{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:D3NTFMTCDGQ4L6UF5SKJB4R3MG","short_pith_number":"pith:D3NTFMTC","canonical_record":{"source":{"id":"2302.05133","kind":"arxiv","version":5},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2023-02-10T09:32:15Z","cross_cats_sorted":["cs.NA","math.NA"],"title_canon_sha256":"da3833d3ec2554d85efabf19a0bcf7fc2a4907a4641c5567335fe2ba6f739c6f","abstract_canon_sha256":"ebe6cea494fc46cd7afd237c3163eb4abf9aabbac0c804fe8e400f520e7e439b"},"schema_version":"1.0"},"canonical_sha256":"1edb32b26219a1c5fa85ec9490f23b61b8aae5b25d01b796dce56aa637d77c81","source":{"kind":"arxiv","id":"2302.05133","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2302.05133","created_at":"2026-07-05T10:07:37Z"},{"alias_kind":"arxiv_version","alias_value":"2302.05133v5","created_at":"2026-07-05T10:07:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2302.05133","created_at":"2026-07-05T10:07:37Z"},{"alias_kind":"pith_short_12","alias_value":"D3NTFMTCDGQ4","created_at":"2026-07-05T10:07:37Z"},{"alias_kind":"pith_short_16","alias_value":"D3NTFMTCDGQ4L6UF","created_at":"2026-07-05T10:07:37Z"},{"alias_kind":"pith_short_8","alias_value":"D3NTFMTC","created_at":"2026-07-05T10:07:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:D3NTFMTCDGQ4L6UF5SKJB4R3MG","target":"record","payload":{"canonical_record":{"source":{"id":"2302.05133","kind":"arxiv","version":5},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2023-02-10T09:32:15Z","cross_cats_sorted":["cs.NA","math.NA"],"title_canon_sha256":"da3833d3ec2554d85efabf19a0bcf7fc2a4907a4641c5567335fe2ba6f739c6f","abstract_canon_sha256":"ebe6cea494fc46cd7afd237c3163eb4abf9aabbac0c804fe8e400f520e7e439b"},"schema_version":"1.0"},"canonical_sha256":"1edb32b26219a1c5fa85ec9490f23b61b8aae5b25d01b796dce56aa637d77c81","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:07:37.913498Z","signature_b64":"612R1zfl3U/WQgSM6lnGTL/6FwIM+8DwXp40fJoUd0vA1k5SUnPGskEM16uJofvVraPoTLI/1ycymgQB1fy6AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1edb32b26219a1c5fa85ec9490f23b61b8aae5b25d01b796dce56aa637d77c81","last_reissued_at":"2026-07-05T10:07:37.913021Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:07:37.913021Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2302.05133","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T10:07:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5BFFw7TZkJT1Q2FwgkkSi3xVtY/z+4OaCQwOlbYRTgA3/sqzI61gFpNCwOe2b99SxYPnLdjiWm3zR/2DKoghDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T20:11:56.610590Z"},"content_sha256":"93ae4f84cf777867b15a43b0bee30bc6815682bdcd8751b2f6024919623f6b73","schema_version":"1.0","event_id":"sha256:93ae4f84cf777867b15a43b0bee30bc6815682bdcd8751b2f6024919623f6b73"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:D3NTFMTCDGQ4L6UF5SKJB4R3MG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Wellposedness, exponential ergodicity and numerical approximation of fully super-linear McKean--Vlasov SDEs and associated particle systems","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA","math.NA"],"primary_cat":"math.PR","authors_text":"Goncalo dos Reis, Wolfgang Stockinger, Xingyuan Chen","submitted_at":"2023-02-10T09:32:15Z","abstract_excerpt":"We study a class of McKean--Vlasov Stochastic Differential Equations (MV-SDEs) with drifts and diffusions having super-linear growth in measure and space -- the maps have general polynomial form but also satisfy a certain monotonicity condition. The combination of the drift's super-linear growth in measure (by way of a convolution) and the super-linear growth in space and measure of the diffusion coefficient requires novel technical elements in order to obtain the main results. We establish wellposedness, propagation of chaos (PoC), and under further assumptions on the model parameters, we sho"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2302.05133","kind":"arxiv","version":5},"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/2302.05133/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":"2026-07-05T10:07:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bMcRKHShDF7dv1vK9A+xqnzV32khTGEonnJTdkSOT7uG9VfyXrCeUFVi0diRppVGPS10niBoPNWq8GmLo0fLCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T20:11:56.611146Z"},"content_sha256":"7c56f0565f5c9db30bd5e3eaed729a11bfd1e825d21dd24b71306e2b1230c3e9","schema_version":"1.0","event_id":"sha256:7c56f0565f5c9db30bd5e3eaed729a11bfd1e825d21dd24b71306e2b1230c3e9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/D3NTFMTCDGQ4L6UF5SKJB4R3MG/bundle.json","state_url":"https://pith.science/pith/D3NTFMTCDGQ4L6UF5SKJB4R3MG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/D3NTFMTCDGQ4L6UF5SKJB4R3MG/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":"2026-08-13T20:11:56Z","links":{"resolver":"https://pith.science/pith/D3NTFMTCDGQ4L6UF5SKJB4R3MG","bundle":"https://pith.science/pith/D3NTFMTCDGQ4L6UF5SKJB4R3MG/bundle.json","state":"https://pith.science/pith/D3NTFMTCDGQ4L6UF5SKJB4R3MG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/D3NTFMTCDGQ4L6UF5SKJB4R3MG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:D3NTFMTCDGQ4L6UF5SKJB4R3MG","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":"ebe6cea494fc46cd7afd237c3163eb4abf9aabbac0c804fe8e400f520e7e439b","cross_cats_sorted":["cs.NA","math.NA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2023-02-10T09:32:15Z","title_canon_sha256":"da3833d3ec2554d85efabf19a0bcf7fc2a4907a4641c5567335fe2ba6f739c6f"},"schema_version":"1.0","source":{"id":"2302.05133","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2302.05133","created_at":"2026-07-05T10:07:37Z"},{"alias_kind":"arxiv_version","alias_value":"2302.05133v5","created_at":"2026-07-05T10:07:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2302.05133","created_at":"2026-07-05T10:07:37Z"},{"alias_kind":"pith_short_12","alias_value":"D3NTFMTCDGQ4","created_at":"2026-07-05T10:07:37Z"},{"alias_kind":"pith_short_16","alias_value":"D3NTFMTCDGQ4L6UF","created_at":"2026-07-05T10:07:37Z"},{"alias_kind":"pith_short_8","alias_value":"D3NTFMTC","created_at":"2026-07-05T10:07:37Z"}],"graph_snapshots":[{"event_id":"sha256:7c56f0565f5c9db30bd5e3eaed729a11bfd1e825d21dd24b71306e2b1230c3e9","target":"graph","created_at":"2026-07-05T10:07:37Z","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/2302.05133/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study a class of McKean--Vlasov Stochastic Differential Equations (MV-SDEs) with drifts and diffusions having super-linear growth in measure and space -- the maps have general polynomial form but also satisfy a certain monotonicity condition. The combination of the drift's super-linear growth in measure (by way of a convolution) and the super-linear growth in space and measure of the diffusion coefficient requires novel technical elements in order to obtain the main results. We establish wellposedness, propagation of chaos (PoC), and under further assumptions on the model parameters, we sho","authors_text":"Goncalo dos Reis, Wolfgang Stockinger, Xingyuan Chen","cross_cats":["cs.NA","math.NA"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2023-02-10T09:32:15Z","title":"Wellposedness, exponential ergodicity and numerical approximation of fully super-linear McKean--Vlasov SDEs and associated particle systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2302.05133","kind":"arxiv","version":5},"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":"sha256:93ae4f84cf777867b15a43b0bee30bc6815682bdcd8751b2f6024919623f6b73","target":"record","created_at":"2026-07-05T10:07:37Z","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":"ebe6cea494fc46cd7afd237c3163eb4abf9aabbac0c804fe8e400f520e7e439b","cross_cats_sorted":["cs.NA","math.NA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2023-02-10T09:32:15Z","title_canon_sha256":"da3833d3ec2554d85efabf19a0bcf7fc2a4907a4641c5567335fe2ba6f739c6f"},"schema_version":"1.0","source":{"id":"2302.05133","kind":"arxiv","version":5}},"canonical_sha256":"1edb32b26219a1c5fa85ec9490f23b61b8aae5b25d01b796dce56aa637d77c81","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1edb32b26219a1c5fa85ec9490f23b61b8aae5b25d01b796dce56aa637d77c81","first_computed_at":"2026-07-05T10:07:37.913021Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:07:37.913021Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"612R1zfl3U/WQgSM6lnGTL/6FwIM+8DwXp40fJoUd0vA1k5SUnPGskEM16uJofvVraPoTLI/1ycymgQB1fy6AA==","signature_status":"signed_v1","signed_at":"2026-07-05T10:07:37.913498Z","signed_message":"canonical_sha256_bytes"},"source_id":"2302.05133","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:93ae4f84cf777867b15a43b0bee30bc6815682bdcd8751b2f6024919623f6b73","sha256:7c56f0565f5c9db30bd5e3eaed729a11bfd1e825d21dd24b71306e2b1230c3e9"],"state_sha256":"af234f3451a584a1c55790abc7be1ba5af1a40a96d826a35985449c3be42ce29"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"De+G4s3THL60eGHgvtctgY4RIrHOp1evulFhIB26ddek9Ptv8N+KCoy1zlTpxs7ZMK3nzH4KgnAEzehk2WLOAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T20:11:56.618227Z","bundle_sha256":"7507cd0ad3b93548d9638a3de661cec032383ea93947fc36b93adcc8d09ca8ac"}}