{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:XSPATN63XMMG2KRYTK266Q3HOM","short_pith_number":"pith:XSPATN63","schema_version":"1.0","canonical_sha256":"bc9e09b7dbbb186d2a389ab5ef4367731d824ddb486b719fe0b2069a2fb1525a","source":{"kind":"arxiv","id":"1312.1606","version":1},"attestation_state":"computed","paper":{"title":"Weak KAM theorem for Hamilton-Jacobi equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.OC"],"primary_cat":"math.DS","authors_text":"Jun Yan, Xifeng SU","submitted_at":"2013-12-05T16:25:56Z","abstract_excerpt":"In this paper, we generalize weak KAM theorem from positive Lagrangian systems to \"proper\" Hamilton-Jacobi equations.\n  We introduce an implicitly defined solution semigroup of evolutionary Hamilton-Jacobi equations. By exploring the properties of the solution semigroup, we prove the convergence of solution semigroup and existence of weak KAM solutions for stationary equations: \\begin{equation*} H(x, u, d_x u)=0. \\end{equation*}"},"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":"1312.1606","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-12-05T16:25:56Z","cross_cats_sorted":["math.AP","math.OC"],"title_canon_sha256":"93e0642a161e5f9f7be5a8dd4d0128367420dc2468c5ad10fa4106a345ebbfce","abstract_canon_sha256":"22c4b4b1c9bf499027a858322f5b2ab36899c763b779213fdcc8dff38f29360c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:05:26.753011Z","signature_b64":"HnwL2aMEK7wBHBm9gT0BJiymWKZ7Kx/drpWeyh7Vxht/McFwumJwYSQmIz3r75WdLwulA8jsjra4ERJC25LxAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bc9e09b7dbbb186d2a389ab5ef4367731d824ddb486b719fe0b2069a2fb1525a","last_reissued_at":"2026-05-18T03:05:26.752527Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:05:26.752527Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Weak KAM theorem for Hamilton-Jacobi equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.OC"],"primary_cat":"math.DS","authors_text":"Jun Yan, Xifeng SU","submitted_at":"2013-12-05T16:25:56Z","abstract_excerpt":"In this paper, we generalize weak KAM theorem from positive Lagrangian systems to \"proper\" Hamilton-Jacobi equations.\n  We introduce an implicitly defined solution semigroup of evolutionary Hamilton-Jacobi equations. By exploring the properties of the solution semigroup, we prove the convergence of solution semigroup and existence of weak KAM solutions for stationary equations: \\begin{equation*} H(x, u, d_x u)=0. \\end{equation*}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.1606","kind":"arxiv","version":1},"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":"1312.1606","created_at":"2026-05-18T03:05:26.752612+00:00"},{"alias_kind":"arxiv_version","alias_value":"1312.1606v1","created_at":"2026-05-18T03:05:26.752612+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.1606","created_at":"2026-05-18T03:05:26.752612+00:00"},{"alias_kind":"pith_short_12","alias_value":"XSPATN63XMMG","created_at":"2026-05-18T12:28:06.772260+00:00"},{"alias_kind":"pith_short_16","alias_value":"XSPATN63XMMG2KRY","created_at":"2026-05-18T12:28:06.772260+00:00"},{"alias_kind":"pith_short_8","alias_value":"XSPATN63","created_at":"2026-05-18T12:28:06.772260+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/XSPATN63XMMG2KRYTK266Q3HOM","json":"https://pith.science/pith/XSPATN63XMMG2KRYTK266Q3HOM.json","graph_json":"https://pith.science/api/pith-number/XSPATN63XMMG2KRYTK266Q3HOM/graph.json","events_json":"https://pith.science/api/pith-number/XSPATN63XMMG2KRYTK266Q3HOM/events.json","paper":"https://pith.science/paper/XSPATN63"},"agent_actions":{"view_html":"https://pith.science/pith/XSPATN63XMMG2KRYTK266Q3HOM","download_json":"https://pith.science/pith/XSPATN63XMMG2KRYTK266Q3HOM.json","view_paper":"https://pith.science/paper/XSPATN63","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1312.1606&json=true","fetch_graph":"https://pith.science/api/pith-number/XSPATN63XMMG2KRYTK266Q3HOM/graph.json","fetch_events":"https://pith.science/api/pith-number/XSPATN63XMMG2KRYTK266Q3HOM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XSPATN63XMMG2KRYTK266Q3HOM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XSPATN63XMMG2KRYTK266Q3HOM/action/storage_attestation","attest_author":"https://pith.science/pith/XSPATN63XMMG2KRYTK266Q3HOM/action/author_attestation","sign_citation":"https://pith.science/pith/XSPATN63XMMG2KRYTK266Q3HOM/action/citation_signature","submit_replication":"https://pith.science/pith/XSPATN63XMMG2KRYTK266Q3HOM/action/replication_record"}},"created_at":"2026-05-18T03:05:26.752612+00:00","updated_at":"2026-05-18T03:05:26.752612+00:00"}