{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:5YOP5TUSJEF3QPZ2TLAA7RG73H","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":"eb4567cd37d29796fc6107f46c3a56af1f48951b39b4d41a077c5641670ce39d","cross_cats_sorted":["nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-04-30T11:19:39Z","title_canon_sha256":"0fb932b6bd7f39db44da0c24aede1a110d474756070813a5b31cb1e15fb6d71f"},"schema_version":"1.0","source":{"id":"1004.5499","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1004.5499","created_at":"2026-05-18T02:17:22Z"},{"alias_kind":"arxiv_version","alias_value":"1004.5499v2","created_at":"2026-05-18T02:17:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.5499","created_at":"2026-05-18T02:17:22Z"},{"alias_kind":"pith_short_12","alias_value":"5YOP5TUSJEF3","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"5YOP5TUSJEF3QPZ2","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"5YOP5TUS","created_at":"2026-05-18T12:26:04Z"}],"graph_snapshots":[{"event_id":"sha256:0d6238d5ab17e27dfabca2ae495bc17d2ad31a19c070cea607a60802b0d18bd0","target":"graph","created_at":"2026-05-18T02:17:22Z","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 billiard motion inside an ellipsoid $Q \\subset \\Rset^{n+1}$ is completely integrable. Its phase space is a symplectic manifold of dimension $2n$, which is mostly foliated with Liouville tori of dimension $n$. The motion on each Liouville torus becomes just a parallel translation with some frequency $\\omega$ that varies with the torus. Besides, any billiard trajectory inside $Q$ is tangent to $n$ caustics $Q_{\\lambda_1},...,Q_{\\lambda_n}$, so the caustic parameters $\\lambda=(\\lambda_1,...,\\lambda_n)$ are integrals of the billiard map. The frequency map $\\lambda \\mapsto \\omega$ is a key tool","authors_text":"Pablo S. Casas, Rafael Ramirez-Ros","cross_cats":["nlin.SI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-04-30T11:19:39Z","title":"The frequency map for billiards inside ellipsoids"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.5499","kind":"arxiv","version":2},"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:d50c93579a8e4f1bf66061bebb6c3df487d7a21d8e671827d77754ae50f1f4fe","target":"record","created_at":"2026-05-18T02:17:22Z","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":"eb4567cd37d29796fc6107f46c3a56af1f48951b39b4d41a077c5641670ce39d","cross_cats_sorted":["nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-04-30T11:19:39Z","title_canon_sha256":"0fb932b6bd7f39db44da0c24aede1a110d474756070813a5b31cb1e15fb6d71f"},"schema_version":"1.0","source":{"id":"1004.5499","kind":"arxiv","version":2}},"canonical_sha256":"ee1cfece92490bb83f3a9ac00fc4dfd9ebd5da3f4c36943fc75aff9596b808c3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ee1cfece92490bb83f3a9ac00fc4dfd9ebd5da3f4c36943fc75aff9596b808c3","first_computed_at":"2026-05-18T02:17:22.236957Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:17:22.236957Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zWx/+dwLr2UtUCddtJIWqiLoA+mdHwQH7JWGOj1GkqpY4U1En5RXIt3uXd5PJs7+O96hvXOx6fGaOdvya09zDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:17:22.237674Z","signed_message":"canonical_sha256_bytes"},"source_id":"1004.5499","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d50c93579a8e4f1bf66061bebb6c3df487d7a21d8e671827d77754ae50f1f4fe","sha256:0d6238d5ab17e27dfabca2ae495bc17d2ad31a19c070cea607a60802b0d18bd0"],"state_sha256":"22436180f973e3c1be4a671e76b744ef3d4b067e005854cb50a90537469c9b4d"}