{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:4MEW5FJ7G6CLJSTHPD3KPK246H","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":"af98cc9c8d0f61c6cb4eb9e016956c05969ddc253073773791dea95a9260ef6d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-01-11T19:32:09Z","title_canon_sha256":"64b47390f4dc4eb6a014717a830571a1a33d6daa7b784c2691144b12f177af87"},"schema_version":"1.0","source":{"id":"1801.03961","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.03961","created_at":"2026-05-17T23:51:54Z"},{"alias_kind":"arxiv_version","alias_value":"1801.03961v2","created_at":"2026-05-17T23:51:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.03961","created_at":"2026-05-17T23:51:54Z"},{"alias_kind":"pith_short_12","alias_value":"4MEW5FJ7G6CL","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_16","alias_value":"4MEW5FJ7G6CLJSTH","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_8","alias_value":"4MEW5FJ7","created_at":"2026-05-18T12:32:05Z"}],"graph_snapshots":[{"event_id":"sha256:ef60847f5c9b22baa121d49ba364e3bc7ed69c33e6c1a45f80750c15c8194eee","target":"graph","created_at":"2026-05-17T23:51:54Z","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 prove invariant Harnack inequalities for certain classes of non-divergence form equations of Kolmogorov type. The operators we consider exhibit invariance properties with respect to a homogeneous Lie group structure. The coefficient matrix is assumed either to satisfy a Cordes-Landis condition on the eigenvalues, or to admit a uniform modulus of continuity.","authors_text":"Farhan Abedin, Giulio Tralli","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-01-11T19:32:09Z","title":"Harnack inequality for a class of Kolmogorov-Fokker-Planck equations in non-divergence form"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.03961","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":"sha256:4500ab273636717c9ad8e4a7e56aa3b4988acdc40eec62ab1a7661e0910cb0df","target":"record","created_at":"2026-05-17T23:51:54Z","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":"af98cc9c8d0f61c6cb4eb9e016956c05969ddc253073773791dea95a9260ef6d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-01-11T19:32:09Z","title_canon_sha256":"64b47390f4dc4eb6a014717a830571a1a33d6daa7b784c2691144b12f177af87"},"schema_version":"1.0","source":{"id":"1801.03961","kind":"arxiv","version":2}},"canonical_sha256":"e3096e953f3784b4ca6778f6a7ab5cf1c25a26b2832b38a327e040362bafc8f9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e3096e953f3784b4ca6778f6a7ab5cf1c25a26b2832b38a327e040362bafc8f9","first_computed_at":"2026-05-17T23:51:54.790986Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:51:54.790986Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GaLXTE1dpdmL5FDQ7P21Y83bbUFdHFvaB9EpqaAVCNq9TcQIX4nQx61TySTNTwNwgExbz0/puF8iXAP9OSx7BA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:51:54.791415Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.03961","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4500ab273636717c9ad8e4a7e56aa3b4988acdc40eec62ab1a7661e0910cb0df","sha256:ef60847f5c9b22baa121d49ba364e3bc7ed69c33e6c1a45f80750c15c8194eee"],"state_sha256":"2efaa6a05de52ce90e53555d9617e323b4695f81e4480222857d910327f0600e"}