{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:2ZKZ47HRVAS2R5ISBWHRW423Z7","short_pith_number":"pith:2ZKZ47HR","schema_version":"1.0","canonical_sha256":"d6559e7cf1a825a8f5120d8f1b735bcfea53e150b86972d558e073073207f073","source":{"kind":"arxiv","id":"1003.2316","version":2},"attestation_state":"computed","paper":{"title":"Pseudographs and Lax-Oleinik semi-group: a geometric and dynamical interpretation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.SG","authors_text":"Marie-Claude Arnaud","submitted_at":"2010-03-11T12:16:58Z","abstract_excerpt":"Let H be a Tonelli Hamiltonian defined on the cotangent bundle of a compact and connected manifold and let u be a semi-concave function defined on M. If E (u) is the set of all the super-differentials of u and (\\phi t) the Hamiltonian flow of H, we prove that for t > 0 small enough, \\phi-t (E (u)) is an exact Lagrangian Lipschitz graph. This provides a geometric interpretation/explanation of a regularization tool that was introduced by P.~Bernard to prove the existence of C 1,1 subsolutions."},"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":"1003.2316","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2010-03-11T12:16:58Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"ffad2e25e4c9125582f68b562132e75747651e1f25646d2c6fe2d2a328781308","abstract_canon_sha256":"dbb16c72d54d5fc2a8c1eb251d1a0503d603dfb9ca5680c6971d9544aad358a2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:08:35.043913Z","signature_b64":"hAkXueIbBezQv5p+/7qWvyQQKwMPbhmk9P0IYwvopC1dUt4T3cPQEXRo2OUfIvJVnN/BhngDfUuK74uev8MXCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d6559e7cf1a825a8f5120d8f1b735bcfea53e150b86972d558e073073207f073","last_reissued_at":"2026-05-18T02:08:35.043270Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:08:35.043270Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Pseudographs and Lax-Oleinik semi-group: a geometric and dynamical interpretation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.SG","authors_text":"Marie-Claude Arnaud","submitted_at":"2010-03-11T12:16:58Z","abstract_excerpt":"Let H be a Tonelli Hamiltonian defined on the cotangent bundle of a compact and connected manifold and let u be a semi-concave function defined on M. If E (u) is the set of all the super-differentials of u and (\\phi t) the Hamiltonian flow of H, we prove that for t > 0 small enough, \\phi-t (E (u)) is an exact Lagrangian Lipschitz graph. This provides a geometric interpretation/explanation of a regularization tool that was introduced by P.~Bernard to prove the existence of C 1,1 subsolutions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.2316","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":"1003.2316","created_at":"2026-05-18T02:08:35.043389+00:00"},{"alias_kind":"arxiv_version","alias_value":"1003.2316v2","created_at":"2026-05-18T02:08:35.043389+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1003.2316","created_at":"2026-05-18T02:08:35.043389+00:00"},{"alias_kind":"pith_short_12","alias_value":"2ZKZ47HRVAS2","created_at":"2026-05-18T12:26:03.138858+00:00"},{"alias_kind":"pith_short_16","alias_value":"2ZKZ47HRVAS2R5IS","created_at":"2026-05-18T12:26:03.138858+00:00"},{"alias_kind":"pith_short_8","alias_value":"2ZKZ47HR","created_at":"2026-05-18T12:26:03.138858+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/2ZKZ47HRVAS2R5ISBWHRW423Z7","json":"https://pith.science/pith/2ZKZ47HRVAS2R5ISBWHRW423Z7.json","graph_json":"https://pith.science/api/pith-number/2ZKZ47HRVAS2R5ISBWHRW423Z7/graph.json","events_json":"https://pith.science/api/pith-number/2ZKZ47HRVAS2R5ISBWHRW423Z7/events.json","paper":"https://pith.science/paper/2ZKZ47HR"},"agent_actions":{"view_html":"https://pith.science/pith/2ZKZ47HRVAS2R5ISBWHRW423Z7","download_json":"https://pith.science/pith/2ZKZ47HRVAS2R5ISBWHRW423Z7.json","view_paper":"https://pith.science/paper/2ZKZ47HR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1003.2316&json=true","fetch_graph":"https://pith.science/api/pith-number/2ZKZ47HRVAS2R5ISBWHRW423Z7/graph.json","fetch_events":"https://pith.science/api/pith-number/2ZKZ47HRVAS2R5ISBWHRW423Z7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2ZKZ47HRVAS2R5ISBWHRW423Z7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2ZKZ47HRVAS2R5ISBWHRW423Z7/action/storage_attestation","attest_author":"https://pith.science/pith/2ZKZ47HRVAS2R5ISBWHRW423Z7/action/author_attestation","sign_citation":"https://pith.science/pith/2ZKZ47HRVAS2R5ISBWHRW423Z7/action/citation_signature","submit_replication":"https://pith.science/pith/2ZKZ47HRVAS2R5ISBWHRW423Z7/action/replication_record"}},"created_at":"2026-05-18T02:08:35.043389+00:00","updated_at":"2026-05-18T02:08:35.043389+00:00"}