{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1999:CJ7N3Y6FISNE5GR6JXMQ66GS76","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":"48f7ddb1ed87f7b1eeade8e5c61c1a5f5feacb0b516fb8bb0617acd3230eae65","cross_cats_sorted":["math.DS","math.MP"],"license":"","primary_cat":"math-ph","submitted_at":"1999-06-01T06:31:14Z","title_canon_sha256":"1e25ef184fe1414573c54ab2b581e87537f1874db6fb83ed98c524d8037c28d4"},"schema_version":"1.0","source":{"id":"math-ph/9906001","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/9906001","created_at":"2026-05-18T01:38:30Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/9906001v1","created_at":"2026-05-18T01:38:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/9906001","created_at":"2026-05-18T01:38:30Z"},{"alias_kind":"pith_short_12","alias_value":"CJ7N3Y6FISNE","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"CJ7N3Y6FISNE5GR6","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"CJ7N3Y6F","created_at":"2026-05-18T12:25:49Z"}],"graph_snapshots":[{"event_id":"sha256:d9d74c16c3fdd6e04a81c956355f85e3398005d1f47d39b299ada6169cbb07df","target":"graph","created_at":"2026-05-18T01:38:30Z","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":"It is shown that any second order dynamic equation on a configuration bundle $Q\\to R$ of non-relativistic mechanics is equivalent to a geodesic equation with respect to a (non-linear) connection on the tangent bundle $TQ\\to Q$. The case of quadratic dynamic equations is analyzed in details. The equation for Jacobi vector fields is constructed and investigated by the geometric methods.","authors_text":"G.Sardanashvily, L.Mangiarotti","cross_cats":["math.DS","math.MP"],"headline":"","license":"","primary_cat":"math-ph","submitted_at":"1999-06-01T06:31:14Z","title":"On the Geodesic Form of Non-Relativistic Dynamic Equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/9906001","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":"sha256:0f572e421d6703cc381f464ce7ec8c26185c153a1fb649d2b06dd1583b97a140","target":"record","created_at":"2026-05-18T01:38:30Z","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":"48f7ddb1ed87f7b1eeade8e5c61c1a5f5feacb0b516fb8bb0617acd3230eae65","cross_cats_sorted":["math.DS","math.MP"],"license":"","primary_cat":"math-ph","submitted_at":"1999-06-01T06:31:14Z","title_canon_sha256":"1e25ef184fe1414573c54ab2b581e87537f1874db6fb83ed98c524d8037c28d4"},"schema_version":"1.0","source":{"id":"math-ph/9906001","kind":"arxiv","version":1}},"canonical_sha256":"127edde3c5449a4e9a3e4dd90f78d2ff9527c44f1d166997c765ca621e098a6d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"127edde3c5449a4e9a3e4dd90f78d2ff9527c44f1d166997c765ca621e098a6d","first_computed_at":"2026-05-18T01:38:30.548658Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:38:30.548658Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VJeJRuKOgyMHle5bPMo3U4v6naGmR4OAm2EHC4DzO9ZXvnMpAxBRNVIGK5IQnnKQv29ow1t6KT7uOG8H8VYKBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:38:30.549380Z","signed_message":"canonical_sha256_bytes"},"source_id":"math-ph/9906001","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0f572e421d6703cc381f464ce7ec8c26185c153a1fb649d2b06dd1583b97a140","sha256:d9d74c16c3fdd6e04a81c956355f85e3398005d1f47d39b299ada6169cbb07df"],"state_sha256":"8e6e7321e94b71a333ef9557f19e888f6953f20b6dd8c2da9f454392346d0e1d"}