{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:O25R2FXOCDNB6DHNN2YYEHTOXJ","short_pith_number":"pith:O25R2FXO","canonical_record":{"source":{"id":"1802.03974","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-02-12T11:03:54Z","cross_cats_sorted":[],"title_canon_sha256":"9097e90ed5a02964321b78a14f7af3fb0e612332a58b8a2c18c35583d49fe773","abstract_canon_sha256":"9611a784cfb385be5615c0b815620795a905ae9743d8b28339af8a7cd0877fb6"},"schema_version":"1.0"},"canonical_sha256":"76bb1d16ee10da1f0ced6eb1821e6eba5afa7e87061ceadadb8c6a3567926806","source":{"kind":"arxiv","id":"1802.03974","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.03974","created_at":"2026-07-05T01:39:09Z"},{"alias_kind":"arxiv_version","alias_value":"1802.03974v3","created_at":"2026-07-05T01:39:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.03974","created_at":"2026-07-05T01:39:09Z"},{"alias_kind":"pith_short_12","alias_value":"O25R2FXOCDNB","created_at":"2026-07-05T01:39:09Z"},{"alias_kind":"pith_short_16","alias_value":"O25R2FXOCDNB6DHN","created_at":"2026-07-05T01:39:09Z"},{"alias_kind":"pith_short_8","alias_value":"O25R2FXO","created_at":"2026-07-05T01:39:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:O25R2FXOCDNB6DHNN2YYEHTOXJ","target":"record","payload":{"canonical_record":{"source":{"id":"1802.03974","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-02-12T11:03:54Z","cross_cats_sorted":[],"title_canon_sha256":"9097e90ed5a02964321b78a14f7af3fb0e612332a58b8a2c18c35583d49fe773","abstract_canon_sha256":"9611a784cfb385be5615c0b815620795a905ae9743d8b28339af8a7cd0877fb6"},"schema_version":"1.0"},"canonical_sha256":"76bb1d16ee10da1f0ced6eb1821e6eba5afa7e87061ceadadb8c6a3567926806","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:39:09.150170Z","signature_b64":"+b8g5Dc1buDC3nb7t2qL7hBlHSURd9XXiUJyWxGdjVT4Zfj7kjpQMj+vbUh1xZKRm2Z9JvHqsqpdkzVlidoPCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"76bb1d16ee10da1f0ced6eb1821e6eba5afa7e87061ceadadb8c6a3567926806","last_reissued_at":"2026-07-05T01:39:09.149735Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:39:09.149735Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1802.03974","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":"2026-07-05T01:39:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lX63CXOuRt0EuZvsx23lmEd9htqoCM3zj4ilfyWhockd7qm0JVxy0DK7wtKhiPtmPM9CdqIbABCIXs6Q8ilrAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T12:02:50.699964Z"},"content_sha256":"43b13a7af555fefeeca587121bf65fd6cab550b425ed6e5b39c52fd35caae907","schema_version":"1.0","event_id":"sha256:43b13a7af555fefeeca587121bf65fd6cab550b425ed6e5b39c52fd35caae907"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:O25R2FXOCDNB6DHNN2YYEHTOXJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"McKean-Vlasov SDEs under Measure Dependent Lyapunov Conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"David \\v{S}i\\v{s}ka, Lukasz Szpruch, William Hammersley","submitted_at":"2018-02-12T11:03:54Z","abstract_excerpt":"We prove the existence of weak solutions to McKean-Vlasov SDEs defined on a domain $D \\subseteq \\mathbb{R}^d$ with continuous and unbounded coefficients that satisfy Lyapunov type conditions, where the Lyapunov function may depend on measure. We propose a new type of {\\em integrated} Lyapunov condition, where the inequality is only required to hold when integrated against the measure on which the Lyapunov function depends , and we show that this is sufficient for the existence of weak solutions to McKean-Vlasov SDEs defined on $D$. The main tool used in the proofs is the concept of a measure d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.03974","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/1802.03974/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":"2026-07-05T01:39:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/UX8GnAWxbwgzqzbg83lpKl/kI0qkG4YDNSSkgc2OuL9Ki8dcDqxXaHSjmlI6eqdcuRnO7nfKsPBfmOsKtJpCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T12:02:50.700484Z"},"content_sha256":"0c4ec0b10a1c4c7c45becb611865da0d675b575833cf5b2c5f72af2bc80346aa","schema_version":"1.0","event_id":"sha256:0c4ec0b10a1c4c7c45becb611865da0d675b575833cf5b2c5f72af2bc80346aa"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/O25R2FXOCDNB6DHNN2YYEHTOXJ/bundle.json","state_url":"https://pith.science/pith/O25R2FXOCDNB6DHNN2YYEHTOXJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/O25R2FXOCDNB6DHNN2YYEHTOXJ/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":"2026-08-16T12:02:50Z","links":{"resolver":"https://pith.science/pith/O25R2FXOCDNB6DHNN2YYEHTOXJ","bundle":"https://pith.science/pith/O25R2FXOCDNB6DHNN2YYEHTOXJ/bundle.json","state":"https://pith.science/pith/O25R2FXOCDNB6DHNN2YYEHTOXJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/O25R2FXOCDNB6DHNN2YYEHTOXJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:O25R2FXOCDNB6DHNN2YYEHTOXJ","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":"9611a784cfb385be5615c0b815620795a905ae9743d8b28339af8a7cd0877fb6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-02-12T11:03:54Z","title_canon_sha256":"9097e90ed5a02964321b78a14f7af3fb0e612332a58b8a2c18c35583d49fe773"},"schema_version":"1.0","source":{"id":"1802.03974","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.03974","created_at":"2026-07-05T01:39:09Z"},{"alias_kind":"arxiv_version","alias_value":"1802.03974v3","created_at":"2026-07-05T01:39:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.03974","created_at":"2026-07-05T01:39:09Z"},{"alias_kind":"pith_short_12","alias_value":"O25R2FXOCDNB","created_at":"2026-07-05T01:39:09Z"},{"alias_kind":"pith_short_16","alias_value":"O25R2FXOCDNB6DHN","created_at":"2026-07-05T01:39:09Z"},{"alias_kind":"pith_short_8","alias_value":"O25R2FXO","created_at":"2026-07-05T01:39:09Z"}],"graph_snapshots":[{"event_id":"sha256:0c4ec0b10a1c4c7c45becb611865da0d675b575833cf5b2c5f72af2bc80346aa","target":"graph","created_at":"2026-07-05T01:39:09Z","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/1802.03974/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove the existence of weak solutions to McKean-Vlasov SDEs defined on a domain $D \\subseteq \\mathbb{R}^d$ with continuous and unbounded coefficients that satisfy Lyapunov type conditions, where the Lyapunov function may depend on measure. We propose a new type of {\\em integrated} Lyapunov condition, where the inequality is only required to hold when integrated against the measure on which the Lyapunov function depends , and we show that this is sufficient for the existence of weak solutions to McKean-Vlasov SDEs defined on $D$. The main tool used in the proofs is the concept of a measure d","authors_text":"David \\v{S}i\\v{s}ka, Lukasz Szpruch, William Hammersley","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-02-12T11:03:54Z","title":"McKean-Vlasov SDEs under Measure Dependent Lyapunov Conditions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.03974","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":"sha256:43b13a7af555fefeeca587121bf65fd6cab550b425ed6e5b39c52fd35caae907","target":"record","created_at":"2026-07-05T01:39:09Z","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":"9611a784cfb385be5615c0b815620795a905ae9743d8b28339af8a7cd0877fb6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-02-12T11:03:54Z","title_canon_sha256":"9097e90ed5a02964321b78a14f7af3fb0e612332a58b8a2c18c35583d49fe773"},"schema_version":"1.0","source":{"id":"1802.03974","kind":"arxiv","version":3}},"canonical_sha256":"76bb1d16ee10da1f0ced6eb1821e6eba5afa7e87061ceadadb8c6a3567926806","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"76bb1d16ee10da1f0ced6eb1821e6eba5afa7e87061ceadadb8c6a3567926806","first_computed_at":"2026-07-05T01:39:09.149735Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:39:09.149735Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+b8g5Dc1buDC3nb7t2qL7hBlHSURd9XXiUJyWxGdjVT4Zfj7kjpQMj+vbUh1xZKRm2Z9JvHqsqpdkzVlidoPCA==","signature_status":"signed_v1","signed_at":"2026-07-05T01:39:09.150170Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.03974","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:43b13a7af555fefeeca587121bf65fd6cab550b425ed6e5b39c52fd35caae907","sha256:0c4ec0b10a1c4c7c45becb611865da0d675b575833cf5b2c5f72af2bc80346aa"],"state_sha256":"ef51118ea8c2c43c79744f2a5ab1388155579329b1f2c58f913cceac262d4d82"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jTbN/LEdeVXBS/dN07wR87z6sHjp8BYq+D6qT0Hf1YmgY1hSDcvCYWlHXR27oJOY3jFz4awQT2FhcDgawZvbBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T12:02:50.706494Z","bundle_sha256":"bfc433fc9462d8f8b0db965e1e9f0afce260a60a011d171519f0ce012d60c9b1"}}