{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:4U4BLRKO7GYRLWIEAL3D4JYW2Z","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":"25f8f7561e2042645b3064ffe6926efd0c5f460eb86a1d0e2260563c58ae7cbc","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-10-24T15:43:01Z","title_canon_sha256":"853f788760d32b2fb8bdcea0d60768d98c8b39445cbd41ff759125b70ceabff0"},"schema_version":"1.0","source":{"id":"1110.5263","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.5263","created_at":"2026-05-18T04:00:01Z"},{"alias_kind":"arxiv_version","alias_value":"1110.5263v2","created_at":"2026-05-18T04:00:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.5263","created_at":"2026-05-18T04:00:01Z"},{"alias_kind":"pith_short_12","alias_value":"4U4BLRKO7GYR","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"4U4BLRKO7GYRLWIE","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"4U4BLRKO","created_at":"2026-05-18T12:26:20Z"}],"graph_snapshots":[{"event_id":"sha256:aee56aabe34a91133dd1e9c04687cc7c92c1167f29a431159f32bd1aa4981bd7","target":"graph","created_at":"2026-05-18T04:00:01Z","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 a Harnack inequality for solutions to $L_A u = 0$ where the elliptic matrix $A$ is adapted to a convex function satisfying minimal geometric conditions. An application to Sobolev inequalities is included.","authors_text":"Diego Maldonado","cross_cats":["math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-10-24T15:43:01Z","title":"Harnack's inequality for solutions to the linearized Monge-Ampere equation under minimal geometric assumptions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.5263","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:a2a19c0f126f0ecd8913068493e8c4e53cc6e9504620872893651a9eca800a00","target":"record","created_at":"2026-05-18T04:00:01Z","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":"25f8f7561e2042645b3064ffe6926efd0c5f460eb86a1d0e2260563c58ae7cbc","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-10-24T15:43:01Z","title_canon_sha256":"853f788760d32b2fb8bdcea0d60768d98c8b39445cbd41ff759125b70ceabff0"},"schema_version":"1.0","source":{"id":"1110.5263","kind":"arxiv","version":2}},"canonical_sha256":"e53815c54ef9b115d90402f63e2716d66d71899139ca469157baa5806e6f777f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e53815c54ef9b115d90402f63e2716d66d71899139ca469157baa5806e6f777f","first_computed_at":"2026-05-18T04:00:01.071366Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:00:01.071366Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6IPUw4HmZw83n9jKq90/c59UAd8VKlGy1hdfFi3HoqqYPmODRvjGmT0lWfQ1sjVszzZ2GQrfiDRFvkE9umK1BA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:00:01.072081Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.5263","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a2a19c0f126f0ecd8913068493e8c4e53cc6e9504620872893651a9eca800a00","sha256:aee56aabe34a91133dd1e9c04687cc7c92c1167f29a431159f32bd1aa4981bd7"],"state_sha256":"ec2df0de12d3b4d2615a60ac36dac096433f91abb824cec24d9675a7c28b2d08"}