{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:BBXM6XGMPORMXYQQ5ZRM76GRWO","short_pith_number":"pith:BBXM6XGM","canonical_record":{"source":{"id":"1404.1475","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-04-05T13:07:59Z","cross_cats_sorted":[],"title_canon_sha256":"c0c8e82bd375d01ef1677aaa9455d6e6538aff6bcdc4c9c4c608e3b6474771e3","abstract_canon_sha256":"f6fb39d701d6740e2bb96c630a71c96e84cb6d7163911c99252037eb249b6538"},"schema_version":"1.0"},"canonical_sha256":"086ecf5ccc7ba2cbe210ee62cff8d1b3802be5525c8cb7b4aa05d7425aec5956","source":{"kind":"arxiv","id":"1404.1475","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.1475","created_at":"2026-05-18T02:54:46Z"},{"alias_kind":"arxiv_version","alias_value":"1404.1475v1","created_at":"2026-05-18T02:54:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.1475","created_at":"2026-05-18T02:54:46Z"},{"alias_kind":"pith_short_12","alias_value":"BBXM6XGMPORM","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"BBXM6XGMPORMXYQQ","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"BBXM6XGM","created_at":"2026-05-18T12:28:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:BBXM6XGMPORMXYQQ5ZRM76GRWO","target":"record","payload":{"canonical_record":{"source":{"id":"1404.1475","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-04-05T13:07:59Z","cross_cats_sorted":[],"title_canon_sha256":"c0c8e82bd375d01ef1677aaa9455d6e6538aff6bcdc4c9c4c608e3b6474771e3","abstract_canon_sha256":"f6fb39d701d6740e2bb96c630a71c96e84cb6d7163911c99252037eb249b6538"},"schema_version":"1.0"},"canonical_sha256":"086ecf5ccc7ba2cbe210ee62cff8d1b3802be5525c8cb7b4aa05d7425aec5956","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:54:46.191542Z","signature_b64":"D/p2tj2UMpbuGzLIjdqU7poJry6DlB7F7T+V7afqNzV+RpKeTfYYO0T/AxZToVDNazjJFPl01NUhNfA6FGC2Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"086ecf5ccc7ba2cbe210ee62cff8d1b3802be5525c8cb7b4aa05d7425aec5956","last_reissued_at":"2026-05-18T02:54:46.191157Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:54:46.191157Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1404.1475","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:54:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CiiGTgYzyiNWFk32sUMnHWKnBmMUoPcjXHYa7W/oGRq7BxHuYuiwUpAdQAGPnup999/AjOjxWQdIBjbbcuFfCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T07:54:45.133116Z"},"content_sha256":"f97949efaa5c8b5d5c694ca505eeb31f4518ea758e6be64c24d1845b5702fc45","schema_version":"1.0","event_id":"sha256:f97949efaa5c8b5d5c694ca505eeb31f4518ea758e6be64c24d1845b5702fc45"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:BBXM6XGMPORMXYQQ5ZRM76GRWO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hybrid spherical approximation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Alessandra De Rossi","submitted_at":"2014-04-05T13:07:59Z","abstract_excerpt":"In this paper a local approximation method on the sphere is presented. As interpolation scheme we consider a partition of unity method, such as the modified spherical Shepard's method, which uses zonal basis functions (ZBFs) plus spherical harmonics as local approximants. Moreover, a spherical zone algorithm is efficiently implemented, which works well also when the amount of data is very large, since it is based on an optimized searching procedure. Numerical results show good accuracy of the method, also on real geomagnetic data."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.1475","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:54:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mQfowQL11oGgUmFXf+hSUAYSOAjy6lDk9qGiie5AKeFOu/WVcxEUdKu01T9YIez399hHTImHG4EjkeHfUHmNAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T07:54:45.133750Z"},"content_sha256":"ea1cf925bd1c51d06a58b2cb2ebdd61cfddf8c1c8bb366634b893f58808ff8dd","schema_version":"1.0","event_id":"sha256:ea1cf925bd1c51d06a58b2cb2ebdd61cfddf8c1c8bb366634b893f58808ff8dd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BBXM6XGMPORMXYQQ5ZRM76GRWO/bundle.json","state_url":"https://pith.science/pith/BBXM6XGMPORMXYQQ5ZRM76GRWO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BBXM6XGMPORMXYQQ5ZRM76GRWO/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-23T07:54:45Z","links":{"resolver":"https://pith.science/pith/BBXM6XGMPORMXYQQ5ZRM76GRWO","bundle":"https://pith.science/pith/BBXM6XGMPORMXYQQ5ZRM76GRWO/bundle.json","state":"https://pith.science/pith/BBXM6XGMPORMXYQQ5ZRM76GRWO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BBXM6XGMPORMXYQQ5ZRM76GRWO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:BBXM6XGMPORMXYQQ5ZRM76GRWO","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":"f6fb39d701d6740e2bb96c630a71c96e84cb6d7163911c99252037eb249b6538","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-04-05T13:07:59Z","title_canon_sha256":"c0c8e82bd375d01ef1677aaa9455d6e6538aff6bcdc4c9c4c608e3b6474771e3"},"schema_version":"1.0","source":{"id":"1404.1475","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.1475","created_at":"2026-05-18T02:54:46Z"},{"alias_kind":"arxiv_version","alias_value":"1404.1475v1","created_at":"2026-05-18T02:54:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.1475","created_at":"2026-05-18T02:54:46Z"},{"alias_kind":"pith_short_12","alias_value":"BBXM6XGMPORM","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"BBXM6XGMPORMXYQQ","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"BBXM6XGM","created_at":"2026-05-18T12:28:22Z"}],"graph_snapshots":[{"event_id":"sha256:ea1cf925bd1c51d06a58b2cb2ebdd61cfddf8c1c8bb366634b893f58808ff8dd","target":"graph","created_at":"2026-05-18T02:54:46Z","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":"In this paper a local approximation method on the sphere is presented. As interpolation scheme we consider a partition of unity method, such as the modified spherical Shepard's method, which uses zonal basis functions (ZBFs) plus spherical harmonics as local approximants. Moreover, a spherical zone algorithm is efficiently implemented, which works well also when the amount of data is very large, since it is based on an optimized searching procedure. Numerical results show good accuracy of the method, also on real geomagnetic data.","authors_text":"Alessandra De Rossi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-04-05T13:07:59Z","title":"Hybrid spherical approximation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.1475","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:f97949efaa5c8b5d5c694ca505eeb31f4518ea758e6be64c24d1845b5702fc45","target":"record","created_at":"2026-05-18T02:54:46Z","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":"f6fb39d701d6740e2bb96c630a71c96e84cb6d7163911c99252037eb249b6538","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-04-05T13:07:59Z","title_canon_sha256":"c0c8e82bd375d01ef1677aaa9455d6e6538aff6bcdc4c9c4c608e3b6474771e3"},"schema_version":"1.0","source":{"id":"1404.1475","kind":"arxiv","version":1}},"canonical_sha256":"086ecf5ccc7ba2cbe210ee62cff8d1b3802be5525c8cb7b4aa05d7425aec5956","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"086ecf5ccc7ba2cbe210ee62cff8d1b3802be5525c8cb7b4aa05d7425aec5956","first_computed_at":"2026-05-18T02:54:46.191157Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:54:46.191157Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"D/p2tj2UMpbuGzLIjdqU7poJry6DlB7F7T+V7afqNzV+RpKeTfYYO0T/AxZToVDNazjJFPl01NUhNfA6FGC2Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:54:46.191542Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.1475","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f97949efaa5c8b5d5c694ca505eeb31f4518ea758e6be64c24d1845b5702fc45","sha256:ea1cf925bd1c51d06a58b2cb2ebdd61cfddf8c1c8bb366634b893f58808ff8dd"],"state_sha256":"d68125947ca39ad188e2c8e4fb2992299f68017ebd4b216727645ce15d5d9031"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"S+r6GiUYGJLunosRlLNtvXggvK7MI3k8Kkkfl5f5ZN6/oauC4jjql8ECiG6XWEIuDhXXs3oMPEI9FfNLbD1nBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-23T07:54:45.137020Z","bundle_sha256":"647a31ef23c2e311f5f3b4bda3c08fc79e368ae33b2b964ecb9d93b8f147e0ad"}}