{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:G4QL56CJKEJ7LO4TKMD57M2FPN","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":"73816d9e16792b39fc1d7edff9d9b28cc58bed740888c7597b6459c10fb1748f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-03-04T22:04:39Z","title_canon_sha256":"82f81b175c9ed8a29d41816714ef49da288718c7f02b77c1773ca5152b574895"},"schema_version":"1.0","source":{"id":"1403.0963","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.0963","created_at":"2026-05-18T02:57:06Z"},{"alias_kind":"arxiv_version","alias_value":"1403.0963v1","created_at":"2026-05-18T02:57:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.0963","created_at":"2026-05-18T02:57:06Z"},{"alias_kind":"pith_short_12","alias_value":"G4QL56CJKEJ7","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"G4QL56CJKEJ7LO4T","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"G4QL56CJ","created_at":"2026-05-18T12:28:28Z"}],"graph_snapshots":[{"event_id":"sha256:478e7abadc31f3ee19b3a426a7c9b3a0f7f3b40b6eba907298a06d93cde15809","target":"graph","created_at":"2026-05-18T02:57:06Z","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":"Analysis on the unit sphere $\\mathbb{S}^{2}$ found many applications in seismology, weather prediction, astrophysics, signal analysis, crystallography, computer vision, computerized tomography, neuroscience, and statistics.\n  In the last two decades, the importance of these and other applications triggered the development of various tools such as splines and wavelet bases suitable for the unit spheres $\\mathbb{S}^{2}$, $\\>\\>\\mathbb{S}^{3}$ and the rotation group $SO(3)$. Present paper is a summary of some of results of the author and his collaborators on generalized (average) variational splin","authors_text":"Isaac Pesenson","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-03-04T22:04:39Z","title":"Splines and Wavelets on Geophysically Relevant Manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.0963","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:a6726d78239790c063019ec75bd568fbc0489cdd93c1f6b22ad75f63b789e039","target":"record","created_at":"2026-05-18T02:57:06Z","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":"73816d9e16792b39fc1d7edff9d9b28cc58bed740888c7597b6459c10fb1748f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-03-04T22:04:39Z","title_canon_sha256":"82f81b175c9ed8a29d41816714ef49da288718c7f02b77c1773ca5152b574895"},"schema_version":"1.0","source":{"id":"1403.0963","kind":"arxiv","version":1}},"canonical_sha256":"3720bef8495113f5bb935307dfb3457b607c63235b780886a0d34e5a17a89f6d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3720bef8495113f5bb935307dfb3457b607c63235b780886a0d34e5a17a89f6d","first_computed_at":"2026-05-18T02:57:06.032424Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:57:06.032424Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IWgSKaghKRbplLi4Bp+O2lrazb0h4HtM1k4+NakU5x6XB3tKp8Cg5l5kudCr8CYKedrjDSX67fS/Q3oVLv25DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:57:06.033074Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.0963","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a6726d78239790c063019ec75bd568fbc0489cdd93c1f6b22ad75f63b789e039","sha256:478e7abadc31f3ee19b3a426a7c9b3a0f7f3b40b6eba907298a06d93cde15809"],"state_sha256":"535f8605182f03a63603a8cf0544e2f50c967ad19dec70e568af680de351fbe3"}