith.science/api/pith-number/3M2UVNI46NHY3YKVLXCDGXR7F5/graph.json","fetch_events":"https://pith.science/api/pith-number/3M2UVNI46NHY3YKVLXCDGXR7F5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3M2UVNI46NHY3YKVLXCDGXR7F5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3M2UVNI46NHY3YKVLXCDGXR7F5/action/storage_attestation","attest_author":"https://pith.science/pith/3M2UVNI46NHY3YKVLXCDGXR7F5/action/author_attestation","sign_citation":"https://pith.science/pith/3M2UVNI46NHY3YKVLXCDGXR7F5/action/citation_signature","submit_replication":"https://pith.science/pith/3M2UVNI46NHY3YKVLXCDGXR7F5/action/replication_record"}},"created_at":"2026-05-18T04:13:27.298372+00:00","updated_at":"2026-05-18T04:13:27.298372+00:00"}