{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:SZ6L2RYFSWL6VAN7YQH2UJMML6","short_pith_number":"pith:SZ6L2RYF","schema_version":"1.0","canonical_sha256":"967cbd47059597ea81bfc40faa258c5f804229990319c1462425c4eba44372b6","source":{"kind":"arxiv","id":"1809.01321","version":1},"attestation_state":"computed","paper":{"title":"An Optimal-Dimensionality Sampling for Spin-$s$ Functions on the Sphere","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"astro-ph.IM","authors_text":"Jason D. McEwen, Rodney A. Kennedy, Usama Elahi, Zubair Khalid","submitted_at":"2018-09-05T04:53:26Z","abstract_excerpt":"For the representation of spin-$s$ band-limited functions on the sphere, we propose a sampling scheme with optimal number of samples equal to the number of degrees of freedom of the function in harmonic space. In comparison to the existing sampling designs, which require ${\\sim}2L^2$ samples for the representation of spin-$s$ functions band-limited at $L$, the proposed scheme requires $N_o=L^2-s^2$ samples for the accurate computation of the spin-$s$ spherical harmonic transform~($s$-SHT). For the proposed sampling scheme, we also develop a method to compute the $s$-SHT. We place the samples i"},"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":"1809.01321","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.IM","submitted_at":"2018-09-05T04:53:26Z","cross_cats_sorted":[],"title_canon_sha256":"84cdfcfd935e47e4fe84fc9f10f51aa56ae1410e555b27202bf6e102f3882c1b","abstract_canon_sha256":"f6a5958d7f2d232950a0abff07cb13a511d3da247a9cf24c0a84f21d455292ac"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:06:28.013992Z","signature_b64":"5v6TxW2LwYGHRYC1FDOoFg1luuzJilSdiuThtUx2FX6K42BLac6yhumhewN5RbJ2+yeRA2sUOf1bgDZq3FGUAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"967cbd47059597ea81bfc40faa258c5f804229990319c1462425c4eba44372b6","last_reissued_at":"2026-05-18T00:06:28.013362Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:06:28.013362Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An Optimal-Dimensionality Sampling for Spin-$s$ Functions on the Sphere","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"astro-ph.IM","authors_text":"Jason D. McEwen, Rodney A. Kennedy, Usama Elahi, Zubair Khalid","submitted_at":"2018-09-05T04:53:26Z","abstract_excerpt":"For the representation of spin-$s$ band-limited functions on the sphere, we propose a sampling scheme with optimal number of samples equal to the number of degrees of freedom of the function in harmonic space. In comparison to the existing sampling designs, which require ${\\sim}2L^2$ samples for the representation of spin-$s$ functions band-limited at $L$, the proposed scheme requires $N_o=L^2-s^2$ samples for the accurate computation of the spin-$s$ spherical harmonic transform~($s$-SHT). For the proposed sampling scheme, we also develop a method to compute the $s$-SHT. We place the samples i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.01321","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":"1809.01321","created_at":"2026-05-18T00:06:28.013468+00:00"},{"alias_kind":"arxiv_version","alias_value":"1809.01321v1","created_at":"2026-05-18T00:06:28.013468+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.01321","created_at":"2026-05-18T00:06:28.013468+00:00"},{"alias_kind":"pith_short_12","alias_value":"SZ6L2RYFSWL6","created_at":"2026-05-18T12:32:53.628368+00:00"},{"alias_kind":"pith_short_16","alias_value":"SZ6L2RYFSWL6VAN7","created_at":"2026-05-18T12:32:53.628368+00:00"},{"alias_kind":"pith_short_8","alias_value":"SZ6L2RYF","created_at":"2026-05-18T12:32:53.628368+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/SZ6L2RYFSWL6VAN7YQH2UJMML6","json":"https://pith.science/pith/SZ6L2RYFSWL6VAN7YQH2UJMML6.json","graph_json":"https://pith.science/api/pith-number/SZ6L2RYFSWL6VAN7YQH2UJMML6/graph.json","events_json":"https://pith.science/api/pith-number/SZ6L2RYFSWL6VAN7YQH2UJMML6/events.json","paper":"https://pith.science/paper/SZ6L2RYF"},"agent_actions":{"view_html":"https://pith.science/pith/SZ6L2RYFSWL6VAN7YQH2UJMML6","download_json":"https://pith.science/pith/SZ6L2RYFSWL6VAN7YQH2UJMML6.json","view_paper":"https://pith.science/paper/SZ6L2RYF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1809.01321&json=true","fetch_graph":"https://pith.science/api/pith-number/SZ6L2RYFSWL6VAN7YQH2UJMML6/graph.json","fetch_events":"https://pith.science/api/pith-number/SZ6L2RYFSWL6VAN7YQH2UJMML6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SZ6L2RYFSWL6VAN7YQH2UJMML6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SZ6L2RYFSWL6VAN7YQH2UJMML6/action/storage_attestation","attest_author":"https://pith.science/pith/SZ6L2RYFSWL6VAN7YQH2UJMML6/action/author_attestation","sign_citation":"https://pith.science/pith/SZ6L2RYFSWL6VAN7YQH2UJMML6/action/citation_signature","submit_replication":"https://pith.science/pith/SZ6L2RYFSWL6VAN7YQH2UJMML6/action/replication_record"}},"created_at":"2026-05-18T00:06:28.013468+00:00","updated_at":"2026-05-18T00:06:28.013468+00:00"}