{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:VQYKBHNDK6MQN7CU2AZGUE4DYP","short_pith_number":"pith:VQYKBHND","canonical_record":{"source":{"id":"1508.04410","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-08-18T19:01:39Z","cross_cats_sorted":["physics.geo-ph"],"title_canon_sha256":"9798394187c336679019c831aa64b520781afb02829227a6f22b9aaf09d4a3bd","abstract_canon_sha256":"75a26ce9e0401d1f20f49ab4380fb8938dabbfcab4092b2ec8efa8cff223c7b3"},"schema_version":"1.0"},"canonical_sha256":"ac30a09da3579906fc54d0326a1383c3f9b1ec478ea68e2f561a308beab99731","source":{"kind":"arxiv","id":"1508.04410","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.04410","created_at":"2026-05-18T01:35:05Z"},{"alias_kind":"arxiv_version","alias_value":"1508.04410v1","created_at":"2026-05-18T01:35:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.04410","created_at":"2026-05-18T01:35:05Z"},{"alias_kind":"pith_short_12","alias_value":"VQYKBHNDK6MQ","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"VQYKBHNDK6MQN7CU","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"VQYKBHND","created_at":"2026-05-18T12:29:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:VQYKBHNDK6MQN7CU2AZGUE4DYP","target":"record","payload":{"canonical_record":{"source":{"id":"1508.04410","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-08-18T19:01:39Z","cross_cats_sorted":["physics.geo-ph"],"title_canon_sha256":"9798394187c336679019c831aa64b520781afb02829227a6f22b9aaf09d4a3bd","abstract_canon_sha256":"75a26ce9e0401d1f20f49ab4380fb8938dabbfcab4092b2ec8efa8cff223c7b3"},"schema_version":"1.0"},"canonical_sha256":"ac30a09da3579906fc54d0326a1383c3f9b1ec478ea68e2f561a308beab99731","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:35:05.440849Z","signature_b64":"WgtOLifNbWRzkvAstBpXp0eePl6V45euBtiOf2nyc1yblXlz6YxSCzrBA8xt/OJBL/hSAfP1+5pQlGn/meiqBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ac30a09da3579906fc54d0326a1383c3f9b1ec478ea68e2f561a308beab99731","last_reissued_at":"2026-05-18T01:35:05.440255Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:35:05.440255Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1508.04410","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":"2026-05-18T01:35:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9n7NPzvI2dUFN3RFNDEZNAT812RBurP/UfIS8fIZR4ksSLc+KKO2WjJMWnoJK6DSbEZTkEtJUMY98hnf8f4oBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T13:46:58.236956Z"},"content_sha256":"4387be0c4b79e6c2fa2f0fb210a76e27a60c65e42d3138fef0f9db6698831866","schema_version":"1.0","event_id":"sha256:4387be0c4b79e6c2fa2f0fb210a76e27a60c65e42d3138fef0f9db6698831866"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:VQYKBHNDK6MQN7CU2AZGUE4DYP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Use of spheroidal models in gravitational tomography","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.geo-ph"],"primary_cat":"math.NA","authors_text":"Valery Sizikov","submitted_at":"2015-08-18T19:01:39Z","abstract_excerpt":"The direct gravimetry problem is solved using the subdivision of each body of a deposit into a set of vertical adjoining bars, and in the inverse problem each body of a deposit is modeled by a uniform ellipsoid of revolution (spheroid). Well-known formulas for z-component of gravitational intensity of a spheroid are transformed to a convenient form. Parameters of a spheroid are determined by minimizing the Tikhonov smoothing functional using constraints on the parameters. This makes the ill-posed inverse problem by unique and stable. The Bulakh algorithm for initial estimating the depth and ma"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.04410","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":"2026-05-18T01:35:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XFzAfS7l9tin/1E3ayIRW4sGCIN+Mw9aRcc8Vl8/bRglnN//Th6c/pIMq6qVFMk5LZw3uP+aUMOKOL8ngn4LCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T13:46:58.237625Z"},"content_sha256":"142436fd8ccbacd0d30b3efdf8c6811655fb258bb59087344ac8f7dd5e5eaa34","schema_version":"1.0","event_id":"sha256:142436fd8ccbacd0d30b3efdf8c6811655fb258bb59087344ac8f7dd5e5eaa34"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VQYKBHNDK6MQN7CU2AZGUE4DYP/bundle.json","state_url":"https://pith.science/pith/VQYKBHNDK6MQN7CU2AZGUE4DYP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VQYKBHNDK6MQN7CU2AZGUE4DYP/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":"2026-05-26T13:46:58Z","links":{"resolver":"https://pith.science/pith/VQYKBHNDK6MQN7CU2AZGUE4DYP","bundle":"https://pith.science/pith/VQYKBHNDK6MQN7CU2AZGUE4DYP/bundle.json","state":"https://pith.science/pith/VQYKBHNDK6MQN7CU2AZGUE4DYP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VQYKBHNDK6MQN7CU2AZGUE4DYP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:VQYKBHNDK6MQN7CU2AZGUE4DYP","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":"75a26ce9e0401d1f20f49ab4380fb8938dabbfcab4092b2ec8efa8cff223c7b3","cross_cats_sorted":["physics.geo-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-08-18T19:01:39Z","title_canon_sha256":"9798394187c336679019c831aa64b520781afb02829227a6f22b9aaf09d4a3bd"},"schema_version":"1.0","source":{"id":"1508.04410","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.04410","created_at":"2026-05-18T01:35:05Z"},{"alias_kind":"arxiv_version","alias_value":"1508.04410v1","created_at":"2026-05-18T01:35:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.04410","created_at":"2026-05-18T01:35:05Z"},{"alias_kind":"pith_short_12","alias_value":"VQYKBHNDK6MQ","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"VQYKBHNDK6MQN7CU","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"VQYKBHND","created_at":"2026-05-18T12:29:47Z"}],"graph_snapshots":[{"event_id":"sha256:142436fd8ccbacd0d30b3efdf8c6811655fb258bb59087344ac8f7dd5e5eaa34","target":"graph","created_at":"2026-05-18T01:35:05Z","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":"The direct gravimetry problem is solved using the subdivision of each body of a deposit into a set of vertical adjoining bars, and in the inverse problem each body of a deposit is modeled by a uniform ellipsoid of revolution (spheroid). Well-known formulas for z-component of gravitational intensity of a spheroid are transformed to a convenient form. Parameters of a spheroid are determined by minimizing the Tikhonov smoothing functional using constraints on the parameters. This makes the ill-posed inverse problem by unique and stable. The Bulakh algorithm for initial estimating the depth and ma","authors_text":"Valery Sizikov","cross_cats":["physics.geo-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-08-18T19:01:39Z","title":"Use of spheroidal models in gravitational tomography"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.04410","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":"sha256:4387be0c4b79e6c2fa2f0fb210a76e27a60c65e42d3138fef0f9db6698831866","target":"record","created_at":"2026-05-18T01:35:05Z","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":"75a26ce9e0401d1f20f49ab4380fb8938dabbfcab4092b2ec8efa8cff223c7b3","cross_cats_sorted":["physics.geo-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-08-18T19:01:39Z","title_canon_sha256":"9798394187c336679019c831aa64b520781afb02829227a6f22b9aaf09d4a3bd"},"schema_version":"1.0","source":{"id":"1508.04410","kind":"arxiv","version":1}},"canonical_sha256":"ac30a09da3579906fc54d0326a1383c3f9b1ec478ea68e2f561a308beab99731","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ac30a09da3579906fc54d0326a1383c3f9b1ec478ea68e2f561a308beab99731","first_computed_at":"2026-05-18T01:35:05.440255Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:35:05.440255Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WgtOLifNbWRzkvAstBpXp0eePl6V45euBtiOf2nyc1yblXlz6YxSCzrBA8xt/OJBL/hSAfP1+5pQlGn/meiqBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:35:05.440849Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.04410","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4387be0c4b79e6c2fa2f0fb210a76e27a60c65e42d3138fef0f9db6698831866","sha256:142436fd8ccbacd0d30b3efdf8c6811655fb258bb59087344ac8f7dd5e5eaa34"],"state_sha256":"17ad1897fce06655fe3aad259f41e61d31058c2aa698a3520a0a5dfeab7118d7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rP+UR94tSLyMfnfntlkPEjsPOluNW2fI/llS0JzSOUqV3zwV52PK0YS4NMXZPibc75IHSBw2zyLbyhPDTwgEDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T13:46:58.241190Z","bundle_sha256":"3bfd9abeecc48e0a17197163985c1e93e785d899afed1c56b7c17637a0c6e768"}}