{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:SSVUM47XVCBLXZZZFQXDJJ3GFO","short_pith_number":"pith:SSVUM47X","canonical_record":{"source":{"id":"2607.29514","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2026-07-31T15:15:06Z","cross_cats_sorted":[],"title_canon_sha256":"aef50cb7cded1b661f33af19890f7891cd54dd2ab98edbf06ef9c62265026833","abstract_canon_sha256":"f2f76d0a159cb3cc481d37ce7293f065292bcc072e649fad127436d886f34dc7"},"schema_version":"1.0"},"canonical_sha256":"94ab4673f7a882bbe7392c2e34a7662bb3f5123310e476b4971a0cb3b1656f24","source":{"kind":"arxiv","id":"2607.29514","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.29514","created_at":"2026-08-03T01:36:57Z"},{"alias_kind":"arxiv_version","alias_value":"2607.29514v1","created_at":"2026-08-03T01:36:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.29514","created_at":"2026-08-03T01:36:57Z"},{"alias_kind":"pith_short_12","alias_value":"SSVUM47XVCBL","created_at":"2026-08-03T01:36:57Z"},{"alias_kind":"pith_short_16","alias_value":"SSVUM47XVCBLXZZZ","created_at":"2026-08-03T01:36:57Z"},{"alias_kind":"pith_short_8","alias_value":"SSVUM47X","created_at":"2026-08-03T01:36:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:SSVUM47XVCBLXZZZFQXDJJ3GFO","target":"record","payload":{"canonical_record":{"source":{"id":"2607.29514","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2026-07-31T15:15:06Z","cross_cats_sorted":[],"title_canon_sha256":"aef50cb7cded1b661f33af19890f7891cd54dd2ab98edbf06ef9c62265026833","abstract_canon_sha256":"f2f76d0a159cb3cc481d37ce7293f065292bcc072e649fad127436d886f34dc7"},"schema_version":"1.0"},"canonical_sha256":"94ab4673f7a882bbe7392c2e34a7662bb3f5123310e476b4971a0cb3b1656f24","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-03T01:36:57.152633Z","signature_b64":"oaXu6cFJAw3n2ikm9qfomkb/Tii1Bu3JxxjCe/o2RTfqn6Q/PfSe3Dp7nsRlsp/Utu+XYCWFuICl5h9Id3MeBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"94ab4673f7a882bbe7392c2e34a7662bb3f5123310e476b4971a0cb3b1656f24","last_reissued_at":"2026-08-03T01:36:57.151101Z","signature_status":"signed_v1","first_computed_at":"2026-08-03T01:36:57.151101Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.29514","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-08-03T01:36:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XZYimS71Scu2wb8Juf0GTrThNthZWZl9sjq8izG7YP3VEKDpHKS3hRPb83q8eZsgv5+Vzd4iLVMUrklg8fcyBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T22:51:05.375598Z"},"content_sha256":"694a7497864a0f6b1dc893b5cc33251f0cf5100973d471a107ab7cbe5c8d28dd","schema_version":"1.0","event_id":"sha256:694a7497864a0f6b1dc893b5cc33251f0cf5100973d471a107ab7cbe5c8d28dd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:SSVUM47XVCBLXZZZFQXDJJ3GFO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Robust mean field control: an application to optimal execution under composite uncertainty","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Chenchen Mou, Defeng Sun, Huafu Liao, Shuhui Liu","submitted_at":"2026-07-31T15:15:06Z","abstract_excerpt":"We provide a framework for robust mean field control problems that describe multi-dimensional optimal liquidation problems under uncertainty from both the underlying stochastic process and the deterministic model parameters. The verification results are established with Hamilton-Jacobi-Bellman-Isaacs (HJBI) equations where the variables are probability measures and the Hamiltonian nonlinearly involves the joint distribution of position and momentum. Using novel a priori estimates, we establish the well-posedness of the HJBI equations featuring general or quadratic Hamiltonians that are neither"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.29514","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.29514/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-08-03T01:36:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lvSj3Lt4v9S5V5M0eFb5oIFiJUJK6XIyOzewspgUdTi5QqPzAijYlRSSStXYPVEaWyU1CvWwwrfAU/Nv7cM8Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T22:51:05.375981Z"},"content_sha256":"0e7238d50f84973feb756b358a487eaad844c8dcec809495baf249ca54865876","schema_version":"1.0","event_id":"sha256:0e7238d50f84973feb756b358a487eaad844c8dcec809495baf249ca54865876"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SSVUM47XVCBLXZZZFQXDJJ3GFO/bundle.json","state_url":"https://pith.science/pith/SSVUM47XVCBLXZZZFQXDJJ3GFO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SSVUM47XVCBLXZZZFQXDJJ3GFO/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-13T22:51:05Z","links":{"resolver":"https://pith.science/pith/SSVUM47XVCBLXZZZFQXDJJ3GFO","bundle":"https://pith.science/pith/SSVUM47XVCBLXZZZFQXDJJ3GFO/bundle.json","state":"https://pith.science/pith/SSVUM47XVCBLXZZZFQXDJJ3GFO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SSVUM47XVCBLXZZZFQXDJJ3GFO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:SSVUM47XVCBLXZZZFQXDJJ3GFO","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"f2f76d0a159cb3cc481d37ce7293f065292bcc072e649fad127436d886f34dc7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2026-07-31T15:15:06Z","title_canon_sha256":"aef50cb7cded1b661f33af19890f7891cd54dd2ab98edbf06ef9c62265026833"},"schema_version":"1.0","source":{"id":"2607.29514","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.29514","created_at":"2026-08-03T01:36:57Z"},{"alias_kind":"arxiv_version","alias_value":"2607.29514v1","created_at":"2026-08-03T01:36:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.29514","created_at":"2026-08-03T01:36:57Z"},{"alias_kind":"pith_short_12","alias_value":"SSVUM47XVCBL","created_at":"2026-08-03T01:36:57Z"},{"alias_kind":"pith_short_16","alias_value":"SSVUM47XVCBLXZZZ","created_at":"2026-08-03T01:36:57Z"},{"alias_kind":"pith_short_8","alias_value":"SSVUM47X","created_at":"2026-08-03T01:36:57Z"}],"graph_snapshots":[{"event_id":"sha256:0e7238d50f84973feb756b358a487eaad844c8dcec809495baf249ca54865876","target":"graph","created_at":"2026-08-03T01:36:57Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2607.29514/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We provide a framework for robust mean field control problems that describe multi-dimensional optimal liquidation problems under uncertainty from both the underlying stochastic process and the deterministic model parameters. The verification results are established with Hamilton-Jacobi-Bellman-Isaacs (HJBI) equations where the variables are probability measures and the Hamiltonian nonlinearly involves the joint distribution of position and momentum. Using novel a priori estimates, we establish the well-posedness of the HJBI equations featuring general or quadratic Hamiltonians that are neither","authors_text":"Chenchen Mou, Defeng Sun, Huafu Liao, Shuhui Liu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2026-07-31T15:15:06Z","title":"Robust mean field control: an application to optimal execution under composite uncertainty"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.29514","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:694a7497864a0f6b1dc893b5cc33251f0cf5100973d471a107ab7cbe5c8d28dd","target":"record","created_at":"2026-08-03T01:36:57Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"f2f76d0a159cb3cc481d37ce7293f065292bcc072e649fad127436d886f34dc7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2026-07-31T15:15:06Z","title_canon_sha256":"aef50cb7cded1b661f33af19890f7891cd54dd2ab98edbf06ef9c62265026833"},"schema_version":"1.0","source":{"id":"2607.29514","kind":"arxiv","version":1}},"canonical_sha256":"94ab4673f7a882bbe7392c2e34a7662bb3f5123310e476b4971a0cb3b1656f24","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"94ab4673f7a882bbe7392c2e34a7662bb3f5123310e476b4971a0cb3b1656f24","first_computed_at":"2026-08-03T01:36:57.151101Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-03T01:36:57.151101Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oaXu6cFJAw3n2ikm9qfomkb/Tii1Bu3JxxjCe/o2RTfqn6Q/PfSe3Dp7nsRlsp/Utu+XYCWFuICl5h9Id3MeBg==","signature_status":"signed_v1","signed_at":"2026-08-03T01:36:57.152633Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.29514","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:694a7497864a0f6b1dc893b5cc33251f0cf5100973d471a107ab7cbe5c8d28dd","sha256:0e7238d50f84973feb756b358a487eaad844c8dcec809495baf249ca54865876"],"state_sha256":"19803f44be3fa53b84a333cc3da327f2188f5e7af3a5c460f387da606de109c9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YqSDNkOt+2Y76EBZdq/56KcNFCREDk6FhkkhdLim56ROds73bUMv3/BM0ioMXwMIGQNWT2zQb7zRZlA7KYNqDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T22:51:05.417244Z","bundle_sha256":"917fe101f7dc85bd5b64a641045d922be9cec6d199dc1c13dfa2e53717fd9d64"}}