{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:6W6M75BQWXGMXTSOLQP6SD7F43","short_pith_number":"pith:6W6M75BQ","schema_version":"1.0","canonical_sha256":"f5bccff430b5cccbce4e5c1fe90fe5e6ff4ac5f1733773e3fd02aa81afd9ae1b","source":{"kind":"arxiv","id":"1504.01872","version":2},"attestation_state":"computed","paper":{"title":"On the convergence of monotone schemes for path-dependent PDE","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.PR","authors_text":"Xiaolu Tan, Zhenjie Ren","submitted_at":"2015-04-08T09:11:27Z","abstract_excerpt":"We propose a reformulation of the convergence theorem of monotone numerical schemes introduced by Zhang and Zhuo for viscosity solutions of path-dependent PDEs, which extends the seminal work of Barles and Souganidis on the viscosity solution of PDE. We prove the convergence theorem under conditions similar to those of the classical theorem in the work of Barles and Souganidis. These conditions are satisfied, to the best of our knowledge, by all classical monotone numerical schemes in the context of stochastic control theory. In particular, the paper provides a unified approach to prove the co"},"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":"1504.01872","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-04-08T09:11:27Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"2dcbb9891f55f6098354dabf3681be7df0e0a51e75978b12ad2f9b6b43ca614c","abstract_canon_sha256":"db410e590b9366e66f14e20854e1ac2b84e052b337d9e4697bdbb362e8b04d99"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:10:20.393064Z","signature_b64":"cvmzkVb0N2/J0CzaYgNDJAcl4acuFuKPNiQWQRh+vEDfhLGPgExy3UtwQOgNAgkN4aFJsgHWOTAWeMLplGmHAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f5bccff430b5cccbce4e5c1fe90fe5e6ff4ac5f1733773e3fd02aa81afd9ae1b","last_reissued_at":"2026-05-18T01:10:20.392553Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:10:20.392553Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the convergence of monotone schemes for path-dependent PDE","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.PR","authors_text":"Xiaolu Tan, Zhenjie Ren","submitted_at":"2015-04-08T09:11:27Z","abstract_excerpt":"We propose a reformulation of the convergence theorem of monotone numerical schemes introduced by Zhang and Zhuo for viscosity solutions of path-dependent PDEs, which extends the seminal work of Barles and Souganidis on the viscosity solution of PDE. We prove the convergence theorem under conditions similar to those of the classical theorem in the work of Barles and Souganidis. These conditions are satisfied, to the best of our knowledge, by all classical monotone numerical schemes in the context of stochastic control theory. In particular, the paper provides a unified approach to prove the co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.01872","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":"1504.01872","created_at":"2026-05-18T01:10:20.392624+00:00"},{"alias_kind":"arxiv_version","alias_value":"1504.01872v2","created_at":"2026-05-18T01:10:20.392624+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.01872","created_at":"2026-05-18T01:10:20.392624+00:00"},{"alias_kind":"pith_short_12","alias_value":"6W6M75BQWXGM","created_at":"2026-05-18T12:29:07.941421+00:00"},{"alias_kind":"pith_short_16","alias_value":"6W6M75BQWXGMXTSO","created_at":"2026-05-18T12:29:07.941421+00:00"},{"alias_kind":"pith_short_8","alias_value":"6W6M75BQ","created_at":"2026-05-18T12:29:07.941421+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/6W6M75BQWXGMXTSOLQP6SD7F43","json":"https://pith.science/pith/6W6M75BQWXGMXTSOLQP6SD7F43.json","graph_json":"https://pith.science/api/pith-number/6W6M75BQWXGMXTSOLQP6SD7F43/graph.json","events_json":"https://pith.science/api/pith-number/6W6M75BQWXGMXTSOLQP6SD7F43/events.json","paper":"https://pith.science/paper/6W6M75BQ"},"agent_actions":{"view_html":"https://pith.science/pith/6W6M75BQWXGMXTSOLQP6SD7F43","download_json":"https://pith.science/pith/6W6M75BQWXGMXTSOLQP6SD7F43.json","view_paper":"https://pith.science/paper/6W6M75BQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1504.01872&json=true","fetch_graph":"https://pith.science/api/pith-number/6W6M75BQWXGMXTSOLQP6SD7F43/graph.json","fetch_events":"https://pith.science/api/pith-number/6W6M75BQWXGMXTSOLQP6SD7F43/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6W6M75BQWXGMXTSOLQP6SD7F43/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6W6M75BQWXGMXTSOLQP6SD7F43/action/storage_attestation","attest_author":"https://pith.science/pith/6W6M75BQWXGMXTSOLQP6SD7F43/action/author_attestation","sign_citation":"https://pith.science/pith/6W6M75BQWXGMXTSOLQP6SD7F43/action/citation_signature","submit_replication":"https://pith.science/pith/6W6M75BQWXGMXTSOLQP6SD7F43/action/replication_record"}},"created_at":"2026-05-18T01:10:20.392624+00:00","updated_at":"2026-05-18T01:10:20.392624+00:00"}