{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:57NQMZ6OCUVU2HD7J7LPGCPTFA","short_pith_number":"pith:57NQMZ6O","schema_version":"1.0","canonical_sha256":"efdb0667ce152b4d1c7f4fd6f309f3280f09fd4c0bec48f1b6ff99d198a247dd","source":{"kind":"arxiv","id":"1312.5856","version":2},"attestation_state":"computed","paper":{"title":"A Combination of Downward Continuation and Local Approximation for Harmonic Potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Christian Gerhards","submitted_at":"2013-12-20T08:56:37Z","abstract_excerpt":"This paper presents a method for the approximation of harmonic potentials that combines downward continuation of globally available data on a sphere $\\Omega_R$ of radius $R$ (e.g., a satellite's orbit) with locally available data on a sphere $\\Omega_r$ of radius $r<R$ (e.g., the spherical Earth's surface). The approximation is based on a two-step algorithm motivated by spherical multiscale expansions: First, a convolution with a scaling kernel $\\Phi_N$ deals with the downward continuation from $\\Omega_R$ to $\\Omega_r$, while in a second step, the result is locally refined by a convolution on $"},"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":"1312.5856","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-12-20T08:56:37Z","cross_cats_sorted":[],"title_canon_sha256":"f67d00d4e55e4f2910edd94379c7dc47a98776307a4e80583abc8150cd899c3d","abstract_canon_sha256":"02fd0721e91004de79ef97c728601de13c37c4875b59cf98e5b08e47af789496"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:37:21.641925Z","signature_b64":"Cw1WWD33phqb2tbhDSaf2xkB7eM3RcYJiYfyaRGWRawISmz8m9gKfG2vyBnu3fD3NkI1A9TA3NnQHy9GBge2CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"efdb0667ce152b4d1c7f4fd6f309f3280f09fd4c0bec48f1b6ff99d198a247dd","last_reissued_at":"2026-05-18T01:37:21.641279Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:37:21.641279Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Combination of Downward Continuation and Local Approximation for Harmonic Potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Christian Gerhards","submitted_at":"2013-12-20T08:56:37Z","abstract_excerpt":"This paper presents a method for the approximation of harmonic potentials that combines downward continuation of globally available data on a sphere $\\Omega_R$ of radius $R$ (e.g., a satellite's orbit) with locally available data on a sphere $\\Omega_r$ of radius $r<R$ (e.g., the spherical Earth's surface). The approximation is based on a two-step algorithm motivated by spherical multiscale expansions: First, a convolution with a scaling kernel $\\Phi_N$ deals with the downward continuation from $\\Omega_R$ to $\\Omega_r$, while in a second step, the result is locally refined by a convolution on $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.5856","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":"1312.5856","created_at":"2026-05-18T01:37:21.641381+00:00"},{"alias_kind":"arxiv_version","alias_value":"1312.5856v2","created_at":"2026-05-18T01:37:21.641381+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.5856","created_at":"2026-05-18T01:37:21.641381+00:00"},{"alias_kind":"pith_short_12","alias_value":"57NQMZ6OCUVU","created_at":"2026-05-18T12:27:34.582898+00:00"},{"alias_kind":"pith_short_16","alias_value":"57NQMZ6OCUVU2HD7","created_at":"2026-05-18T12:27:34.582898+00:00"},{"alias_kind":"pith_short_8","alias_value":"57NQMZ6O","created_at":"2026-05-18T12:27:34.582898+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/57NQMZ6OCUVU2HD7J7LPGCPTFA","json":"https://pith.science/pith/57NQMZ6OCUVU2HD7J7LPGCPTFA.json","graph_json":"https://pith.science/api/pith-number/57NQMZ6OCUVU2HD7J7LPGCPTFA/graph.json","events_json":"https://pith.science/api/pith-number/57NQMZ6OCUVU2HD7J7LPGCPTFA/events.json","paper":"https://pith.science/paper/57NQMZ6O"},"agent_actions":{"view_html":"https://pith.science/pith/57NQMZ6OCUVU2HD7J7LPGCPTFA","download_json":"https://pith.science/pith/57NQMZ6OCUVU2HD7J7LPGCPTFA.json","view_paper":"https://pith.science/paper/57NQMZ6O","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1312.5856&json=true","fetch_graph":"https://pith.science/api/pith-number/57NQMZ6OCUVU2HD7J7LPGCPTFA/graph.json","fetch_events":"https://pith.science/api/pith-number/57NQMZ6OCUVU2HD7J7LPGCPTFA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/57NQMZ6OCUVU2HD7J7LPGCPTFA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/57NQMZ6OCUVU2HD7J7LPGCPTFA/action/storage_attestation","attest_author":"https://pith.science/pith/57NQMZ6OCUVU2HD7J7LPGCPTFA/action/author_attestation","sign_citation":"https://pith.science/pith/57NQMZ6OCUVU2HD7J7LPGCPTFA/action/citation_signature","submit_replication":"https://pith.science/pith/57NQMZ6OCUVU2HD7J7LPGCPTFA/action/replication_record"}},"created_at":"2026-05-18T01:37:21.641381+00:00","updated_at":"2026-05-18T01:37:21.641381+00:00"}