{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:3UIQOC55KO5FH7BIAHSL7H66HD","short_pith_number":"pith:3UIQOC55","canonical_record":{"source":{"id":"2106.13751","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2021-06-25T16:40:51Z","cross_cats_sorted":["math.PR","stat.ME","stat.TH"],"title_canon_sha256":"aa92cd023b191dbd2ac520ce212797764c7bb36f5bc770c8019d03497a1e7a73","abstract_canon_sha256":"858a8d7f779463ed1a0292a08a7eadc3da32a8e54086c43e6272a24bc1f6780b"},"schema_version":"1.0"},"canonical_sha256":"dd11070bbd53ba53fc2801e4bf9fde38fac69c29b1f024d0f30ebb4d177dc886","source":{"kind":"arxiv","id":"2106.13751","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2106.13751","created_at":"2026-07-05T05:19:10Z"},{"alias_kind":"arxiv_version","alias_value":"2106.13751v3","created_at":"2026-07-05T05:19:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2106.13751","created_at":"2026-07-05T05:19:10Z"},{"alias_kind":"pith_short_12","alias_value":"3UIQOC55KO5F","created_at":"2026-07-05T05:19:10Z"},{"alias_kind":"pith_short_16","alias_value":"3UIQOC55KO5FH7BI","created_at":"2026-07-05T05:19:10Z"},{"alias_kind":"pith_short_8","alias_value":"3UIQOC55","created_at":"2026-07-05T05:19:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:3UIQOC55KO5FH7BIAHSL7H66HD","target":"record","payload":{"canonical_record":{"source":{"id":"2106.13751","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2021-06-25T16:40:51Z","cross_cats_sorted":["math.PR","stat.ME","stat.TH"],"title_canon_sha256":"aa92cd023b191dbd2ac520ce212797764c7bb36f5bc770c8019d03497a1e7a73","abstract_canon_sha256":"858a8d7f779463ed1a0292a08a7eadc3da32a8e54086c43e6272a24bc1f6780b"},"schema_version":"1.0"},"canonical_sha256":"dd11070bbd53ba53fc2801e4bf9fde38fac69c29b1f024d0f30ebb4d177dc886","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:19:10.733149Z","signature_b64":"QpG5k1mizH2t/1UBwDkhOpXELdvJ35bU2+dlZmpa9j72xZJO0BdCzAUv/PjYQSFJ63eWwaW2PR99keE+B2EoAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dd11070bbd53ba53fc2801e4bf9fde38fac69c29b1f024d0f30ebb4d177dc886","last_reissued_at":"2026-07-05T05:19:10.732726Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:19:10.732726Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2106.13751","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T05:19:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"E3K464++jvjUb3kxYWTWE/8nEWSswd5uJZf6TIS79AMrR8dAm/VbszEuCJrk5WLXPBMBlA6cZi8KfztyBEozBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T18:02:36.800368Z"},"content_sha256":"2d668e1c923ffbee2c40810b9c9cfba0db55cd415843d9fdcceab5cd7e13a66f","schema_version":"1.0","event_id":"sha256:2d668e1c923ffbee2c40810b9c9cfba0db55cd415843d9fdcceab5cd7e13a66f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:3UIQOC55KO5FH7BIAHSL7H66HD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Parameter Estimation for the McKean-Vlasov Stochastic Differential Equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR","stat.ME","stat.TH"],"primary_cat":"math.ST","authors_text":"Grigorios A. Pavliotis, Louis Sharrock, Nikolas Kantas, Panos Parpas","submitted_at":"2021-06-25T16:40:51Z","abstract_excerpt":"We consider the problem of parameter estimation for a stochastic McKean-Vlasov equation, and the associated system of weakly interacting particles. We study two cases: one in which we observe multiple independent trajectories of the McKean-Vlasov SDE, and another in which we observe multiple particles from the interacting particle system. In each case, we begin by establishing consistency and asymptotic normality of the (approximate) offline maximum likelihood estimator, in the limit as the number of observations $N\\rightarrow\\infty$. We then propose an online maximum likelihood estimator, whi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2106.13751","kind":"arxiv","version":3},"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/2106.13751/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":"2026-07-05T05:19:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4r+2As4T7vyp/y/oV+LvyYtoIfRSUlY8AxnmsmpCG/e0cc9aFi8xmRpydJpURsUuB2FTMmJ6Ygvv9xgDAWSsDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T18:02:36.800899Z"},"content_sha256":"e6c6e3fbaad9d9e477901ab1bdba7cdad3ee8aeaec88281cec4c7212774b1b2d","schema_version":"1.0","event_id":"sha256:e6c6e3fbaad9d9e477901ab1bdba7cdad3ee8aeaec88281cec4c7212774b1b2d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3UIQOC55KO5FH7BIAHSL7H66HD/bundle.json","state_url":"https://pith.science/pith/3UIQOC55KO5FH7BIAHSL7H66HD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3UIQOC55KO5FH7BIAHSL7H66HD/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":"2026-08-08T18:02:36Z","links":{"resolver":"https://pith.science/pith/3UIQOC55KO5FH7BIAHSL7H66HD","bundle":"https://pith.science/pith/3UIQOC55KO5FH7BIAHSL7H66HD/bundle.json","state":"https://pith.science/pith/3UIQOC55KO5FH7BIAHSL7H66HD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3UIQOC55KO5FH7BIAHSL7H66HD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:3UIQOC55KO5FH7BIAHSL7H66HD","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":"858a8d7f779463ed1a0292a08a7eadc3da32a8e54086c43e6272a24bc1f6780b","cross_cats_sorted":["math.PR","stat.ME","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2021-06-25T16:40:51Z","title_canon_sha256":"aa92cd023b191dbd2ac520ce212797764c7bb36f5bc770c8019d03497a1e7a73"},"schema_version":"1.0","source":{"id":"2106.13751","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2106.13751","created_at":"2026-07-05T05:19:10Z"},{"alias_kind":"arxiv_version","alias_value":"2106.13751v3","created_at":"2026-07-05T05:19:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2106.13751","created_at":"2026-07-05T05:19:10Z"},{"alias_kind":"pith_short_12","alias_value":"3UIQOC55KO5F","created_at":"2026-07-05T05:19:10Z"},{"alias_kind":"pith_short_16","alias_value":"3UIQOC55KO5FH7BI","created_at":"2026-07-05T05:19:10Z"},{"alias_kind":"pith_short_8","alias_value":"3UIQOC55","created_at":"2026-07-05T05:19:10Z"}],"graph_snapshots":[{"event_id":"sha256:e6c6e3fbaad9d9e477901ab1bdba7cdad3ee8aeaec88281cec4c7212774b1b2d","target":"graph","created_at":"2026-07-05T05:19:10Z","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/2106.13751/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider the problem of parameter estimation for a stochastic McKean-Vlasov equation, and the associated system of weakly interacting particles. We study two cases: one in which we observe multiple independent trajectories of the McKean-Vlasov SDE, and another in which we observe multiple particles from the interacting particle system. In each case, we begin by establishing consistency and asymptotic normality of the (approximate) offline maximum likelihood estimator, in the limit as the number of observations $N\\rightarrow\\infty$. We then propose an online maximum likelihood estimator, whi","authors_text":"Grigorios A. Pavliotis, Louis Sharrock, Nikolas Kantas, Panos Parpas","cross_cats":["math.PR","stat.ME","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2021-06-25T16:40:51Z","title":"Parameter Estimation for the McKean-Vlasov Stochastic Differential Equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2106.13751","kind":"arxiv","version":3},"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":"sha256:2d668e1c923ffbee2c40810b9c9cfba0db55cd415843d9fdcceab5cd7e13a66f","target":"record","created_at":"2026-07-05T05:19:10Z","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":"858a8d7f779463ed1a0292a08a7eadc3da32a8e54086c43e6272a24bc1f6780b","cross_cats_sorted":["math.PR","stat.ME","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2021-06-25T16:40:51Z","title_canon_sha256":"aa92cd023b191dbd2ac520ce212797764c7bb36f5bc770c8019d03497a1e7a73"},"schema_version":"1.0","source":{"id":"2106.13751","kind":"arxiv","version":3}},"canonical_sha256":"dd11070bbd53ba53fc2801e4bf9fde38fac69c29b1f024d0f30ebb4d177dc886","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dd11070bbd53ba53fc2801e4bf9fde38fac69c29b1f024d0f30ebb4d177dc886","first_computed_at":"2026-07-05T05:19:10.732726Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:19:10.732726Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QpG5k1mizH2t/1UBwDkhOpXELdvJ35bU2+dlZmpa9j72xZJO0BdCzAUv/PjYQSFJ63eWwaW2PR99keE+B2EoAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T05:19:10.733149Z","signed_message":"canonical_sha256_bytes"},"source_id":"2106.13751","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2d668e1c923ffbee2c40810b9c9cfba0db55cd415843d9fdcceab5cd7e13a66f","sha256:e6c6e3fbaad9d9e477901ab1bdba7cdad3ee8aeaec88281cec4c7212774b1b2d"],"state_sha256":"e66277ae9ba0094adc76122454b438e3d2e4f531151b31eb250df6bd10eb74ed"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"s/4bDqMmrKcd29MQzoxWo/wNEw9YUa+6ST3ImONs4AXUwMNzzyMMQol87tdppC5PluHW9ruoV4c8f2kGHuBrAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T18:02:36.807554Z","bundle_sha256":"e7ad4b2b29bca03a674e77664ada894434a888c30ed5cb69efcd0ff046480fef"}}