{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:AI7UE7AY5Q73FOQG5LOCCTXHCC","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":"1732986d1130c57e93ea8260ab6618efa6348d19874f5bc9f04c544d22d2e06e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.space-ph","submitted_at":"2019-02-14T15:56:59Z","title_canon_sha256":"709f529a886e1c6ab7c6ea6747c19c49d120340c6a3fefda0a52849ca963f30b"},"schema_version":"1.0","source":{"id":"1902.05463","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.05463","created_at":"2026-05-17T23:53:58Z"},{"alias_kind":"arxiv_version","alias_value":"1902.05463v1","created_at":"2026-05-17T23:53:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.05463","created_at":"2026-05-17T23:53:58Z"},{"alias_kind":"pith_short_12","alias_value":"AI7UE7AY5Q73","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_16","alias_value":"AI7UE7AY5Q73FOQG","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_8","alias_value":"AI7UE7AY","created_at":"2026-05-18T12:33:12Z"}],"graph_snapshots":[{"event_id":"sha256:f324538c006705ac00dff67e96f7d22fafcce1aebf5dc5549af89c053c4e75e5","target":"graph","created_at":"2026-05-17T23:53:58Z","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 the context of general perturbation theories, the main problem of the artificial satellite analyses the motion of an orbiter around an Earth-like planet, only perturbed by its equatorial bulge or J2 effect. By means of a Lie transform and the Krylov-Bogoliubov-Mitropolsky method, a first-order theory in closed form of the eccentricity is produced. During the evaluation of the theory it is necessary to solve a generalization of the classical Kepler's equation. In this work, the application of a numerical technique and three initial guesses to the Generalized Kepler's equation are discussed.","authors_text":"Denis Hautesserres, Juan F\\'elix San-Juan, Rosario L\\'opez","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.space-ph","submitted_at":"2019-02-14T15:56:59Z","title":"The solution of the Generalized Kepler's equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.05463","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:fc8b15d0b97234f0c271142adb9b307f2dd74ff473b4e3544f0a22ceb3d99d3a","target":"record","created_at":"2026-05-17T23:53:58Z","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":"1732986d1130c57e93ea8260ab6618efa6348d19874f5bc9f04c544d22d2e06e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.space-ph","submitted_at":"2019-02-14T15:56:59Z","title_canon_sha256":"709f529a886e1c6ab7c6ea6747c19c49d120340c6a3fefda0a52849ca963f30b"},"schema_version":"1.0","source":{"id":"1902.05463","kind":"arxiv","version":1}},"canonical_sha256":"023f427c18ec3fb2ba06eadc214ee710a4ee780cc6d41ab1d3d0455ac43cfe32","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"023f427c18ec3fb2ba06eadc214ee710a4ee780cc6d41ab1d3d0455ac43cfe32","first_computed_at":"2026-05-17T23:53:58.633123Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:53:58.633123Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rmdbGidUTwJshwuucKS9Psu7dteM7Vm2ZCMXjlLfUgPrUSyUrWy3X7oksNrpQUoPbZIaAUa5yTZ6JIgcliBfBQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:53:58.633868Z","signed_message":"canonical_sha256_bytes"},"source_id":"1902.05463","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fc8b15d0b97234f0c271142adb9b307f2dd74ff473b4e3544f0a22ceb3d99d3a","sha256:f324538c006705ac00dff67e96f7d22fafcce1aebf5dc5549af89c053c4e75e5"],"state_sha256":"1b9d18f51dc31d71c3b2ce66c5d957fbdbaebcdaa5598e607d919f607c3dc3c8"}