{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:AF4WW3F2JFTB2AXBZP5K53LYXG","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":"7f8530c083d0ca2133bd53d9cb2a15c3458646d64adef02ef681e609e712d069","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-01-19T15:33:27Z","title_canon_sha256":"605c52357f32460668d8a1361f66c06c5601657ae04fa88800c31613249818a7"},"schema_version":"1.0","source":{"id":"1401.4681","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.4681","created_at":"2026-05-18T02:51:14Z"},{"alias_kind":"arxiv_version","alias_value":"1401.4681v1","created_at":"2026-05-18T02:51:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.4681","created_at":"2026-05-18T02:51:14Z"},{"alias_kind":"pith_short_12","alias_value":"AF4WW3F2JFTB","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"AF4WW3F2JFTB2AXB","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"AF4WW3F2","created_at":"2026-05-18T12:28:19Z"}],"graph_snapshots":[{"event_id":"sha256:104730b620ef639e84ec95d05da96aa1c981d997978191807c0e8114b8a79a14","target":"graph","created_at":"2026-05-18T02:51:14Z","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":"We obtain an approximate solution $\\tilde{E}=\\tilde{E}(e,M)$ of Kepler's equation $E-e\\sin(E)=M$ for any $e\\in[0,1)$ and $M\\in[0,\\pi]$. Our solution is guaranteed, via Smale's $\\alpha$-theory, to converge to the actual solution $E$ through Newton's method at quadratic speed, i.e. the $n$-th iteration produces a value $E_n$ such that $|E_n-E|\\leq (\\frac12)^{2^n-1}|\\tilde{E}-E|$. The formula provided for $\\tilde{E}$ is a piecewise rational function with conditions defined by polynomial inequalities, except for a small region near $e=1$ and $M=0$, where a single cubic root is used. We also show t","authors_text":"Jorge Ortigas-Galindo, Martin Avendano, Ver\\'onica Mart\\'in-Molina","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-01-19T15:33:27Z","title":"Solving Kepler's equation via Smale's $\\alpha$-theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.4681","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":"sha256:1dbf5e3c229f95fa8148fb700fa97c8bac56fb46acabaed9bb3e3da03046ca02","target":"record","created_at":"2026-05-18T02:51:14Z","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":"7f8530c083d0ca2133bd53d9cb2a15c3458646d64adef02ef681e609e712d069","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-01-19T15:33:27Z","title_canon_sha256":"605c52357f32460668d8a1361f66c06c5601657ae04fa88800c31613249818a7"},"schema_version":"1.0","source":{"id":"1401.4681","kind":"arxiv","version":1}},"canonical_sha256":"01796b6cba49661d02e1cbfaaeed78b9b6b1f0285046ac5a7a4cf31059e23900","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"01796b6cba49661d02e1cbfaaeed78b9b6b1f0285046ac5a7a4cf31059e23900","first_computed_at":"2026-05-18T02:51:14.901304Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:51:14.901304Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5X0u/sPOwmyrso8dYR78CwWvomxb7uOdjEKiD7okazTdB6U24W3HxvDp4dGoSSqoYkFcPOPJ2J4krS4lXwbYAw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:51:14.901838Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.4681","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1dbf5e3c229f95fa8148fb700fa97c8bac56fb46acabaed9bb3e3da03046ca02","sha256:104730b620ef639e84ec95d05da96aa1c981d997978191807c0e8114b8a79a14"],"state_sha256":"68432a99afd6c38e04c5b4ca7dc0de0471c825f0d918920f064f45a0150cbc02"}