{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1997:VGSLVPDV5NVGPAHHAAHPONPLJS","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":"056f21f8d65bdd1f1d6bdc512c3fcd3113a7c2a5a38536799a1b0ebe41f8b171","cross_cats_sorted":["math.DG"],"license":"","primary_cat":"dg-ga","submitted_at":"1997-12-23T16:01:12Z","title_canon_sha256":"938bcf4dfb823f43c69f745f3983c5a38b3a4164fa2c174ce85cec76fd4eb89b"},"schema_version":"1.0","source":{"id":"dg-ga/9712017","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"dg-ga/9712017","created_at":"2026-05-18T04:15:05Z"},{"alias_kind":"arxiv_version","alias_value":"dg-ga/9712017v1","created_at":"2026-05-18T04:15:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.dg-ga/9712017","created_at":"2026-05-18T04:15:05Z"},{"alias_kind":"pith_short_12","alias_value":"VGSLVPDV5NVG","created_at":"2026-05-18T12:25:48Z"},{"alias_kind":"pith_short_16","alias_value":"VGSLVPDV5NVGPAHH","created_at":"2026-05-18T12:25:48Z"},{"alias_kind":"pith_short_8","alias_value":"VGSLVPDV","created_at":"2026-05-18T12:25:48Z"}],"graph_snapshots":[{"event_id":"sha256:b18e657806f175715447cebb9c03325a2d53b81a0beda03c47bb81239e8ec204","target":"graph","created_at":"2026-05-18T04:15:05Z","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":"We show that an invariant surface allows to construct the Jacobi vector field along a geodesic and construct the formula for the normal component of the Jacobi field. If a geodesic is the transversal intersection of two invariant surfaces (such situation we have, for example, if the geodesic is hyperbolic), then we can construct a fundamental solution of the the Jacobi-Hill equation. This is done for quadratically integrable geodesic flows.","authors_text":"Institute of Mathematics, P.J. Topalov (BAS, Sofia), V.S. Matveev (Bremen University)","cross_cats":["math.DG"],"headline":"","license":"","primary_cat":"dg-ga","submitted_at":"1997-12-23T16:01:12Z","title":"Jacobi vector fields of integrable geodesic flows"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"dg-ga/9712017","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:e8e62b4bc71d5ea59bf47a1043acaf865429c2ed614e386f6697f1ad9b6df7be","target":"record","created_at":"2026-05-18T04:15:05Z","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":"056f21f8d65bdd1f1d6bdc512c3fcd3113a7c2a5a38536799a1b0ebe41f8b171","cross_cats_sorted":["math.DG"],"license":"","primary_cat":"dg-ga","submitted_at":"1997-12-23T16:01:12Z","title_canon_sha256":"938bcf4dfb823f43c69f745f3983c5a38b3a4164fa2c174ce85cec76fd4eb89b"},"schema_version":"1.0","source":{"id":"dg-ga/9712017","kind":"arxiv","version":1}},"canonical_sha256":"a9a4babc75eb6a6780e7000ef735eb4c803e3eba22295ad79c07fc183d384fc1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a9a4babc75eb6a6780e7000ef735eb4c803e3eba22295ad79c07fc183d384fc1","first_computed_at":"2026-05-18T04:15:05.699242Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:15:05.699242Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"g4w6n+xYfvyZt+C5uyRxZ0A51BShXtZLvoIB8SoWK+ZSpnqE5uItUUchLWIwowSh5u+mkNULR92Yjsn86u6ZCg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:15:05.699733Z","signed_message":"canonical_sha256_bytes"},"source_id":"dg-ga/9712017","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e8e62b4bc71d5ea59bf47a1043acaf865429c2ed614e386f6697f1ad9b6df7be","sha256:b18e657806f175715447cebb9c03325a2d53b81a0beda03c47bb81239e8ec204"],"state_sha256":"b351e5c1c57b5d6675dbade689821a3a9ad56c6aa716fdd5a701e1997200cead"}