{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:WMEVANWQAHC5GU34GLQKVHZTVY","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":"cda2ee7a1037e6339a866eec7a6033b111ec2e79562f2008e73cc05bce1d77c5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-04-18T18:01:16Z","title_canon_sha256":"b18ff679289e87b0b9626f6ccb68385c21941bb18039220d5f59f468201a4bc2"},"schema_version":"1.0","source":{"id":"1604.05268","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.05268","created_at":"2026-05-18T01:13:47Z"},{"alias_kind":"arxiv_version","alias_value":"1604.05268v2","created_at":"2026-05-18T01:13:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.05268","created_at":"2026-05-18T01:13:47Z"},{"alias_kind":"pith_short_12","alias_value":"WMEVANWQAHC5","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"WMEVANWQAHC5GU34","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"WMEVANWQ","created_at":"2026-05-18T12:30:48Z"}],"graph_snapshots":[{"event_id":"sha256:0f40bd429740923d41bb1c661e4aeb5ab3b47f85f886bdd54fad5fdc7fca75cf","target":"graph","created_at":"2026-05-18T01:13:47Z","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 consider hypoelliptic Kolmogorov equations in $n+1$ spatial dimensions, with $n\\geq 1$, where the differential operator in the first $n$ spatial variables featuring in the equation is second-order elliptic, and with respect to the $(n+1)$st spatial variable the equation contains a pure transport term only and is therefore first-order hyperbolic. If the two differential operators, in the first $n$ and in the $(n+1)$st co-ordinate directions, do not commute, we benefit from hypoelliptic regularization in time, and the solution for $t>0$ is smooth even for a Dirac initial datum prescribed at $","authors_text":"Alan Whitley, Christoph Reisinger, Endre S\\\"uli","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-04-18T18:01:16Z","title":"A partial Fourier transform method for a class of hypoelliptic Kolmogorov equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.05268","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":"sha256:0a83f6a7a7a3a6e960be6c50509239b607049a92f0e2bc33050cf13db9913d7b","target":"record","created_at":"2026-05-18T01:13:47Z","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":"cda2ee7a1037e6339a866eec7a6033b111ec2e79562f2008e73cc05bce1d77c5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-04-18T18:01:16Z","title_canon_sha256":"b18ff679289e87b0b9626f6ccb68385c21941bb18039220d5f59f468201a4bc2"},"schema_version":"1.0","source":{"id":"1604.05268","kind":"arxiv","version":2}},"canonical_sha256":"b3095036d001c5d3537c32e0aa9f33ae018d745fd480a342679831b69078ed21","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b3095036d001c5d3537c32e0aa9f33ae018d745fd480a342679831b69078ed21","first_computed_at":"2026-05-18T01:13:47.787124Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:13:47.787124Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wyzaPhqlVQ/sPdfCNzYkCUR2kHHlWUF5YTlrRwZkp84Lu8x/rTS678XYHx3Vf0wJbFsZR5q04qQLhErX/3SpBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:13:47.788004Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.05268","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0a83f6a7a7a3a6e960be6c50509239b607049a92f0e2bc33050cf13db9913d7b","sha256:0f40bd429740923d41bb1c661e4aeb5ab3b47f85f886bdd54fad5fdc7fca75cf"],"state_sha256":"543d1be843ed0fcb209a2db8bbe055765324afb2ff57e45fbc560eacf7839c99"}