{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:YIODU7A23HIIYRCWBNFNMY3HZT","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":"1552deb8b80793a0df11eb2dde1847221ead89accefd9f73005e0c92b22a2fca","cross_cats_sorted":["math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-01-25T17:43:13Z","title_canon_sha256":"fbf4d99226f390372b1e5ee62fafa66c364430247db2acf1d7439f11be851911"},"schema_version":"1.0","source":{"id":"1601.06692","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.06692","created_at":"2026-05-17T23:57:59Z"},{"alias_kind":"arxiv_version","alias_value":"1601.06692v3","created_at":"2026-05-17T23:57:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.06692","created_at":"2026-05-17T23:57:59Z"},{"alias_kind":"pith_short_12","alias_value":"YIODU7A23HII","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_16","alias_value":"YIODU7A23HIIYRCW","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_8","alias_value":"YIODU7A2","created_at":"2026-05-18T12:30:53Z"}],"graph_snapshots":[{"event_id":"sha256:f78a346c40b985dfbe7af15a74bd415d4564118e76a055a03106c8f58430a1ff","target":"graph","created_at":"2026-05-17T23:57:59Z","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 prove that, on a closed surface, a Lagrangian system defined by a Tonelli Lagrangian $L$ possesses a periodic orbit that is a local minimizer of the free-period action functional on every energy level belonging to the low range of energies $(e_0(L),c_{\\mathrm{u}}(L))$. We also prove that almost every energy level in $(e_0(L),c_{\\mathrm{u}}(L))$ possesses infinitely many periodic orbits. These statements extend two results, respectively due to Taimanov and Abbondandolo-Macarini-Mazzucchelli-Paternain, valid for the special case of electromagnetic Lagrangians.","authors_text":"Luca Asselle, Marco Mazzucchelli","cross_cats":["math.SG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-01-25T17:43:13Z","title":"On Tonelli periodic orbits with low energy on surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.06692","kind":"arxiv","version":3},"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":"sha256:4ccee6667a122fef959742598203a02262f37d73ca3a9db3be197e9364be472c","target":"record","created_at":"2026-05-17T23:57:59Z","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":"1552deb8b80793a0df11eb2dde1847221ead89accefd9f73005e0c92b22a2fca","cross_cats_sorted":["math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-01-25T17:43:13Z","title_canon_sha256":"fbf4d99226f390372b1e5ee62fafa66c364430247db2acf1d7439f11be851911"},"schema_version":"1.0","source":{"id":"1601.06692","kind":"arxiv","version":3}},"canonical_sha256":"c21c3a7c1ad9d08c44560b4ad66367cce83e777e3704fcbc31a0e72e47b94ec9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c21c3a7c1ad9d08c44560b4ad66367cce83e777e3704fcbc31a0e72e47b94ec9","first_computed_at":"2026-05-17T23:57:59.962196Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:57:59.962196Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5bsGwXcrBUywvj+ENvDjtZ1WNbuxj9Vw87VxMOu6oB3jLf3Erz5wEzeYtFyw9eUWpuFwzLZwxZFU3hGjzpdCCQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:57:59.962637Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.06692","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4ccee6667a122fef959742598203a02262f37d73ca3a9db3be197e9364be472c","sha256:f78a346c40b985dfbe7af15a74bd415d4564118e76a055a03106c8f58430a1ff"],"state_sha256":"b41a9fd122f4e057fafa7a15b4eb20f222d2bd6ee3fff5299256314b9d43a783"}