{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:ZSDJMFKQZ3SXJHHZXTOV3GUKGU","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":"6bcb9aca5c19fa59e095d5481420ee1e6e4e7e2a0bdd8b0753c0f1c8077c3fc3","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-03-21T12:27:58Z","title_canon_sha256":"b04b2e9e2e0f4dbf62c53454e6e8c070849ba42a95f94d91fdcacb69b04cf71d"},"schema_version":"1.0","source":{"id":"1803.07884","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.07884","created_at":"2026-05-18T00:20:13Z"},{"alias_kind":"arxiv_version","alias_value":"1803.07884v2","created_at":"2026-05-18T00:20:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.07884","created_at":"2026-05-18T00:20:13Z"},{"alias_kind":"pith_short_12","alias_value":"ZSDJMFKQZ3SX","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_16","alias_value":"ZSDJMFKQZ3SXJHHZ","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_8","alias_value":"ZSDJMFKQ","created_at":"2026-05-18T12:33:07Z"}],"graph_snapshots":[{"event_id":"sha256:8aa96ffd28e3524183ff0d047decd43d2e257a1de381f41aa07ab74d59d12378","target":"graph","created_at":"2026-05-18T00:20:13Z","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":"This article focuses on parabolic equations with rough diffusion coefficients which are ill-posed in the classical sense of distributions due to the presence of a singular forcing. Inspired by the philosophy of rough paths and regularity structures, we introduce a notion of modelled distribution which is suitable in this context. We prove two general tools for reconstruction and integration, as well as a product lemma which is tailor made for the reconstruction of the rough diffusion operator. This yields a partially automated deterministic theory, which we apply to obtain an existence and uni","authors_text":"Felix Otto, Hendrik Weber, Jonas Sauer, Scott Smith","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-03-21T12:27:58Z","title":"Parabolic equations with rough coefficients and singular forcing"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.07884","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":"sha256:2cf28c0a705c75afcfed8eb1b633d5fa783d2cffc158183d511e5c0f1143ecb5","target":"record","created_at":"2026-05-18T00:20:13Z","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":"6bcb9aca5c19fa59e095d5481420ee1e6e4e7e2a0bdd8b0753c0f1c8077c3fc3","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-03-21T12:27:58Z","title_canon_sha256":"b04b2e9e2e0f4dbf62c53454e6e8c070849ba42a95f94d91fdcacb69b04cf71d"},"schema_version":"1.0","source":{"id":"1803.07884","kind":"arxiv","version":2}},"canonical_sha256":"cc86961550cee5749cf9bcdd5d9a8a350a4ce0731b40fed1e5424530288692dc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cc86961550cee5749cf9bcdd5d9a8a350a4ce0731b40fed1e5424530288692dc","first_computed_at":"2026-05-18T00:20:13.292137Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:20:13.292137Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SGEoualpuw08Fy9PGxZ5/FvMZ5fY739VqG1rZwiGle0G5qCSj4vCFgJwg5/xF1FLELmcM1yqR1OCKgxk0XW/Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:20:13.292612Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.07884","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2cf28c0a705c75afcfed8eb1b633d5fa783d2cffc158183d511e5c0f1143ecb5","sha256:8aa96ffd28e3524183ff0d047decd43d2e257a1de381f41aa07ab74d59d12378"],"state_sha256":"6a1929a9c3e38f4e3f7723c464470935dfc5b8c6f87f6b39a2eba4cd4c4429b5"}