{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:6X2NDZPPL4E2FEW3TDLSJNI6ZE","short_pith_number":"pith:6X2NDZPP","schema_version":"1.0","canonical_sha256":"f5f4d1e5ef5f09a292db98d724b51ec921af7a8b8141cdfa5ace6638f0e7e4a8","source":{"kind":"arxiv","id":"1410.7281","version":1},"attestation_state":"computed","paper":{"title":"Comparison of Viscosity Solutions of Semi-linear Path-Dependent PDEs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.PR","authors_text":"Jianfeng Zhang, Nizar Touzi, Zhenjie Ren","submitted_at":"2014-10-27T15:48:08Z","abstract_excerpt":"This paper provides a probabilistic proof of the comparison result for viscosity solutions of path-dependent semilinear PDEs. We consider the notion of viscosity solutions introduced in \\cite{EKTZ} which considers as test functions all those smooth processes which are tangent in mean. When restricted to the Markovian case, this definition induces a larger set of test functions, and reduces to the notion of stochastic viscosity solutions analyzed in \\cite{BayraktarSirbu1,BayraktarSirbu2}. Our main result takes advantage of this enlargement of the test functions, and provides an easier proof of "},"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":"1410.7281","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-10-27T15:48:08Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"85dc8fb78d739509b9d5fd88ce4ac98b02108578cb63f21cb5267fade317e703","abstract_canon_sha256":"84aaafc55f37fa81e698bb48054d33ebd86d17416a151d88c7708f239c7a95ba"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:39:17.656410Z","signature_b64":"gdq4MELzoO8//cwgsEMngxIJhh2zP14lEMcZcWwR2nELcJu/bCqnO61JciHJbX5PJJ1FgZfXLEnh/DoWxqzGBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f5f4d1e5ef5f09a292db98d724b51ec921af7a8b8141cdfa5ace6638f0e7e4a8","last_reissued_at":"2026-05-18T02:39:17.655924Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:39:17.655924Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Comparison of Viscosity Solutions of Semi-linear Path-Dependent PDEs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.PR","authors_text":"Jianfeng Zhang, Nizar Touzi, Zhenjie Ren","submitted_at":"2014-10-27T15:48:08Z","abstract_excerpt":"This paper provides a probabilistic proof of the comparison result for viscosity solutions of path-dependent semilinear PDEs. We consider the notion of viscosity solutions introduced in \\cite{EKTZ} which considers as test functions all those smooth processes which are tangent in mean. When restricted to the Markovian case, this definition induces a larger set of test functions, and reduces to the notion of stochastic viscosity solutions analyzed in \\cite{BayraktarSirbu1,BayraktarSirbu2}. Our main result takes advantage of this enlargement of the test functions, and provides an easier proof of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.7281","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":"1410.7281","created_at":"2026-05-18T02:39:17.656001+00:00"},{"alias_kind":"arxiv_version","alias_value":"1410.7281v1","created_at":"2026-05-18T02:39:17.656001+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.7281","created_at":"2026-05-18T02:39:17.656001+00:00"},{"alias_kind":"pith_short_12","alias_value":"6X2NDZPPL4E2","created_at":"2026-05-18T12:28:16.859392+00:00"},{"alias_kind":"pith_short_16","alias_value":"6X2NDZPPL4E2FEW3","created_at":"2026-05-18T12:28:16.859392+00:00"},{"alias_kind":"pith_short_8","alias_value":"6X2NDZPP","created_at":"2026-05-18T12:28:16.859392+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/6X2NDZPPL4E2FEW3TDLSJNI6ZE","json":"https://pith.science/pith/6X2NDZPPL4E2FEW3TDLSJNI6ZE.json","graph_json":"https://pith.science/api/pith-number/6X2NDZPPL4E2FEW3TDLSJNI6ZE/graph.json","events_json":"https://pith.science/api/pith-number/6X2NDZPPL4E2FEW3TDLSJNI6ZE/events.json","paper":"https://pith.science/paper/6X2NDZPP"},"agent_actions":{"view_html":"https://pith.science/pith/6X2NDZPPL4E2FEW3TDLSJNI6ZE","download_json":"https://pith.science/pith/6X2NDZPPL4E2FEW3TDLSJNI6ZE.json","view_paper":"https://pith.science/paper/6X2NDZPP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1410.7281&json=true","fetch_graph":"https://pith.science/api/pith-number/6X2NDZPPL4E2FEW3TDLSJNI6ZE/graph.json","fetch_events":"https://pith.science/api/pith-number/6X2NDZPPL4E2FEW3TDLSJNI6ZE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6X2NDZPPL4E2FEW3TDLSJNI6ZE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6X2NDZPPL4E2FEW3TDLSJNI6ZE/action/storage_attestation","attest_author":"https://pith.science/pith/6X2NDZPPL4E2FEW3TDLSJNI6ZE/action/author_attestation","sign_citation":"https://pith.science/pith/6X2NDZPPL4E2FEW3TDLSJNI6ZE/action/citation_signature","submit_replication":"https://pith.science/pith/6X2NDZPPL4E2FEW3TDLSJNI6ZE/action/replication_record"}},"created_at":"2026-05-18T02:39:17.656001+00:00","updated_at":"2026-05-18T02:39:17.656001+00:00"}