{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:M5RXXKOTF7CBAO4QRSUU5CJDAT","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"387b9cbbe0f309743fcf0ad935b8ec16c60cbf5d1ab75d7e692b8c68ce397d8f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2014-03-30T04:13:46Z","title_canon_sha256":"9a3d492a4b347edece6122a52afedd7c5c7a7d004dad188f108299daaa16eb79"},"schema_version":"1.0","source":{"id":"1403.7698","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.7698","created_at":"2026-05-18T02:55:12Z"},{"alias_kind":"arxiv_version","alias_value":"1403.7698v1","created_at":"2026-05-18T02:55:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.7698","created_at":"2026-05-18T02:55:12Z"},{"alias_kind":"pith_short_12","alias_value":"M5RXXKOTF7CB","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"M5RXXKOTF7CBAO4Q","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"M5RXXKOT","created_at":"2026-05-18T12:28:38Z"}],"graph_snapshots":[{"event_id":"sha256:d51cf1ceb585943969b12c32cd77f7700eefa09d647326b7ef73705005fce8b3","target":"graph","created_at":"2026-05-18T02:55:12Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Computation of the spherical harmonic rotation coefficients or elements of Wigner's d-matrix is important in a number of quantum mechanics and mathematical physics applications. Particularly, this is important for the Fast Multipole Methods in three dimensions for the Helmholtz, Laplace and related equations, if rotation-based decomposition of translation operators are used. In these and related problems related to representation of functions on a sphere via spherical harmonic expansions computation of the rotation coefficients of large degree $n$ (of the order of thousands and more) may be ne","authors_text":"Nail A. Gumerov, Ramani Duraiswami","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2014-03-30T04:13:46Z","title":"Recursive computation of spherical harmonic rotation coefficients of large degree"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.7698","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:138f347b034c7f51676a7eb8b022e102f2cc6ac49ea2e75f957a129481a32ee1","target":"record","created_at":"2026-05-18T02:55:12Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"387b9cbbe0f309743fcf0ad935b8ec16c60cbf5d1ab75d7e692b8c68ce397d8f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2014-03-30T04:13:46Z","title_canon_sha256":"9a3d492a4b347edece6122a52afedd7c5c7a7d004dad188f108299daaa16eb79"},"schema_version":"1.0","source":{"id":"1403.7698","kind":"arxiv","version":1}},"canonical_sha256":"67637ba9d32fc4103b908ca94e892304d3c6ab451713109b9f3e2439da92c741","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"67637ba9d32fc4103b908ca94e892304d3c6ab451713109b9f3e2439da92c741","first_computed_at":"2026-05-18T02:55:12.633132Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:55:12.633132Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vQnWmH6f6VU8mUFBE0+YAlp5KEVFdjqJ17msYOBe0x+vqGZ4llXoFwpk3zakAADXQ1oZVyfgAFvtJioCRamyCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:55:12.633617Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.7698","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:138f347b034c7f51676a7eb8b022e102f2cc6ac49ea2e75f957a129481a32ee1","sha256:d51cf1ceb585943969b12c32cd77f7700eefa09d647326b7ef73705005fce8b3"],"state_sha256":"f5ff6316991459de9d0bca01a52a67ac6fc56abb58383213ee8e2012961d5066"}