{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:XSYUD3DTJEYXPI6CMQCD5HCW25","short_pith_number":"pith:XSYUD3DT","schema_version":"1.0","canonical_sha256":"bcb141ec73493177a3c264043e9c56d762c1b0febc8fedfd8c6d60d6c78c778f","source":{"kind":"arxiv","id":"2301.10478","version":2},"attestation_state":"computed","paper":{"title":"Convergence of the solutions of the nonlinear discounted Hamilton-Jacobi equation: The central role of Mather measures","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Albert Fathi, Jianlu Zhang, Maxime Zavidovique, Qinbo Chen","submitted_at":"2023-01-25T09:25:41Z","abstract_excerpt":"Given a continuous Hamiltonian $H : (x,p,u) \\mapsto H(x,p,u)$ defined on $ T^*M \\times \\mathbb R $, where $M$ is a closed connected manifold, we study viscosity solutions, $u_\\lambda : M\\to \\mathbb R$, of discounted equations: $ H(x, d_x u_\\lambda, \\lambda u_\\lambda(x))=c$ in $M$, where $\\lambda >0$ is called a discount factor and $c$ is the critical value of $H(\\cdot, \\cdot , 0)$.\n  When $H$ is convex and superlinear in $p$ and non--decreasing in $u$, under an additional non--degeneracy condition, we obtain existence and uniqueness (with comparison principles) results of solutions and we prov"},"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":"2301.10478","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2023-01-25T09:25:41Z","cross_cats_sorted":[],"title_canon_sha256":"c1b3a454e5867a7f9015ecfdd4edb6c937f9fa8dbcb1006762761010c396b875","abstract_canon_sha256":"1ad70914fe606bdc5eb4560888513aa998eea98e4976da9c0b54ea5af12310e4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:36:20.893885Z","signature_b64":"WW1QwUNdbVqIOSOdlOL+UWZAmfzcwXahM5/LwSwQOJsNMqoo7WTfhbhb+puknGiHkFTWVZG+kqu6KJcDV1l3Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bcb141ec73493177a3c264043e9c56d762c1b0febc8fedfd8c6d60d6c78c778f","last_reissued_at":"2026-07-05T05:36:20.893483Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:36:20.893483Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Convergence of the solutions of the nonlinear discounted Hamilton-Jacobi equation: The central role of Mather measures","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Albert Fathi, Jianlu Zhang, Maxime Zavidovique, Qinbo Chen","submitted_at":"2023-01-25T09:25:41Z","abstract_excerpt":"Given a continuous Hamiltonian $H : (x,p,u) \\mapsto H(x,p,u)$ defined on $ T^*M \\times \\mathbb R $, where $M$ is a closed connected manifold, we study viscosity solutions, $u_\\lambda : M\\to \\mathbb R$, of discounted equations: $ H(x, d_x u_\\lambda, \\lambda u_\\lambda(x))=c$ in $M$, where $\\lambda >0$ is called a discount factor and $c$ is the critical value of $H(\\cdot, \\cdot , 0)$.\n  When $H$ is convex and superlinear in $p$ and non--decreasing in $u$, under an additional non--degeneracy condition, we obtain existence and uniqueness (with comparison principles) results of solutions and we prov"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2301.10478","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2301.10478/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2301.10478","created_at":"2026-07-05T05:36:20.893534+00:00"},{"alias_kind":"arxiv_version","alias_value":"2301.10478v2","created_at":"2026-07-05T05:36:20.893534+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2301.10478","created_at":"2026-07-05T05:36:20.893534+00:00"},{"alias_kind":"pith_short_12","alias_value":"XSYUD3DTJEYX","created_at":"2026-07-05T05:36:20.893534+00:00"},{"alias_kind":"pith_short_16","alias_value":"XSYUD3DTJEYXPI6C","created_at":"2026-07-05T05:36:20.893534+00:00"},{"alias_kind":"pith_short_8","alias_value":"XSYUD3DT","created_at":"2026-07-05T05:36:20.893534+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/XSYUD3DTJEYXPI6CMQCD5HCW25","json":"https://pith.science/pith/XSYUD3DTJEYXPI6CMQCD5HCW25.json","graph_json":"https://pith.science/api/pith-number/XSYUD3DTJEYXPI6CMQCD5HCW25/graph.json","events_json":"https://pith.science/api/pith-number/XSYUD3DTJEYXPI6CMQCD5HCW25/events.json","paper":"https://pith.science/paper/XSYUD3DT"},"agent_actions":{"view_html":"https://pith.science/pith/XSYUD3DTJEYXPI6CMQCD5HCW25","download_json":"https://pith.science/pith/XSYUD3DTJEYXPI6CMQCD5HCW25.json","view_paper":"https://pith.science/paper/XSYUD3DT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2301.10478&json=true","fetch_graph":"https://pith.science/api/pith-number/XSYUD3DTJEYXPI6CMQCD5HCW25/graph.json","fetch_events":"https://pith.science/api/pith-number/XSYUD3DTJEYXPI6CMQCD5HCW25/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XSYUD3DTJEYXPI6CMQCD5HCW25/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XSYUD3DTJEYXPI6CMQCD5HCW25/action/storage_attestation","attest_author":"https://pith.science/pith/XSYUD3DTJEYXPI6CMQCD5HCW25/action/author_attestation","sign_citation":"https://pith.science/pith/XSYUD3DTJEYXPI6CMQCD5HCW25/action/citation_signature","submit_replication":"https://pith.science/pith/XSYUD3DTJEYXPI6CMQCD5HCW25/action/replication_record"}},"created_at":"2026-07-05T05:36:20.893534+00:00","updated_at":"2026-07-05T05:36:20.893534+00:00"}