{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:AG5B2I2K23NYAL5ZRJ36ZQUM3W","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":"ca144e9806748802e38ee61a6df972ed6a44a01700938664d6ac8499a87cde94","cross_cats_sorted":["cs.LG","cs.SY","eess.SY","math.PR","math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2025-04-22T10:07:43Z","title_canon_sha256":"a1ab4dd9d47b423fdd1aaeedd4c692f1c4e2d14e1fcc52141f3c7d209724e3aa"},"schema_version":"1.0","source":{"id":"2504.15753","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2504.15753","created_at":"2026-07-05T10:52:29Z"},{"alias_kind":"arxiv_version","alias_value":"2504.15753v1","created_at":"2026-07-05T10:52:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.15753","created_at":"2026-07-05T10:52:29Z"},{"alias_kind":"pith_short_12","alias_value":"AG5B2I2K23NY","created_at":"2026-07-05T10:52:29Z"},{"alias_kind":"pith_short_16","alias_value":"AG5B2I2K23NYAL5Z","created_at":"2026-07-05T10:52:29Z"},{"alias_kind":"pith_short_8","alias_value":"AG5B2I2K","created_at":"2026-07-05T10:52:29Z"}],"graph_snapshots":[{"event_id":"sha256:5e77056551692f1c820fa29e624e5763b9405863d54cab80652d1519ca4d0e3e","target":"graph","created_at":"2026-07-05T10:52:29Z","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/2504.15753/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"For a controllable linear time-varying (LTV) pair $(\\boldsymbol{A}_t,\\boldsymbol{B}_t)$ and $\\boldsymbol{Q}_{t}$ positive semidefinite, we derive the Markov kernel for the It\\^{o} diffusion ${\\mathrm{d}}\\boldsymbol{x}_{t}=\\boldsymbol{A}_{t}\\boldsymbol{x}_t {\\mathrm{d}} t + \\sqrt{2}\\boldsymbol{B}_{t}{\\mathrm{d}}\\boldsymbol{w}_{t}$ with an accompanying killing of probability mass at rate $\\frac{1}{2}\\boldsymbol{x}^{\\top}\\boldsymbol{Q}_{t}\\boldsymbol{x}$. This Markov kernel is the Green's function for an associated linear reaction-advection-diffusion partial differential equation. Our result gene","authors_text":"Abhishek Halder, Alexis M.H. Teter, Sachin Shivakumar, Wenqing Wang","cross_cats":["cs.LG","cs.SY","eess.SY","math.PR","math.ST","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2025-04-22T10:07:43Z","title":"Markov Kernels, Distances and Optimal Control: A Parable of Linear Quadratic Non-Gaussian Distribution Steering"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.15753","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":"sha256:30fef464e9c16f253cdff0c4411833020799eb3da5ca1d1ce1925d4e132517c3","target":"record","created_at":"2026-07-05T10:52:29Z","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":"ca144e9806748802e38ee61a6df972ed6a44a01700938664d6ac8499a87cde94","cross_cats_sorted":["cs.LG","cs.SY","eess.SY","math.PR","math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2025-04-22T10:07:43Z","title_canon_sha256":"a1ab4dd9d47b423fdd1aaeedd4c692f1c4e2d14e1fcc52141f3c7d209724e3aa"},"schema_version":"1.0","source":{"id":"2504.15753","kind":"arxiv","version":1}},"canonical_sha256":"01ba1d234ad6db802fb98a77ecc28cddb78e4dd7628bdbfbe333a9e7345891a3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"01ba1d234ad6db802fb98a77ecc28cddb78e4dd7628bdbfbe333a9e7345891a3","first_computed_at":"2026-07-05T10:52:29.590565Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:52:29.590565Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WgPlurAsMRzeWZe4vPL5N+XF3RdjqpAMH3IvUQhSAE7lCywK6vJQvdgHdmIRoFn6tQyIUMt97R42wAR5aDiBBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T10:52:29.591072Z","signed_message":"canonical_sha256_bytes"},"source_id":"2504.15753","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:30fef464e9c16f253cdff0c4411833020799eb3da5ca1d1ce1925d4e132517c3","sha256:5e77056551692f1c820fa29e624e5763b9405863d54cab80652d1519ca4d0e3e"],"state_sha256":"79779a17790713384339efe383554be37157ec8349b070a28a1398ba252efa31"}