{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:DPIJ3YOKIFHZMD4IZXUUFHFGZE","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":"55a27974f486ff7b9bb398a177eddf02b40cbe6353ec2b893660715913499c5d","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-10-16T05:46:49Z","title_canon_sha256":"3120b6645b8212ad176161629b344dca0e93ed3ab00782f594140575d4e0e047"},"schema_version":"1.0","source":{"id":"1610.04822","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.04822","created_at":"2026-05-18T00:27:53Z"},{"alias_kind":"arxiv_version","alias_value":"1610.04822v1","created_at":"2026-05-18T00:27:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.04822","created_at":"2026-05-18T00:27:53Z"},{"alias_kind":"pith_short_12","alias_value":"DPIJ3YOKIFHZ","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"DPIJ3YOKIFHZMD4I","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"DPIJ3YOK","created_at":"2026-05-18T12:30:12Z"}],"graph_snapshots":[{"event_id":"sha256:cd14277168e4fa5424450a4b70fdda05a7c4e200f8dbaabdbde689640a567298","target":"graph","created_at":"2026-05-18T00:27:53Z","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 problem of the existence of an additional (independent on the energy) first integral, of a geodesic (or magnetic geodesic) flow, which is polynomial in momenta is studied. The relation of this problem to the existence of nontrivial solutions of stationary dispersionless limits of two-dimensional soliton equations is demonstrated. The nonexistence of an additional quadratic first integral is established for certain classes of magnetic geodesic flows.","authors_text":"I.A. Taimanov","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-10-16T05:46:49Z","title":"On first integrals of geodesic flows on a two-torus"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.04822","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:bd1a49110aea9c72999f8f491acf134ad0e7bc2b0bab9b81c8e7ffcac7096e6c","target":"record","created_at":"2026-05-18T00:27:53Z","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":"55a27974f486ff7b9bb398a177eddf02b40cbe6353ec2b893660715913499c5d","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-10-16T05:46:49Z","title_canon_sha256":"3120b6645b8212ad176161629b344dca0e93ed3ab00782f594140575d4e0e047"},"schema_version":"1.0","source":{"id":"1610.04822","kind":"arxiv","version":1}},"canonical_sha256":"1bd09de1ca414f960f88cde9429ca6c92fcd4d5cc13d64f8698ba05f1aabcb61","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1bd09de1ca414f960f88cde9429ca6c92fcd4d5cc13d64f8698ba05f1aabcb61","first_computed_at":"2026-05-18T00:27:53.089912Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:27:53.089912Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2cQFFhanTihhiWvgjWmmdgF9s9loD3GNe7lPgELdFYOy0r+jhnMwsWq/KNty+5UEihBrTOlUjtybkOQsdFgOAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:27:53.090572Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.04822","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bd1a49110aea9c72999f8f491acf134ad0e7bc2b0bab9b81c8e7ffcac7096e6c","sha256:cd14277168e4fa5424450a4b70fdda05a7c4e200f8dbaabdbde689640a567298"],"state_sha256":"a5cd185a7aa4db8f1fa7ed61722e29b5f5e3e16d3b8d86b22c5547d1e89b594d"}