{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:R3MMM6ILB7N2ATBQGI436QOLPE","short_pith_number":"pith:R3MMM6IL","schema_version":"1.0","canonical_sha256":"8ed8c6790b0fdba04c303239bf41cb790521e0a1274ca60c67aac881808e3d4d","source":{"kind":"arxiv","id":"2402.07665","version":2},"attestation_state":"computed","paper":{"title":"Uniqueness of semi-concave weak solutions for Hamilton-Jacobi equations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Victor Issa","submitted_at":"2024-02-12T14:20:12Z","abstract_excerpt":"It is well known that when the nonlinearity is convex, the Hamilton-Jacobi PDE admits a unique semi-convex weak solution, which is the viscosity solution. In this paper, motivated by problems arising from spin glasses, we show that if the Hamilton-Jacobi PDE with strictly convex nonlinearity and regular enough initial condition admits a semi-concave weak solution, then this solution is the viscosity solution."},"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":"2402.07665","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2024-02-12T14:20:12Z","cross_cats_sorted":[],"title_canon_sha256":"bb39029277fe958748043d8e06594290493d39de52c68044a8551683d71f517a","abstract_canon_sha256":"d01b32748e7a0a069810e7f61929bcf2010837b13ab14b661cedc0f603de8150"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:45:33.472277Z","signature_b64":"Sz+slB7vNIBIvJW2WUmfjW6rsph77M9Lwxt8RbAkaasiZ203uqMv0k8wp+BZGpJkpEOr8uvVQVaB1dzkwGSGAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8ed8c6790b0fdba04c303239bf41cb790521e0a1274ca60c67aac881808e3d4d","last_reissued_at":"2026-07-05T07:45:33.471774Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:45:33.471774Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Uniqueness of semi-concave weak solutions for Hamilton-Jacobi equations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Victor Issa","submitted_at":"2024-02-12T14:20:12Z","abstract_excerpt":"It is well known that when the nonlinearity is convex, the Hamilton-Jacobi PDE admits a unique semi-convex weak solution, which is the viscosity solution. In this paper, motivated by problems arising from spin glasses, we show that if the Hamilton-Jacobi PDE with strictly convex nonlinearity and regular enough initial condition admits a semi-concave weak solution, then this solution is the viscosity solution."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2402.07665","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/2402.07665/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":"2402.07665","created_at":"2026-07-05T07:45:33.471839+00:00"},{"alias_kind":"arxiv_version","alias_value":"2402.07665v2","created_at":"2026-07-05T07:45:33.471839+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2402.07665","created_at":"2026-07-05T07:45:33.471839+00:00"},{"alias_kind":"pith_short_12","alias_value":"R3MMM6ILB7N2","created_at":"2026-07-05T07:45:33.471839+00:00"},{"alias_kind":"pith_short_16","alias_value":"R3MMM6ILB7N2ATBQ","created_at":"2026-07-05T07:45:33.471839+00:00"},{"alias_kind":"pith_short_8","alias_value":"R3MMM6IL","created_at":"2026-07-05T07:45:33.471839+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2508.17313","citing_title":"The Free Energy of an Enriched Continuous Random Energy Model in the Weak Correlation Regime","ref_index":2024,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/R3MMM6ILB7N2ATBQGI436QOLPE","json":"https://pith.science/pith/R3MMM6ILB7N2ATBQGI436QOLPE.json","graph_json":"https://pith.science/api/pith-number/R3MMM6ILB7N2ATBQGI436QOLPE/graph.json","events_json":"https://pith.science/api/pith-number/R3MMM6ILB7N2ATBQGI436QOLPE/events.json","paper":"https://pith.science/paper/R3MMM6IL"},"agent_actions":{"view_html":"https://pith.science/pith/R3MMM6ILB7N2ATBQGI436QOLPE","download_json":"https://pith.science/pith/R3MMM6ILB7N2ATBQGI436QOLPE.json","view_paper":"https://pith.science/paper/R3MMM6IL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2402.07665&json=true","fetch_graph":"https://pith.science/api/pith-number/R3MMM6ILB7N2ATBQGI436QOLPE/graph.json","fetch_events":"https://pith.science/api/pith-number/R3MMM6ILB7N2ATBQGI436QOLPE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/R3MMM6ILB7N2ATBQGI436QOLPE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/R3MMM6ILB7N2ATBQGI436QOLPE/action/storage_attestation","attest_author":"https://pith.science/pith/R3MMM6ILB7N2ATBQGI436QOLPE/action/author_attestation","sign_citation":"https://pith.science/pith/R3MMM6ILB7N2ATBQGI436QOLPE/action/citation_signature","submit_replication":"https://pith.science/pith/R3MMM6ILB7N2ATBQGI436QOLPE/action/replication_record"}},"created_at":"2026-07-05T07:45:33.471839+00:00","updated_at":"2026-07-05T07:45:33.471839+00:00"}