{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:DHTCUKQGJ57XQWR42OCKOBEOAW","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":"9df6ad52b1bfb9d24bcfb827d5b420428d6543a88d626eb241d5b60b50478820","cross_cats_sorted":["cs.AI"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-06-16T17:18:54Z","title_canon_sha256":"61a2dcf7ffa9276545ff8e01866ea4da7700270229b044fca0819cd62b9e7f48"},"schema_version":"1.0","source":{"id":"2606.18186","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.18186","created_at":"2026-06-19T16:10:50Z"},{"alias_kind":"arxiv_version","alias_value":"2606.18186v1","created_at":"2026-06-19T16:10:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.18186","created_at":"2026-06-19T16:10:50Z"},{"alias_kind":"pith_short_12","alias_value":"DHTCUKQGJ57X","created_at":"2026-06-19T16:10:50Z"},{"alias_kind":"pith_short_16","alias_value":"DHTCUKQGJ57XQWR4","created_at":"2026-06-19T16:10:50Z"},{"alias_kind":"pith_short_8","alias_value":"DHTCUKQG","created_at":"2026-06-19T16:10:50Z"}],"graph_snapshots":[{"event_id":"sha256:96c73751d7eeaf6205e1a1603184f45ece6184118a823f4e3e38452b61c2e777","target":"graph","created_at":"2026-06-19T16:10:50Z","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/2606.18186/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Finite-dimensional (FD) diffusion policies exhibit temporal drift owing to discretization artifacts that degrade long-horizon performance (when deployed on physical systems). We introduce a backward Kolmogorov equation that lifts diffusion policies to a Cameron-Martin space -- a subset of the Hilbert space. Essentially, replacing stochastic score matching with a deterministic boundary-value PDE problem. Our core innovation thrives on Gaussian measure theory whereupon the diffusion noise covariance operator is realized from a colored noise distribution which prescribes a notion of regularity on","authors_text":"Lekan Molu","cross_cats":["cs.AI"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-06-16T17:18:54Z","title":"Kolmogorov Regression for Robust Diffusion Policies"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.18186","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":"sha256:92a59f29f65fb490a13edcff082cee17678833d02d74bf1d741dfba7405c27f9","target":"record","created_at":"2026-06-19T16:10:50Z","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":"9df6ad52b1bfb9d24bcfb827d5b420428d6543a88d626eb241d5b60b50478820","cross_cats_sorted":["cs.AI"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-06-16T17:18:54Z","title_canon_sha256":"61a2dcf7ffa9276545ff8e01866ea4da7700270229b044fca0819cd62b9e7f48"},"schema_version":"1.0","source":{"id":"2606.18186","kind":"arxiv","version":1}},"canonical_sha256":"19e62a2a064f7f785a3cd384a7048e059be8d1f449340a984f321425f230b504","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"19e62a2a064f7f785a3cd384a7048e059be8d1f449340a984f321425f230b504","first_computed_at":"2026-06-19T16:10:50.527821Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-19T16:10:50.527821Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tkNghGpn7drl3DAsxDxH5qpBV/4omhp9ou8fYKfkfip2IlnlgNJ38/LSLW5RP0un8QkYYT8ndle5Pr09G9ZJAQ==","signature_status":"signed_v1","signed_at":"2026-06-19T16:10:50.528165Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.18186","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:92a59f29f65fb490a13edcff082cee17678833d02d74bf1d741dfba7405c27f9","sha256:96c73751d7eeaf6205e1a1603184f45ece6184118a823f4e3e38452b61c2e777"],"state_sha256":"dbed06f25cb0aecb38b9ae4d95205a5103faf459f03719ce72e70b12c34b44e1"}