{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:Q5YRWANVOWW725NXIY4B6SML3X","short_pith_number":"pith:Q5YRWANV","canonical_record":{"source":{"id":"1703.10920","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-03-31T14:39:07Z","cross_cats_sorted":["math.NA"],"title_canon_sha256":"0b17125cb7ca165c30de93450bf095513a1f66a5399db7881f0d45717401ab76","abstract_canon_sha256":"950ced8568021dffa09d9f5f523203b3a43d53a39315e137f9ceda0ac371a533"},"schema_version":"1.0"},"canonical_sha256":"87711b01b575adfd75b746381f498bddc51bb003f305b6eac0cd3b7071e84164","source":{"kind":"arxiv","id":"1703.10920","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.10920","created_at":"2026-05-18T00:39:12Z"},{"alias_kind":"arxiv_version","alias_value":"1703.10920v2","created_at":"2026-05-18T00:39:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.10920","created_at":"2026-05-18T00:39:12Z"},{"alias_kind":"pith_short_12","alias_value":"Q5YRWANVOWW7","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"Q5YRWANVOWW725NX","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"Q5YRWANV","created_at":"2026-05-18T12:31:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:Q5YRWANVOWW725NXIY4B6SML3X","target":"record","payload":{"canonical_record":{"source":{"id":"1703.10920","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-03-31T14:39:07Z","cross_cats_sorted":["math.NA"],"title_canon_sha256":"0b17125cb7ca165c30de93450bf095513a1f66a5399db7881f0d45717401ab76","abstract_canon_sha256":"950ced8568021dffa09d9f5f523203b3a43d53a39315e137f9ceda0ac371a533"},"schema_version":"1.0"},"canonical_sha256":"87711b01b575adfd75b746381f498bddc51bb003f305b6eac0cd3b7071e84164","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:39:12.459836Z","signature_b64":"adXUzFy8RsF8PTCG+gQnvOHsnkdIeXb3s0sJnVERHEpjF/bfjRguCGhU1TlMoCjZ65L0xfo3TCZtH2A09OM9Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"87711b01b575adfd75b746381f498bddc51bb003f305b6eac0cd3b7071e84164","last_reissued_at":"2026-05-18T00:39:12.459271Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:39:12.459271Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1703.10920","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:39:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Nhqkq+Q5c4Zjb9afOgDByghn8B0Fx/kZVSgI2VNAWIOqT8/jDmhs6oFyx68gTT2/JYkAhnCpUSUJKBZtjrYbBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T19:04:27.322780Z"},"content_sha256":"af1fa7e242273d871364f27cbd99c2c20ac7eb9c447d2ff2e9f628b65b23b01a","schema_version":"1.0","event_id":"sha256:af1fa7e242273d871364f27cbd99c2c20ac7eb9c447d2ff2e9f628b65b23b01a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:Q5YRWANVOWW725NXIY4B6SML3X","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Recovery of Core and Crustal Components of Geomagnetic Potential Fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA"],"primary_cat":"math.AP","authors_text":"Christian Gerhards, Laurent Baratchart","submitted_at":"2017-03-31T14:39:07Z","abstract_excerpt":"In Geomagnetism it is of interest to separate the Earth's core magnetic field from the crustal magnetic field. However, measurements by satellites can only sense the sum of the two contributions. In practice, the measured magnetic field is expanded in spherical harmonics and separation into crust and core contribution is achieved empirically, by a sharp cutoff in the spectral domain. In this paper, we derive a mathematical setup in which the two contributions are modeled by harmonic potentials $\\Phi_0$ and $\\Phi_1$ generated on two different spheres $\\mathbb{S}_{R_0}$ (crust) and $\\mathbb{S}_{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.10920","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:39:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xGA4slTjMUeMbLptitelnwl5UtdImEE8Ui4xBDN8kvoiuXQVGHSbb9Fb9XXqLgD97TJyjQSJTu9YYj8h7ShCCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T19:04:27.323121Z"},"content_sha256":"8dbbd7b475dc35fe1fcd0e26896f4c44db0046a22d00d65ac997bd5eb2bdae0d","schema_version":"1.0","event_id":"sha256:8dbbd7b475dc35fe1fcd0e26896f4c44db0046a22d00d65ac997bd5eb2bdae0d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Q5YRWANVOWW725NXIY4B6SML3X/bundle.json","state_url":"https://pith.science/pith/Q5YRWANVOWW725NXIY4B6SML3X/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Q5YRWANVOWW725NXIY4B6SML3X/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":"2026-06-27T19:04:27Z","links":{"resolver":"https://pith.science/pith/Q5YRWANVOWW725NXIY4B6SML3X","bundle":"https://pith.science/pith/Q5YRWANVOWW725NXIY4B6SML3X/bundle.json","state":"https://pith.science/pith/Q5YRWANVOWW725NXIY4B6SML3X/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Q5YRWANVOWW725NXIY4B6SML3X/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:Q5YRWANVOWW725NXIY4B6SML3X","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":"950ced8568021dffa09d9f5f523203b3a43d53a39315e137f9ceda0ac371a533","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-03-31T14:39:07Z","title_canon_sha256":"0b17125cb7ca165c30de93450bf095513a1f66a5399db7881f0d45717401ab76"},"schema_version":"1.0","source":{"id":"1703.10920","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.10920","created_at":"2026-05-18T00:39:12Z"},{"alias_kind":"arxiv_version","alias_value":"1703.10920v2","created_at":"2026-05-18T00:39:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.10920","created_at":"2026-05-18T00:39:12Z"},{"alias_kind":"pith_short_12","alias_value":"Q5YRWANVOWW7","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"Q5YRWANVOWW725NX","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"Q5YRWANV","created_at":"2026-05-18T12:31:37Z"}],"graph_snapshots":[{"event_id":"sha256:8dbbd7b475dc35fe1fcd0e26896f4c44db0046a22d00d65ac997bd5eb2bdae0d","target":"graph","created_at":"2026-05-18T00:39:12Z","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":"In Geomagnetism it is of interest to separate the Earth's core magnetic field from the crustal magnetic field. However, measurements by satellites can only sense the sum of the two contributions. In practice, the measured magnetic field is expanded in spherical harmonics and separation into crust and core contribution is achieved empirically, by a sharp cutoff in the spectral domain. In this paper, we derive a mathematical setup in which the two contributions are modeled by harmonic potentials $\\Phi_0$ and $\\Phi_1$ generated on two different spheres $\\mathbb{S}_{R_0}$ (crust) and $\\mathbb{S}_{","authors_text":"Christian Gerhards, Laurent Baratchart","cross_cats":["math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-03-31T14:39:07Z","title":"On the Recovery of Core and Crustal Components of Geomagnetic Potential Fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.10920","kind":"arxiv","version":2},"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:af1fa7e242273d871364f27cbd99c2c20ac7eb9c447d2ff2e9f628b65b23b01a","target":"record","created_at":"2026-05-18T00:39:12Z","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":"950ced8568021dffa09d9f5f523203b3a43d53a39315e137f9ceda0ac371a533","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-03-31T14:39:07Z","title_canon_sha256":"0b17125cb7ca165c30de93450bf095513a1f66a5399db7881f0d45717401ab76"},"schema_version":"1.0","source":{"id":"1703.10920","kind":"arxiv","version":2}},"canonical_sha256":"87711b01b575adfd75b746381f498bddc51bb003f305b6eac0cd3b7071e84164","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"87711b01b575adfd75b746381f498bddc51bb003f305b6eac0cd3b7071e84164","first_computed_at":"2026-05-18T00:39:12.459271Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:39:12.459271Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"adXUzFy8RsF8PTCG+gQnvOHsnkdIeXb3s0sJnVERHEpjF/bfjRguCGhU1TlMoCjZ65L0xfo3TCZtH2A09OM9Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:39:12.459836Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.10920","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:af1fa7e242273d871364f27cbd99c2c20ac7eb9c447d2ff2e9f628b65b23b01a","sha256:8dbbd7b475dc35fe1fcd0e26896f4c44db0046a22d00d65ac997bd5eb2bdae0d"],"state_sha256":"f9b8e18ff32d2efbfd699fb5d0b2137926572165fddfb4d4f93d35b262dd9447"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cpfm0MxPs41h2Yyynz8jYgeO1F2M9ZHWEIU8y/s4nHQ5/2N9CNE4Lrp5MRGrZscY8ofvR6+/R+Fi5fYspe27CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T19:04:27.324983Z","bundle_sha256":"ea74590743c7eee1e16a4e5134c3a24babce34b8e210b71c05cd90424b8b15e1"}}