{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1996:7GGYRVVEL2IGX6TT4Q23DOVFR6","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":"b363bcd7ef1cf64982a77092f8c2f593c835cec04d2b2460e493abd6735dfea5","cross_cats_sorted":[],"license":"","primary_cat":"math.DS","submitted_at":"1996-01-15T00:00:00Z","title_canon_sha256":"839aeeea41d2cb9be564aecc774c63bec53d7daeb3b6a0a56c611d89b017a229"},"schema_version":"1.0","source":{"id":"math/9601212","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9601212","created_at":"2026-05-18T01:05:47Z"},{"alias_kind":"arxiv_version","alias_value":"math/9601212v1","created_at":"2026-05-18T01:05:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9601212","created_at":"2026-05-18T01:05:47Z"},{"alias_kind":"pith_short_12","alias_value":"7GGYRVVEL2IG","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_16","alias_value":"7GGYRVVEL2IGX6TT","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_8","alias_value":"7GGYRVVE","created_at":"2026-05-18T12:25:47Z"}],"graph_snapshots":[{"event_id":"sha256:01be806d7f4dcf5c877ec17ae81af4a387eafb1083a164c985d850395e153250","target":"graph","created_at":"2026-05-18T01:05:47Z","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":"This paper gives two results that show that the dynamics of a time-periodic Lagrangian system on a hyperbolic manifold are at least as complicated as the geodesic flow of a hyperbolic metric. Given a hyperbolic geodesic in the Poincar\\'e ball, Theorem A asserts that there are minimizers of the lift of the Lagrangian system that are a bounded distance away and have a variety of approximate speeds. Theorem B gives the existence of a collection of compact invariant sets of the Euler-Lagrange flow that are semiconjugate to the geodesic flow of a hyperbolic metric. These results can be viewed as a ","authors_text":"Christopher Gol\\'e, Philip Boyland","cross_cats":[],"headline":"","license":"","primary_cat":"math.DS","submitted_at":"1996-01-15T00:00:00Z","title":"Lagrangian systems on hyperbolic manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9601212","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:e49a8453bf4852be5b973e433abc022f8995f7b1caa8f07983c4785c1b36fd14","target":"record","created_at":"2026-05-18T01:05:47Z","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":"b363bcd7ef1cf64982a77092f8c2f593c835cec04d2b2460e493abd6735dfea5","cross_cats_sorted":[],"license":"","primary_cat":"math.DS","submitted_at":"1996-01-15T00:00:00Z","title_canon_sha256":"839aeeea41d2cb9be564aecc774c63bec53d7daeb3b6a0a56c611d89b017a229"},"schema_version":"1.0","source":{"id":"math/9601212","kind":"arxiv","version":1}},"canonical_sha256":"f98d88d6a45e906bfa73e435b1baa58fafd44e8695bda4a6f287b6212d41b0eb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f98d88d6a45e906bfa73e435b1baa58fafd44e8695bda4a6f287b6212d41b0eb","first_computed_at":"2026-05-18T01:05:47.882748Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:47.882748Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Zv8WSbxw7gV2TATj6d8USWB55fRb7FSe7u2CiXQn4gHIfXoFNrf5XGobW9VtDNM8sY9YUJJZntoGuV6CglspBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:47.883251Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/9601212","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e49a8453bf4852be5b973e433abc022f8995f7b1caa8f07983c4785c1b36fd14","sha256:01be806d7f4dcf5c877ec17ae81af4a387eafb1083a164c985d850395e153250"],"state_sha256":"d10a20122b72d16aa9babd8a246a2ea054e443e18171b41dd393ae70746e72d8"}