{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:GQYP7T3DRUX5EGFACKWERW7O2T","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":"df3403eea28c51e66459a2a52ce905f0ab03893f6de577079a11ae4952bf9dab","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-10-07T21:46:44Z","title_canon_sha256":"466d992f9f5638dda0f1c3d1e52db9aab9877a8ec5968df4cac15b7ff7eddf3b"},"schema_version":"1.0","source":{"id":"1010.1554","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.1554","created_at":"2026-05-18T04:39:40Z"},{"alias_kind":"arxiv_version","alias_value":"1010.1554v1","created_at":"2026-05-18T04:39:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.1554","created_at":"2026-05-18T04:39:40Z"},{"alias_kind":"pith_short_12","alias_value":"GQYP7T3DRUX5","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"GQYP7T3DRUX5EGFA","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"GQYP7T3D","created_at":"2026-05-18T12:26:07Z"}],"graph_snapshots":[{"event_id":"sha256:3b844c876c0afc007f81e1efe190eabc3b9cc9155d988628920a2c31a91ee544","target":"graph","created_at":"2026-05-18T04:39:40Z","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":"This paper deals with two separate but related results. First we consider weak solutions to a parabolic operator with H\\\"ormander vector fields. Adapting the iteration scheme of J\\\"urgen Moser for elliptic and parabolic equations in $\\mathbb{R}^n$ we show a parabolic Harnack inequality. Then, after proving the Harnack inequality for weak solutions to equations of the form $u_t = \\sum X_i (a_{ij} X_j u)$ we use this to show H\\\"older continuity. We assume the coefficients are bounded and elliptic. The iteration scheme is a tool that may be adapted to many settings and we extend this to nonlinear","authors_text":"Garrett Rea","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-10-07T21:46:44Z","title":"A Harnack inequality and H\\\"older continuity for weak solutions to parabolic operators involving H\\\"ormander vector fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.1554","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:fa49e1002fe8acc549dc341d1d3b911cea4ff70f2e5508e6a19fccc91ea3ed80","target":"record","created_at":"2026-05-18T04:39:40Z","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":"df3403eea28c51e66459a2a52ce905f0ab03893f6de577079a11ae4952bf9dab","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-10-07T21:46:44Z","title_canon_sha256":"466d992f9f5638dda0f1c3d1e52db9aab9877a8ec5968df4cac15b7ff7eddf3b"},"schema_version":"1.0","source":{"id":"1010.1554","kind":"arxiv","version":1}},"canonical_sha256":"3430ffcf638d2fd218a012ac48dbeed4fcb14996463cc53dc3fab11464711f51","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3430ffcf638d2fd218a012ac48dbeed4fcb14996463cc53dc3fab11464711f51","first_computed_at":"2026-05-18T04:39:40.231613Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:39:40.231613Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YI63igWY+EIRi//IDLq24/KElKSeZn4r1TY6ZN6uBIx+DtAl+acDkn1jvuRHuQIgfX52YFCk9G89J5zscFxADA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:39:40.232279Z","signed_message":"canonical_sha256_bytes"},"source_id":"1010.1554","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fa49e1002fe8acc549dc341d1d3b911cea4ff70f2e5508e6a19fccc91ea3ed80","sha256:3b844c876c0afc007f81e1efe190eabc3b9cc9155d988628920a2c31a91ee544"],"state_sha256":"e19fe57912bf29b2993d4f90cff7d32b75d85925df40f1b9b259bb04ea449469"}