{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:XLCGLW5T327DLYKK2AHNCLEL3O","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":"2d9ecd34e893ff6886ff3e441161e0e63f67b97afa0f839fb60a76120818fa8f","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-07-21T15:07:37Z","title_canon_sha256":"1afe615a731cb6a94e59e95510ab6e4b1e0c3901fc13891339b68bc4c020af5d"},"schema_version":"1.0","source":{"id":"2607.19173","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.19173","created_at":"2026-07-22T01:24:12Z"},{"alias_kind":"arxiv_version","alias_value":"2607.19173v1","created_at":"2026-07-22T01:24:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.19173","created_at":"2026-07-22T01:24:12Z"},{"alias_kind":"pith_short_12","alias_value":"XLCGLW5T327D","created_at":"2026-07-22T01:24:12Z"},{"alias_kind":"pith_short_16","alias_value":"XLCGLW5T327DLYKK","created_at":"2026-07-22T01:24:12Z"},{"alias_kind":"pith_short_8","alias_value":"XLCGLW5T","created_at":"2026-07-22T01:24:12Z"}],"graph_snapshots":[{"event_id":"sha256:49225445420d120d61988352a86217b2a97c8d7815d24214437bd544f5c84888","target":"graph","created_at":"2026-07-22T01:24:12Z","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/2607.19173/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Neural stochastic differential equations (SDEs) have emerged as powerful tools for learning noisy or stochastic dynamics directly from data; however, existing approaches largely assume uncoupled and continuous noise, limiting their applicability to realistic stochastic drivers, and often scale poorly in time, requiring expensive autoregressive training. To address these limitations, we propose Neural Kolmogorov Equations (NKEs), a deterministic, infinite-dimensional reformulation of Neural SDEs based on the Kolmogorov Forward equation, transforming the learning problem from modelling individua","authors_text":"Arthur Bizzi, Olga Fink","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-07-21T15:07:37Z","title":"Neural Kolmogorov Equations: Parallelizable Learning of Stochastic Dynamics under General Noise"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.19173","kind":"arxiv","version":1},"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":"sha256:1d3fc363f0879124ed070c2c4e557cc90480b6d89d73be54e1d6ca72aa00931d","target":"record","created_at":"2026-07-22T01:24:12Z","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":"2d9ecd34e893ff6886ff3e441161e0e63f67b97afa0f839fb60a76120818fa8f","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-07-21T15:07:37Z","title_canon_sha256":"1afe615a731cb6a94e59e95510ab6e4b1e0c3901fc13891339b68bc4c020af5d"},"schema_version":"1.0","source":{"id":"2607.19173","kind":"arxiv","version":1}},"canonical_sha256":"bac465dbb3debe35e14ad00ed12c8bdb91d4ee5dd0d050f9d6ec566326682ca0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bac465dbb3debe35e14ad00ed12c8bdb91d4ee5dd0d050f9d6ec566326682ca0","first_computed_at":"2026-07-22T01:24:12.157249Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-22T01:24:12.157249Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NVrJqqTGR7HL1/a5gOG1FmDFFe2Yb9vY6Ve3yX+G7Fm707zPhcDj8nPi3y07q6INh6OaZv3Y1w6Z2qtAMVHMAw==","signature_status":"signed_v1","signed_at":"2026-07-22T01:24:12.158110Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.19173","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1d3fc363f0879124ed070c2c4e557cc90480b6d89d73be54e1d6ca72aa00931d","sha256:49225445420d120d61988352a86217b2a97c8d7815d24214437bd544f5c84888"],"state_sha256":"675fe373272b9746ef076e027c06a5a037cd586a7fbf08dbbb20d1aee28ddce4"}