{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2000:XHQRHHZ7I25EX2AXGHHDREA5U4","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":"426d837564decc1319e189be3b387230e4aa6c4d4dbdffe8a5223a808240a098","cross_cats_sorted":[],"license":"","primary_cat":"math.DS","submitted_at":"2000-11-01T00:00:00Z","title_canon_sha256":"1d357a32dfa486b33559ccaea931d6aeafeacde4065567837b025276fb0850a5"},"schema_version":"1.0","source":{"id":"math/0011268","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0011268","created_at":"2026-05-18T01:05:38Z"},{"alias_kind":"arxiv_version","alias_value":"math/0011268v1","created_at":"2026-05-18T01:05:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0011268","created_at":"2026-05-18T01:05:38Z"},{"alias_kind":"pith_short_12","alias_value":"XHQRHHZ7I25E","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"XHQRHHZ7I25EX2AX","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"XHQRHHZ7","created_at":"2026-05-18T12:25:50Z"}],"graph_snapshots":[{"event_id":"sha256:12610800f386f9ce75033dcc987048a6d3445b394529ce53b6f6549b3c3b9897","target":"graph","created_at":"2026-05-18T01:05:38Z","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":"Using a variational method, we exhibit a surprisingly simple periodic orbit for the newtonian problem of three equal masses in the plane. The orbit has zero angular momentum and a very rich symmetry pattern. Its most surprising feature is that the three bodies chase each other around a fixed eight-shaped curve. Setting aside collinear motions, the only other known motion along a fixed curve in the inertial plane is the ``Lagrange relative equilibrium\" in which the three bodies form a rigid equilateral triangle which rotates at constant angular velocity within its circumscribing circle. Our orb","authors_text":"Alain Chenciner, Richard Montgomery","cross_cats":[],"headline":"","license":"","primary_cat":"math.DS","submitted_at":"2000-11-01T00:00:00Z","title":"A remarkable periodic solution of the three-body problem in the case of equal masses"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0011268","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":"sha256:49c1945aa122408bd59bb8e29afa4c558bbbe1f6392f6d202a60d96f747f37a3","target":"record","created_at":"2026-05-18T01:05:38Z","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":"426d837564decc1319e189be3b387230e4aa6c4d4dbdffe8a5223a808240a098","cross_cats_sorted":[],"license":"","primary_cat":"math.DS","submitted_at":"2000-11-01T00:00:00Z","title_canon_sha256":"1d357a32dfa486b33559ccaea931d6aeafeacde4065567837b025276fb0850a5"},"schema_version":"1.0","source":{"id":"math/0011268","kind":"arxiv","version":1}},"canonical_sha256":"b9e1139f3f46ba4be81731ce38901da73d06122c99c967431f2016a326028929","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b9e1139f3f46ba4be81731ce38901da73d06122c99c967431f2016a326028929","first_computed_at":"2026-05-18T01:05:38.051810Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:38.051810Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PSlakZShVVAxRaceDyou63Qw0gyc7B796oE1Qu8b5UjWqJFjJdhGRje59drCA8MMllsBVll6t2nabpbPtFspCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:38.052374Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0011268","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:49c1945aa122408bd59bb8e29afa4c558bbbe1f6392f6d202a60d96f747f37a3","sha256:12610800f386f9ce75033dcc987048a6d3445b394529ce53b6f6549b3c3b9897"],"state_sha256":"3b7a6c6da0b33fb7707b3218f8bbc34642c529d71d4a4be58e3ccef08c5b3c2d"}