{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:ETZZDUCIX2CQ6XJRPPLWWCVRSU","short_pith_number":"pith:ETZZDUCI","schema_version":"1.0","canonical_sha256":"24f391d048be850f5d317bd76b0ab1950e99d589496dde2177c2ddf67f4a0b5c","source":{"kind":"arxiv","id":"2401.04920","version":2},"attestation_state":"computed","paper":{"title":"Viscosity Solutions for HJB Equations on the Process Space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.OC","authors_text":"Jianfeng Zhang, Jianjun Zhou, Nizar Touzi","submitted_at":"2024-01-10T04:06:39Z","abstract_excerpt":"In this paper we investigate a path dependent optimal control problem on the process space with both drift and volatility controls, with possibly degenerate volatility. The dynamic value function is characterized by a fully nonlinear second order path dependent HJB equation on the process space, which is by nature infinite dimensional. In particular, our model covers mean field control problems with common noise as a special case. We shall introduce a new notion of viscosity solutions and establish both the existence and the comparison principle, under merely Lipschitz/Holder continuity assump"},"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":"2401.04920","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2024-01-10T04:06:39Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"61fc59f1db99bdb4b4bac489c7d5ca4d8963ccede9300602438238078225b2c9","abstract_canon_sha256":"9b1d786ae159936a603634a3f1214762ed003e50c3cf90d536a969c6784cac09"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:40:47.359979Z","signature_b64":"vGWuAk7j2PyMjZ9GAFYEHQhcYqnifoMrV2qa4nSLrsvaKlSsRRvuB7bFNWM9/c0pn3o4cl9ZR6q5q9cw2gw6Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"24f391d048be850f5d317bd76b0ab1950e99d589496dde2177c2ddf67f4a0b5c","last_reissued_at":"2026-07-05T11:40:47.359519Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:40:47.359519Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Viscosity Solutions for HJB Equations on the Process Space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.OC","authors_text":"Jianfeng Zhang, Jianjun Zhou, Nizar Touzi","submitted_at":"2024-01-10T04:06:39Z","abstract_excerpt":"In this paper we investigate a path dependent optimal control problem on the process space with both drift and volatility controls, with possibly degenerate volatility. The dynamic value function is characterized by a fully nonlinear second order path dependent HJB equation on the process space, which is by nature infinite dimensional. In particular, our model covers mean field control problems with common noise as a special case. We shall introduce a new notion of viscosity solutions and establish both the existence and the comparison principle, under merely Lipschitz/Holder continuity assump"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.04920","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/2401.04920/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":"2401.04920","created_at":"2026-07-05T11:40:47.359588+00:00"},{"alias_kind":"arxiv_version","alias_value":"2401.04920v2","created_at":"2026-07-05T11:40:47.359588+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2401.04920","created_at":"2026-07-05T11:40:47.359588+00:00"},{"alias_kind":"pith_short_12","alias_value":"ETZZDUCIX2CQ","created_at":"2026-07-05T11:40:47.359588+00:00"},{"alias_kind":"pith_short_16","alias_value":"ETZZDUCIX2CQ6XJR","created_at":"2026-07-05T11:40:47.359588+00:00"},{"alias_kind":"pith_short_8","alias_value":"ETZZDUCI","created_at":"2026-07-05T11:40:47.359588+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":6,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.04377","citing_title":"A comparison principle for Wasserstein PDEs with state- and law-dependent common noise","ref_index":44,"is_internal_anchor":false},{"citing_arxiv_id":"2407.05356","citing_title":"Extended mean-field control problems with Poissonian common noise: Stochastic maximum principle and Hamiltonian-Jacobi-Bellman equation","ref_index":54,"is_internal_anchor":false},{"citing_arxiv_id":"2501.12731","citing_title":"Constrained mean-field control with singular controls: Existence, stochastic maximum principle and constrained FBSDE","ref_index":32,"is_internal_anchor":false},{"citing_arxiv_id":"2605.20593","citing_title":"Viscosity Solutions of Stochastic Hamilton--Jacobi--Bellman Equations with Jumps","ref_index":28,"is_internal_anchor":false},{"citing_arxiv_id":"2601.10586","citing_title":"Comparison of viscosity solutions for a class of non-linear PDEs on the space of finite nonnegative measures","ref_index":26,"is_internal_anchor":false},{"citing_arxiv_id":"2604.27372","citing_title":"Continuous-time q-learning for mean-field control with common noise, part-I: Theoretical foundations","ref_index":51,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ETZZDUCIX2CQ6XJRPPLWWCVRSU","json":"https://pith.science/pith/ETZZDUCIX2CQ6XJRPPLWWCVRSU.json","graph_json":"https://pith.science/api/pith-number/ETZZDUCIX2CQ6XJRPPLWWCVRSU/graph.json","events_json":"https://pith.science/api/pith-number/ETZZDUCIX2CQ6XJRPPLWWCVRSU/events.json","paper":"https://pith.science/paper/ETZZDUCI"},"agent_actions":{"view_html":"https://pith.science/pith/ETZZDUCIX2CQ6XJRPPLWWCVRSU","download_json":"https://pith.science/pith/ETZZDUCIX2CQ6XJRPPLWWCVRSU.json","view_paper":"https://pith.science/paper/ETZZDUCI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2401.04920&json=true","fetch_graph":"https://pith.science/api/pith-number/ETZZDUCIX2CQ6XJRPPLWWCVRSU/graph.json","fetch_events":"https://pith.science/api/pith-number/ETZZDUCIX2CQ6XJRPPLWWCVRSU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ETZZDUCIX2CQ6XJRPPLWWCVRSU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ETZZDUCIX2CQ6XJRPPLWWCVRSU/action/storage_attestation","attest_author":"https://pith.science/pith/ETZZDUCIX2CQ6XJRPPLWWCVRSU/action/author_attestation","sign_citation":"https://pith.science/pith/ETZZDUCIX2CQ6XJRPPLWWCVRSU/action/citation_signature","submit_replication":"https://pith.science/pith/ETZZDUCIX2CQ6XJRPPLWWCVRSU/action/replication_record"}},"created_at":"2026-07-05T11:40:47.359588+00:00","updated_at":"2026-07-05T11:40:47.359588+00:00"}