{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:RTRDOXQWO6GU6T3OCGTELOU5YU","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":"fcb69949f2d85fa4aa17282dc4bf88aa5d32db1c7c02824163144a2b23e74ac3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-08-29T16:48:16Z","title_canon_sha256":"81e2d2a635259140f205f32b8e128f2d8b91fe56dd403152328dfc43500c8d50"},"schema_version":"1.0","source":{"id":"1308.6518","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.6518","created_at":"2026-05-18T03:14:39Z"},{"alias_kind":"arxiv_version","alias_value":"1308.6518v1","created_at":"2026-05-18T03:14:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.6518","created_at":"2026-05-18T03:14:39Z"},{"alias_kind":"pith_short_12","alias_value":"RTRDOXQWO6GU","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"RTRDOXQWO6GU6T3O","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"RTRDOXQW","created_at":"2026-05-18T12:27:59Z"}],"graph_snapshots":[{"event_id":"sha256:83c8fdd68690d8b5692f5ab287fd143f351f33b04a2a5e81b740329686ace212","target":"graph","created_at":"2026-05-18T03:14:39Z","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 study Tonelli Lagrangian systems on the 2-torus in energy levels above Ma\\~n\\'e's strict critical value and analyize the structure of global minimizers in the spirit of Morse, Hedlund and Bangert. In the case where the topological entropy of the Euler-Lagrange flow on the fixed energy level vanishes, we show that there are invariant tori for all rotation vectors indicating integrable-like behavior on a large scale. On the other hand, using a construction of Katok, we give examples of reversible Finsler geodesic flows with vanishing topological entropy, but having ergodic components of posit","authors_text":"Jan Philipp Schr\\\"oder","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-08-29T16:48:16Z","title":"Tonelli Lagrangian systems on the 2-torus and topological entropy"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.6518","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":"sha256:6a681df5c40f30fba39c8e4f88d2b85c59770886bc064762e57a55738519f17d","target":"record","created_at":"2026-05-18T03:14:39Z","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":"fcb69949f2d85fa4aa17282dc4bf88aa5d32db1c7c02824163144a2b23e74ac3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-08-29T16:48:16Z","title_canon_sha256":"81e2d2a635259140f205f32b8e128f2d8b91fe56dd403152328dfc43500c8d50"},"schema_version":"1.0","source":{"id":"1308.6518","kind":"arxiv","version":1}},"canonical_sha256":"8ce2375e16778d4f4f6e11a645ba9dc5354ba5044cdf5f6cc2db922605ad200e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8ce2375e16778d4f4f6e11a645ba9dc5354ba5044cdf5f6cc2db922605ad200e","first_computed_at":"2026-05-18T03:14:39.664171Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:14:39.664171Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FHSshrHk8J+J4eOulAap+yLdn8EYTYGIZuwbgI70BUahH3TfqsCjQ4+uw7fc5+GlRhenpn1hh+89Z8VnIhUzDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:14:39.664871Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.6518","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6a681df5c40f30fba39c8e4f88d2b85c59770886bc064762e57a55738519f17d","sha256:83c8fdd68690d8b5692f5ab287fd143f351f33b04a2a5e81b740329686ace212"],"state_sha256":"3750aebcb576ee50955d4d256b1fbf7c3338d36778101c38ae380c4c6e2c13ce"}