{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:GOH4GNYGS3N2UE53ZY7VQVXSFE","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":"b0685f498e25e7231af57cafbf8ba9bafefd0e10d61dd14e8f53b5c34d260347","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-10-03T09:21:04Z","title_canon_sha256":"96b730bde980e9054c5c4bdae9fab04989cef815ed1244060f8df429e436e636"},"schema_version":"1.0","source":{"id":"1710.01043","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.01043","created_at":"2026-05-18T00:17:24Z"},{"alias_kind":"arxiv_version","alias_value":"1710.01043v2","created_at":"2026-05-18T00:17:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.01043","created_at":"2026-05-18T00:17:24Z"},{"alias_kind":"pith_short_12","alias_value":"GOH4GNYGS3N2","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"GOH4GNYGS3N2UE53","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"GOH4GNYG","created_at":"2026-05-18T12:31:18Z"}],"graph_snapshots":[{"event_id":"sha256:69fac413af69a0567a804a39317e7d69be8b22f0840382c4e1efd99cacee14d9","target":"graph","created_at":"2026-05-18T00:17:24Z","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"},"paper":{"abstract_excerpt":"By using the ultracontractivity of a reference diffusion semigroup, Krylov's estimate is established for a class of degenerate SDEs with singular drifts, which leads to existence and pathwise uniqueness by means of Zvonkin's transformation. The main result is applied to singular SDEs on generalized Heisenberg groups.","authors_text":"Feng-Yu Wang, Xing Huang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-10-03T09:21:04Z","title":"Degenerate SDEs with Singular Drift and Applications to Heisenberg Groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.01043","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":"sha256:7ff002dba0141152a22bc2b8a618940518704edd436dc5208799c89d8671bd7d","target":"record","created_at":"2026-05-18T00:17:24Z","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":"b0685f498e25e7231af57cafbf8ba9bafefd0e10d61dd14e8f53b5c34d260347","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-10-03T09:21:04Z","title_canon_sha256":"96b730bde980e9054c5c4bdae9fab04989cef815ed1244060f8df429e436e636"},"schema_version":"1.0","source":{"id":"1710.01043","kind":"arxiv","version":2}},"canonical_sha256":"338fc3370696dbaa13bbce3f5856f229201ee85705c353d455bd3b375765829e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"338fc3370696dbaa13bbce3f5856f229201ee85705c353d455bd3b375765829e","first_computed_at":"2026-05-18T00:17:24.110092Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:17:24.110092Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MoyZHBDWFB5z4VZoRNgO2QYt0TgT5MeNs7HmG+H3O4fLstWWVoXjelQhgqqs76si9hzUpmYdnREUTrm13uP+CA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:17:24.110724Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.01043","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7ff002dba0141152a22bc2b8a618940518704edd436dc5208799c89d8671bd7d","sha256:69fac413af69a0567a804a39317e7d69be8b22f0840382c4e1efd99cacee14d9"],"state_sha256":"2cff2b97f01dcd551efa937a3572c6a78c46add1a05e9ca8716f9500b723b05b"}