{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:JREWRXUY3ZKVC4IUC7ZIPO3V4T","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":"ebdf7235d5df51ea322b1a34b44654d3ff69d40fe3591b03995cc27d92edaec3","cross_cats_sorted":["math.DS","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-08-23T04:57:10Z","title_canon_sha256":"e0c5b9e1133594b75801f51248562ebc824dde015e1bb60f93c0a1c489aff062"},"schema_version":"1.0","source":{"id":"1808.07633","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.07633","created_at":"2026-05-18T00:07:26Z"},{"alias_kind":"arxiv_version","alias_value":"1808.07633v1","created_at":"2026-05-18T00:07:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.07633","created_at":"2026-05-18T00:07:26Z"},{"alias_kind":"pith_short_12","alias_value":"JREWRXUY3ZKV","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_16","alias_value":"JREWRXUY3ZKVC4IU","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_8","alias_value":"JREWRXUY","created_at":"2026-05-18T12:32:31Z"}],"graph_snapshots":[{"event_id":"sha256:132ee30737203256ed0b0027608b302e91aa855ca97a76f55e3dc7e3a31d7912","target":"graph","created_at":"2026-05-18T00:07:26Z","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 first integral characteristic of the two--centres problem is proven to be an approximate integral (in the sense of N.N.Nekhorossev) to the three--body problem, at least if the masses are very different and the particles are constrained on the same plane. The proof uses a new normal form result, carefully designed around the degeneracies of the problem, and a new study of the phase portrait of the unperturbed problem. Applications to the prediction of collisions between the two minor bodies are shown.","authors_text":"Gabriella Pinzari","cross_cats":["math.DS","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-08-23T04:57:10Z","title":"Exponential stability of Euler integral in the three--body problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.07633","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:a7d5f637610ff827fa03808543cc681adfb463bed53f6433b30fa123edae7e81","target":"record","created_at":"2026-05-18T00:07:26Z","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":"ebdf7235d5df51ea322b1a34b44654d3ff69d40fe3591b03995cc27d92edaec3","cross_cats_sorted":["math.DS","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-08-23T04:57:10Z","title_canon_sha256":"e0c5b9e1133594b75801f51248562ebc824dde015e1bb60f93c0a1c489aff062"},"schema_version":"1.0","source":{"id":"1808.07633","kind":"arxiv","version":1}},"canonical_sha256":"4c4968de98de5551711417f287bb75e4ecd7bdbed6796c7cf49274746aba6db2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4c4968de98de5551711417f287bb75e4ecd7bdbed6796c7cf49274746aba6db2","first_computed_at":"2026-05-18T00:07:26.666994Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:07:26.666994Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"icSiZrCX0FG9YUmiFCaVr3aS6rbFO4bqiKIT3LhD+g/bq7y2Z/zAlk1RrvUT30DTbQISQ1/pRSOaM8CpQ9WGCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:07:26.667556Z","signed_message":"canonical_sha256_bytes"},"source_id":"1808.07633","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a7d5f637610ff827fa03808543cc681adfb463bed53f6433b30fa123edae7e81","sha256:132ee30737203256ed0b0027608b302e91aa855ca97a76f55e3dc7e3a31d7912"],"state_sha256":"010d467fdd8163c09d2ec00c5b3fa1bb0943ca5d390da6e981164ff1115f5bff"}