{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:QJAF6BD33J5BZKLW4DA6ECGIZC","short_pith_number":"pith:QJAF6BD3","schema_version":"1.0","canonical_sha256":"82405f047bda7a1ca976e0c1e208c8c8bb92bdf26f90e18f8abb8779917e822d","source":{"kind":"arxiv","id":"1507.05883","version":2},"attestation_state":"computed","paper":{"title":"On the existence of Euler-Lagrange orbits satisfying the conormal boundary conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SG"],"primary_cat":"math.DS","authors_text":"Luca Asselle","submitted_at":"2015-07-21T15:58:37Z","abstract_excerpt":"Let $(M,g)$ be a closed Riemannian manifold, $L: TM\\rightarrow \\mathbb R$ be a Tonelli Lagrangian. Given two closed submanifolds $Q_0$ and $Q_1$ of $M$ and a real number $k$, we study the existence of Euler-Lagrange orbits with energy $k$ connecting $Q_0$ to $Q_1$ and satisfying the conormal boundary conditions. We introduce the Ma\\~n\\'e critical value which is relevant for this problem and discuss existence results for supercritical and subcritical energies. We also provide counterexamples showing that all the results are sharp."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1507.05883","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-07-21T15:58:37Z","cross_cats_sorted":["math.SG"],"title_canon_sha256":"f41f71eff61b370005d5fd598e0e20c9b6ddb28168c80dafdeca6a2eeeb3c518","abstract_canon_sha256":"3a5d74d06aa114c6c71e86639e7c27806db4288660d50903ce41edca7de74cd4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:56:46.717089Z","signature_b64":"RC9QfOYirEwCqmk8c2CwDpK6aDpXHPhhxdx7qwYDE8/G9SHMFRYvEOXT2KqsNfhGqrfh2pxLo9N8ZU9QBFKvBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"82405f047bda7a1ca976e0c1e208c8c8bb92bdf26f90e18f8abb8779917e822d","last_reissued_at":"2026-05-18T00:56:46.716643Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:56:46.716643Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the existence of Euler-Lagrange orbits satisfying the conormal boundary conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SG"],"primary_cat":"math.DS","authors_text":"Luca Asselle","submitted_at":"2015-07-21T15:58:37Z","abstract_excerpt":"Let $(M,g)$ be a closed Riemannian manifold, $L: TM\\rightarrow \\mathbb R$ be a Tonelli Lagrangian. Given two closed submanifolds $Q_0$ and $Q_1$ of $M$ and a real number $k$, we study the existence of Euler-Lagrange orbits with energy $k$ connecting $Q_0$ to $Q_1$ and satisfying the conormal boundary conditions. We introduce the Ma\\~n\\'e critical value which is relevant for this problem and discuss existence results for supercritical and subcritical energies. We also provide counterexamples showing that all the results are sharp."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.05883","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1507.05883","created_at":"2026-05-18T00:56:46.716711+00:00"},{"alias_kind":"arxiv_version","alias_value":"1507.05883v2","created_at":"2026-05-18T00:56:46.716711+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.05883","created_at":"2026-05-18T00:56:46.716711+00:00"},{"alias_kind":"pith_short_12","alias_value":"QJAF6BD33J5B","created_at":"2026-05-18T12:29:37.295048+00:00"},{"alias_kind":"pith_short_16","alias_value":"QJAF6BD33J5BZKLW","created_at":"2026-05-18T12:29:37.295048+00:00"},{"alias_kind":"pith_short_8","alias_value":"QJAF6BD3","created_at":"2026-05-18T12:29:37.295048+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/QJAF6BD33J5BZKLW4DA6ECGIZC","json":"https://pith.science/pith/QJAF6BD33J5BZKLW4DA6ECGIZC.json","graph_json":"https://pith.science/api/pith-number/QJAF6BD33J5BZKLW4DA6ECGIZC/graph.json","events_json":"https://pith.science/api/pith-number/QJAF6BD33J5BZKLW4DA6ECGIZC/events.json","paper":"https://pith.science/paper/QJAF6BD3"},"agent_actions":{"view_html":"https://pith.science/pith/QJAF6BD33J5BZKLW4DA6ECGIZC","download_json":"https://pith.science/pith/QJAF6BD33J5BZKLW4DA6ECGIZC.json","view_paper":"https://pith.science/paper/QJAF6BD3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1507.05883&json=true","fetch_graph":"https://pith.science/api/pith-number/QJAF6BD33J5BZKLW4DA6ECGIZC/graph.json","fetch_events":"https://pith.science/api/pith-number/QJAF6BD33J5BZKLW4DA6ECGIZC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QJAF6BD33J5BZKLW4DA6ECGIZC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QJAF6BD33J5BZKLW4DA6ECGIZC/action/storage_attestation","attest_author":"https://pith.science/pith/QJAF6BD33J5BZKLW4DA6ECGIZC/action/author_attestation","sign_citation":"https://pith.science/pith/QJAF6BD33J5BZKLW4DA6ECGIZC/action/citation_signature","submit_replication":"https://pith.science/pith/QJAF6BD33J5BZKLW4DA6ECGIZC/action/replication_record"}},"created_at":"2026-05-18T00:56:46.716711+00:00","updated_at":"2026-05-18T00:56:46.716711+00:00"}