{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:EXIJZMTJYEEESHDKXWQBAHIVUZ","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":"49575d68043faf5ec4d42e47ecaa426748884c8b3b3a2f1265775ef49240ac01","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-07-11T17:03:35Z","title_canon_sha256":"a3a5afb76c7385ce39ef5053b56897d1620bc8ae2b909106e37c5f74b8793c4c"},"schema_version":"1.0","source":{"id":"1407.3218","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.3218","created_at":"2026-05-18T01:59:53Z"},{"alias_kind":"arxiv_version","alias_value":"1407.3218v2","created_at":"2026-05-18T01:59:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.3218","created_at":"2026-05-18T01:59:53Z"},{"alias_kind":"pith_short_12","alias_value":"EXIJZMTJYEEE","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"EXIJZMTJYEEESHDK","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"EXIJZMTJ","created_at":"2026-05-18T12:28:28Z"}],"graph_snapshots":[{"event_id":"sha256:e350df5ee0287d21db7d237981a9128887e8bc48bf12eef5a17cf8bce3caf4dd","target":"graph","created_at":"2026-05-18T01:59:53Z","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":"We introduce a generalized notion of semilinear elliptic partial differential equations where the corresponding second order partial differential operator $L$ has a generalized drift. We investigate existence and uniqueness of generalized solutions of class $C^1$. The generator $L$ is associated with a Markov process $X$ which is the solution of a stochastic differential equation with distributional drift. If the semilinear PDE admits boundary conditions, its solution is naturally associated with a backward stochastic differential equation (BSDE) with random terminal time, where the forward pr","authors_text":"Francesco Russo (ENSTA ParisTech UMA), Lukas Wurzer","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-07-11T17:03:35Z","title":"Elliptic PDEs with distributional drift and backward SDEs driven by a c{\\`a}dl{\\`a}g martingale with random terminal time"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.3218","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":"sha256:9635a6e6449d639f716b1db98f20f8fa0887ed7af2676fdd739d424c180f087e","target":"record","created_at":"2026-05-18T01:59:53Z","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":"49575d68043faf5ec4d42e47ecaa426748884c8b3b3a2f1265775ef49240ac01","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-07-11T17:03:35Z","title_canon_sha256":"a3a5afb76c7385ce39ef5053b56897d1620bc8ae2b909106e37c5f74b8793c4c"},"schema_version":"1.0","source":{"id":"1407.3218","kind":"arxiv","version":2}},"canonical_sha256":"25d09cb269c108491c6abda0101d15a667bd6cf7799c10cbe1d1a891b0ebf59c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"25d09cb269c108491c6abda0101d15a667bd6cf7799c10cbe1d1a891b0ebf59c","first_computed_at":"2026-05-18T01:59:53.580093Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:59:53.580093Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aibjLlNGfhdShmGQK4m5PaILlsZN9GfiPpg4ejhljEXG9BBxXvQbZzAlMBNhYRYZuuKi8yz4vb6AVrhBR5naBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:59:53.580683Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.3218","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9635a6e6449d639f716b1db98f20f8fa0887ed7af2676fdd739d424c180f087e","sha256:e350df5ee0287d21db7d237981a9128887e8bc48bf12eef5a17cf8bce3caf4dd"],"state_sha256":"66f59cb3a8b39899fff561ad0989d010d718d1bfd00406a50b2f7e90d56b76a4"}