{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:MFRNSIBEITBLOHM5NYB64CAHM7","short_pith_number":"pith:MFRNSIBE","canonical_record":{"source":{"id":"2412.15906","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-12-20T13:59:04Z","cross_cats_sorted":[],"title_canon_sha256":"a3c45092f432036eee00f9fe93894d1e6fba60d4e95746a38d60c6b1a56118aa","abstract_canon_sha256":"95113edd50c271ba88addf66e00dd09932c13cfb82e38db72011ec6c29f7702d"},"schema_version":"1.0"},"canonical_sha256":"6162d9202444c2b71d9d6e03ee080767c5816d90ee424d0d3eb148db9aaa27b8","source":{"kind":"arxiv","id":"2412.15906","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.15906","created_at":"2026-07-05T10:46:59Z"},{"alias_kind":"arxiv_version","alias_value":"2412.15906v2","created_at":"2026-07-05T10:46:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.15906","created_at":"2026-07-05T10:46:59Z"},{"alias_kind":"pith_short_12","alias_value":"MFRNSIBEITBL","created_at":"2026-07-05T10:46:59Z"},{"alias_kind":"pith_short_16","alias_value":"MFRNSIBEITBLOHM5","created_at":"2026-07-05T10:46:59Z"},{"alias_kind":"pith_short_8","alias_value":"MFRNSIBE","created_at":"2026-07-05T10:46:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:MFRNSIBEITBLOHM5NYB64CAHM7","target":"record","payload":{"canonical_record":{"source":{"id":"2412.15906","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-12-20T13:59:04Z","cross_cats_sorted":[],"title_canon_sha256":"a3c45092f432036eee00f9fe93894d1e6fba60d4e95746a38d60c6b1a56118aa","abstract_canon_sha256":"95113edd50c271ba88addf66e00dd09932c13cfb82e38db72011ec6c29f7702d"},"schema_version":"1.0"},"canonical_sha256":"6162d9202444c2b71d9d6e03ee080767c5816d90ee424d0d3eb148db9aaa27b8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:46:59.560698Z","signature_b64":"7j0Be0HWls/+4hO2VsJT8u0vloOpRtIG4NrDpHg1f48P8zSzUzlHmL6i+tnWLZrP157HQA1yzCtRgFKOSp4uAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6162d9202444c2b71d9d6e03ee080767c5816d90ee424d0d3eb148db9aaa27b8","last_reissued_at":"2026-07-05T10:46:59.560202Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:46:59.560202Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2412.15906","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T10:46:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hWx0xcc0VDTtW9aO+aG03Ji7MHOskgOXveiL1w4F9l++az9PFTwKq/2TTxBsa9VC90ZftMXYZ4I3oKwWwk4eDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T23:38:12.250045Z"},"content_sha256":"e33c2501735364a223ddff39003814c3efe98d45b499a0cd8882ee38361353e5","schema_version":"1.0","event_id":"sha256:e33c2501735364a223ddff39003814c3efe98d45b499a0cd8882ee38361353e5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:MFRNSIBEITBLOHM5NYB64CAHM7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sensitivity of functionals of McKean-Vlasov SDE's with respect to the initial distribution","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Fausto Gozzi, Filippo de Feo, Nizar Touzi, Salvatore Federico","submitted_at":"2024-12-20T13:59:04Z","abstract_excerpt":"We examine the sensitivity at the origin of the distributional robust optimization problem in the context of a model generated by a mean field stochastic differential equation. We adapt the finite dimensional argument developed by Bartl, Drapeau, Obloj \\& Wiesel to our framework involving the infinite dimensional gradient of the solution of the mean field SDE with respect to its initial data. We revisit the derivation of this gradient process as previously introduced by Buckdahn, Li \\& Peng, and we complement the existing properties so as to satisfy the requirement of our main result."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.15906","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/2412.15906/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":"2026-07-05T10:46:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EsKkRLMd5LLGHrMmLVnOApSGRicUWDG/HEWwRXbIhpLckIcoglMnNBhwe40/+978pGNNqLvaAexM4dlP3SmCBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T23:38:12.250545Z"},"content_sha256":"0ca070589f94e6692a8d49f42fb838d427e91ad3cca4e3044d3746b7b4d71c61","schema_version":"1.0","event_id":"sha256:0ca070589f94e6692a8d49f42fb838d427e91ad3cca4e3044d3746b7b4d71c61"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MFRNSIBEITBLOHM5NYB64CAHM7/bundle.json","state_url":"https://pith.science/pith/MFRNSIBEITBLOHM5NYB64CAHM7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MFRNSIBEITBLOHM5NYB64CAHM7/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":"2026-08-08T23:38:12Z","links":{"resolver":"https://pith.science/pith/MFRNSIBEITBLOHM5NYB64CAHM7","bundle":"https://pith.science/pith/MFRNSIBEITBLOHM5NYB64CAHM7/bundle.json","state":"https://pith.science/pith/MFRNSIBEITBLOHM5NYB64CAHM7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MFRNSIBEITBLOHM5NYB64CAHM7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:MFRNSIBEITBLOHM5NYB64CAHM7","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":"95113edd50c271ba88addf66e00dd09932c13cfb82e38db72011ec6c29f7702d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-12-20T13:59:04Z","title_canon_sha256":"a3c45092f432036eee00f9fe93894d1e6fba60d4e95746a38d60c6b1a56118aa"},"schema_version":"1.0","source":{"id":"2412.15906","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.15906","created_at":"2026-07-05T10:46:59Z"},{"alias_kind":"arxiv_version","alias_value":"2412.15906v2","created_at":"2026-07-05T10:46:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.15906","created_at":"2026-07-05T10:46:59Z"},{"alias_kind":"pith_short_12","alias_value":"MFRNSIBEITBL","created_at":"2026-07-05T10:46:59Z"},{"alias_kind":"pith_short_16","alias_value":"MFRNSIBEITBLOHM5","created_at":"2026-07-05T10:46:59Z"},{"alias_kind":"pith_short_8","alias_value":"MFRNSIBE","created_at":"2026-07-05T10:46:59Z"}],"graph_snapshots":[{"event_id":"sha256:0ca070589f94e6692a8d49f42fb838d427e91ad3cca4e3044d3746b7b4d71c61","target":"graph","created_at":"2026-07-05T10:46:59Z","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/2412.15906/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We examine the sensitivity at the origin of the distributional robust optimization problem in the context of a model generated by a mean field stochastic differential equation. We adapt the finite dimensional argument developed by Bartl, Drapeau, Obloj \\& Wiesel to our framework involving the infinite dimensional gradient of the solution of the mean field SDE with respect to its initial data. We revisit the derivation of this gradient process as previously introduced by Buckdahn, Li \\& Peng, and we complement the existing properties so as to satisfy the requirement of our main result.","authors_text":"Fausto Gozzi, Filippo de Feo, Nizar Touzi, Salvatore Federico","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-12-20T13:59:04Z","title":"Sensitivity of functionals of McKean-Vlasov SDE's with respect to the initial distribution"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.15906","kind":"arxiv","version":2},"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:e33c2501735364a223ddff39003814c3efe98d45b499a0cd8882ee38361353e5","target":"record","created_at":"2026-07-05T10:46:59Z","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":"95113edd50c271ba88addf66e00dd09932c13cfb82e38db72011ec6c29f7702d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-12-20T13:59:04Z","title_canon_sha256":"a3c45092f432036eee00f9fe93894d1e6fba60d4e95746a38d60c6b1a56118aa"},"schema_version":"1.0","source":{"id":"2412.15906","kind":"arxiv","version":2}},"canonical_sha256":"6162d9202444c2b71d9d6e03ee080767c5816d90ee424d0d3eb148db9aaa27b8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6162d9202444c2b71d9d6e03ee080767c5816d90ee424d0d3eb148db9aaa27b8","first_computed_at":"2026-07-05T10:46:59.560202Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:46:59.560202Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7j0Be0HWls/+4hO2VsJT8u0vloOpRtIG4NrDpHg1f48P8zSzUzlHmL6i+tnWLZrP157HQA1yzCtRgFKOSp4uAA==","signature_status":"signed_v1","signed_at":"2026-07-05T10:46:59.560698Z","signed_message":"canonical_sha256_bytes"},"source_id":"2412.15906","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e33c2501735364a223ddff39003814c3efe98d45b499a0cd8882ee38361353e5","sha256:0ca070589f94e6692a8d49f42fb838d427e91ad3cca4e3044d3746b7b4d71c61"],"state_sha256":"0f586823552d68c13a6339db5f23ae19424d013e1c74579c1866bd2931965033"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Va0lCa/YN1Xgmy9xWy3vUk4+PrZSvQmKxfbHHMh75pZj9E2pOQymLqe4eV3EdIcx7Xlex9TndeRA2DOCy2RUBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T23:38:12.255019Z","bundle_sha256":"2ce175df4c807967eaae2605d2f9e12453bb6da12fcb5eadbddf1af89a554bc0"}}