{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:M5JOCE2Q5BEF2JHBUGLGWF46OF","short_pith_number":"pith:M5JOCE2Q","schema_version":"1.0","canonical_sha256":"6752e11350e8485d24e1a1966b179e717bb47fdacc1ae45f9d3815a83bdc00d9","source":{"kind":"arxiv","id":"1508.03101","version":2},"attestation_state":"computed","paper":{"title":"A novel sampling theorem on the rotation group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["astro-ph.IM","math.IT"],"primary_cat":"cs.IT","authors_text":"B. Leistedt, H. V. Peiris, J. D. McEwen, M. B\\\"uttner, Y. Wiaux","submitted_at":"2015-08-13T02:11:23Z","abstract_excerpt":"We develop a novel sampling theorem for functions defined on the three-dimensional rotation group SO(3) by connecting the rotation group to the three-torus through a periodic extension. Our sampling theorem requires $4L^3$ samples to capture all of the information content of a signal band-limited at $L$, reducing the number of required samples by a factor of two compared to other equiangular sampling theorems. We present fast algorithms to compute the associated Fourier transform on the rotation group, the so-called Wigner transform, which scale as $O(L^4)$, compared to the naive scaling of $O"},"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":"1508.03101","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-08-13T02:11:23Z","cross_cats_sorted":["astro-ph.IM","math.IT"],"title_canon_sha256":"44eb03dc6bb46afb941f0ef436f75ac3aafa02b5dea5584543a1b184b493670d","abstract_canon_sha256":"4625e7c9a524160eb1d256d8f1d8a0d8fa9e75fae6ba98318d48b6814abe39a8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:23:12.029566Z","signature_b64":"RgJ7T0wpVb2K5FMbqLjBIAbmTDEzjobfaaMVvpaXmuw+xfFCVkvTZR4Ot7u5WFEOSHPzKiRl/aOzMUiYLyQ0Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6752e11350e8485d24e1a1966b179e717bb47fdacc1ae45f9d3815a83bdc00d9","last_reissued_at":"2026-05-18T01:23:12.028989Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:23:12.028989Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A novel sampling theorem on the rotation group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["astro-ph.IM","math.IT"],"primary_cat":"cs.IT","authors_text":"B. Leistedt, H. V. Peiris, J. D. McEwen, M. B\\\"uttner, Y. Wiaux","submitted_at":"2015-08-13T02:11:23Z","abstract_excerpt":"We develop a novel sampling theorem for functions defined on the three-dimensional rotation group SO(3) by connecting the rotation group to the three-torus through a periodic extension. Our sampling theorem requires $4L^3$ samples to capture all of the information content of a signal band-limited at $L$, reducing the number of required samples by a factor of two compared to other equiangular sampling theorems. We present fast algorithms to compute the associated Fourier transform on the rotation group, the so-called Wigner transform, which scale as $O(L^4)$, compared to the naive scaling of $O"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.03101","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":"1508.03101","created_at":"2026-05-18T01:23:12.029070+00:00"},{"alias_kind":"arxiv_version","alias_value":"1508.03101v2","created_at":"2026-05-18T01:23:12.029070+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.03101","created_at":"2026-05-18T01:23:12.029070+00:00"},{"alias_kind":"pith_short_12","alias_value":"M5JOCE2Q5BEF","created_at":"2026-05-18T12:29:32.376354+00:00"},{"alias_kind":"pith_short_16","alias_value":"M5JOCE2Q5BEF2JHB","created_at":"2026-05-18T12:29:32.376354+00:00"},{"alias_kind":"pith_short_8","alias_value":"M5JOCE2Q","created_at":"2026-05-18T12:29:32.376354+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/M5JOCE2Q5BEF2JHBUGLGWF46OF","json":"https://pith.science/pith/M5JOCE2Q5BEF2JHBUGLGWF46OF.json","graph_json":"https://pith.science/api/pith-number/M5JOCE2Q5BEF2JHBUGLGWF46OF/graph.json","events_json":"https://pith.science/api/pith-number/M5JOCE2Q5BEF2JHBUGLGWF46OF/events.json","paper":"https://pith.science/paper/M5JOCE2Q"},"agent_actions":{"view_html":"https://pith.science/pith/M5JOCE2Q5BEF2JHBUGLGWF46OF","download_json":"https://pith.science/pith/M5JOCE2Q5BEF2JHBUGLGWF46OF.json","view_paper":"https://pith.science/paper/M5JOCE2Q","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1508.03101&json=true","fetch_graph":"https://pith.science/api/pith-number/M5JOCE2Q5BEF2JHBUGLGWF46OF/graph.json","fetch_events":"https://pith.science/api/pith-number/M5JOCE2Q5BEF2JHBUGLGWF46OF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/M5JOCE2Q5BEF2JHBUGLGWF46OF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/M5JOCE2Q5BEF2JHBUGLGWF46OF/action/storage_attestation","attest_author":"https://pith.science/pith/M5JOCE2Q5BEF2JHBUGLGWF46OF/action/author_attestation","sign_citation":"https://pith.science/pith/M5JOCE2Q5BEF2JHBUGLGWF46OF/action/citation_signature","submit_replication":"https://pith.science/pith/M5JOCE2Q5BEF2JHBUGLGWF46OF/action/replication_record"}},"created_at":"2026-05-18T01:23:12.029070+00:00","updated_at":"2026-05-18T01:23:12.029070+00:00"}