{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:YBKNYELVCEJQBX26QT2IXLBEDR","short_pith_number":"pith:YBKNYELV","canonical_record":{"source":{"id":"2107.04325","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2021-07-09T09:33:06Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"3ae9cd02f43ee5231e7b4ed99fc08393ecb6f839842891f8e9c0562bc4e056d5","abstract_canon_sha256":"a473bfeb43815c3db1781401b19e3601e16fb06e7ffed4c3b1daee4dbe2fc44e"},"schema_version":"1.0"},"canonical_sha256":"c054dc1175111300df5e84f48bac241c7261ba9414ada30ae8cf83a1602d71f6","source":{"kind":"arxiv","id":"2107.04325","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2107.04325","created_at":"2026-07-05T05:54:10Z"},{"alias_kind":"arxiv_version","alias_value":"2107.04325v3","created_at":"2026-07-05T05:54:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2107.04325","created_at":"2026-07-05T05:54:10Z"},{"alias_kind":"pith_short_12","alias_value":"YBKNYELVCEJQ","created_at":"2026-07-05T05:54:10Z"},{"alias_kind":"pith_short_16","alias_value":"YBKNYELVCEJQBX26","created_at":"2026-07-05T05:54:10Z"},{"alias_kind":"pith_short_8","alias_value":"YBKNYELV","created_at":"2026-07-05T05:54:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:YBKNYELVCEJQBX26QT2IXLBEDR","target":"record","payload":{"canonical_record":{"source":{"id":"2107.04325","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2021-07-09T09:33:06Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"3ae9cd02f43ee5231e7b4ed99fc08393ecb6f839842891f8e9c0562bc4e056d5","abstract_canon_sha256":"a473bfeb43815c3db1781401b19e3601e16fb06e7ffed4c3b1daee4dbe2fc44e"},"schema_version":"1.0"},"canonical_sha256":"c054dc1175111300df5e84f48bac241c7261ba9414ada30ae8cf83a1602d71f6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:54:10.471279Z","signature_b64":"fhpm/5BDgBUBjjn5Qfih+2WJeA1vlsRMCjHsN6Ng5RqVmivkeX/L/b+t42MHzCcIl5Wa131WQWxqbtHMSbvdBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c054dc1175111300df5e84f48bac241c7261ba9414ada30ae8cf83a1602d71f6","last_reissued_at":"2026-07-05T05:54:10.470852Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:54:10.470852Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2107.04325","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":"2026-07-05T05:54:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9u2d9O3kISSaVHB0c+5fp9lxcoDiLGCrsSVWM9OgghRFYb7Z+DKa66JYiVHYrYsM504w64n3eTF7UwWFa+CYBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T09:02:55.358903Z"},"content_sha256":"0a0ce69a151166c54d4cc563a786481a05516e816db4a7d45dbd4f410551bdc7","schema_version":"1.0","event_id":"sha256:0a0ce69a151166c54d4cc563a786481a05516e816db4a7d45dbd4f410551bdc7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:YBKNYELVCEJQBX26QT2IXLBEDR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Weak well-posedness for degenerate SDEs driven by L\\'evy processes","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.AP","authors_text":"L. Marino (LaMME), S. Menozzi (LaMME)","submitted_at":"2021-07-09T09:33:06Z","abstract_excerpt":"In this article, we study the effects of the propagation of a non-degenerate L\\'evy noise through a chain of deterministic differential equations whose coefficients are H\\\"older continuous and satisfy a weak H\\\"ormander-like condition. In particular, we assume some non-degeneracy with respect to the components which transmit the noise. Moreover, we characterize, for some specific dynamics, through suitable counterexamples , the almost sharp regularity exponents that ensure the weak well-posedness for the associated SDE. As a by-product of our approach, we also derive some Krylov-type estimates"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2107.04325","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/2107.04325/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":"2026-07-05T05:54:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"alZ8SJYCQ820csctD9mVrpqX+JDPXH/DC8ZZnZTJbu7Kr5eQ/UpATiQcdUHbGSaALrGNZRqotvDdP/5aaZhmBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T09:02:55.359279Z"},"content_sha256":"b0dfea1f617998d5f655f276c43db3d2d0c73b084b6e333af8593b079cd382f8","schema_version":"1.0","event_id":"sha256:b0dfea1f617998d5f655f276c43db3d2d0c73b084b6e333af8593b079cd382f8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YBKNYELVCEJQBX26QT2IXLBEDR/bundle.json","state_url":"https://pith.science/pith/YBKNYELVCEJQBX26QT2IXLBEDR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YBKNYELVCEJQBX26QT2IXLBEDR/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":"2026-07-07T09:02:55Z","links":{"resolver":"https://pith.science/pith/YBKNYELVCEJQBX26QT2IXLBEDR","bundle":"https://pith.science/pith/YBKNYELVCEJQBX26QT2IXLBEDR/bundle.json","state":"https://pith.science/pith/YBKNYELVCEJQBX26QT2IXLBEDR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YBKNYELVCEJQBX26QT2IXLBEDR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:YBKNYELVCEJQBX26QT2IXLBEDR","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":"a473bfeb43815c3db1781401b19e3601e16fb06e7ffed4c3b1daee4dbe2fc44e","cross_cats_sorted":["math.PR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2021-07-09T09:33:06Z","title_canon_sha256":"3ae9cd02f43ee5231e7b4ed99fc08393ecb6f839842891f8e9c0562bc4e056d5"},"schema_version":"1.0","source":{"id":"2107.04325","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2107.04325","created_at":"2026-07-05T05:54:10Z"},{"alias_kind":"arxiv_version","alias_value":"2107.04325v3","created_at":"2026-07-05T05:54:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2107.04325","created_at":"2026-07-05T05:54:10Z"},{"alias_kind":"pith_short_12","alias_value":"YBKNYELVCEJQ","created_at":"2026-07-05T05:54:10Z"},{"alias_kind":"pith_short_16","alias_value":"YBKNYELVCEJQBX26","created_at":"2026-07-05T05:54:10Z"},{"alias_kind":"pith_short_8","alias_value":"YBKNYELV","created_at":"2026-07-05T05:54:10Z"}],"graph_snapshots":[{"event_id":"sha256:b0dfea1f617998d5f655f276c43db3d2d0c73b084b6e333af8593b079cd382f8","target":"graph","created_at":"2026-07-05T05:54:10Z","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/2107.04325/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this article, we study the effects of the propagation of a non-degenerate L\\'evy noise through a chain of deterministic differential equations whose coefficients are H\\\"older continuous and satisfy a weak H\\\"ormander-like condition. In particular, we assume some non-degeneracy with respect to the components which transmit the noise. Moreover, we characterize, for some specific dynamics, through suitable counterexamples , the almost sharp regularity exponents that ensure the weak well-posedness for the associated SDE. As a by-product of our approach, we also derive some Krylov-type estimates","authors_text":"L. Marino (LaMME), S. Menozzi (LaMME)","cross_cats":["math.PR"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2021-07-09T09:33:06Z","title":"Weak well-posedness for degenerate SDEs driven by L\\'evy processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2107.04325","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":"sha256:0a0ce69a151166c54d4cc563a786481a05516e816db4a7d45dbd4f410551bdc7","target":"record","created_at":"2026-07-05T05:54:10Z","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":"a473bfeb43815c3db1781401b19e3601e16fb06e7ffed4c3b1daee4dbe2fc44e","cross_cats_sorted":["math.PR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2021-07-09T09:33:06Z","title_canon_sha256":"3ae9cd02f43ee5231e7b4ed99fc08393ecb6f839842891f8e9c0562bc4e056d5"},"schema_version":"1.0","source":{"id":"2107.04325","kind":"arxiv","version":3}},"canonical_sha256":"c054dc1175111300df5e84f48bac241c7261ba9414ada30ae8cf83a1602d71f6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c054dc1175111300df5e84f48bac241c7261ba9414ada30ae8cf83a1602d71f6","first_computed_at":"2026-07-05T05:54:10.470852Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:54:10.470852Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fhpm/5BDgBUBjjn5Qfih+2WJeA1vlsRMCjHsN6Ng5RqVmivkeX/L/b+t42MHzCcIl5Wa131WQWxqbtHMSbvdBg==","signature_status":"signed_v1","signed_at":"2026-07-05T05:54:10.471279Z","signed_message":"canonical_sha256_bytes"},"source_id":"2107.04325","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0a0ce69a151166c54d4cc563a786481a05516e816db4a7d45dbd4f410551bdc7","sha256:b0dfea1f617998d5f655f276c43db3d2d0c73b084b6e333af8593b079cd382f8"],"state_sha256":"564f83417f6318710d3c739c23610c725519be2ca244e7795b297568d0bd40b7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rS4EjuUxU9ZO+fwTf+W/VlTrVLaDXH+houGZV/JH5DgU3n/cvhL79uiPafSGPy8GMZ+Uwu4Gl+1Dnd5P0zyKAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-07T09:02:55.361296Z","bundle_sha256":"51f834de72a920476880d3e12e4be8ebde2e7b4bea64033e9e598e33277da4ea"}}