{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:QFVLWE65JISI6HEW4P7YJYVZ7G","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":"9b9b768d4830b400551d86dbf3ea4d2bef380de893ad6ddbf619ece17c66e996","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-08-28T11:15:17Z","title_canon_sha256":"37a2279aee5c2c8911e2d9f0e56a5834e50f52f9e5b21be0c99555ff81213be7"},"schema_version":"1.0","source":{"id":"1308.6129","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.6129","created_at":"2026-05-18T02:07:32Z"},{"alias_kind":"arxiv_version","alias_value":"1308.6129v5","created_at":"2026-05-18T02:07:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.6129","created_at":"2026-05-18T02:07:32Z"},{"alias_kind":"pith_short_12","alias_value":"QFVLWE65JISI","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"QFVLWE65JISI6HEW","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"QFVLWE65","created_at":"2026-05-18T12:27:57Z"}],"graph_snapshots":[{"event_id":"sha256:707c211d5e5252ad3cbcf08030c8819dc0049c95f6c5ebf5fde6117ecf8e4dca","target":"graph","created_at":"2026-05-18T02:07:32Z","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":"The dimension free Harnack inequality for the heat semigroup is established on the $\\RCD(K,\\infty)$ space, which is a non-smooth metric measure space having the Ricci curvature bounded from below in the sense of Lott-Sturm-Villani plus the Cheeger energy being quadratic. As its applications, the heat semigroup entropy-cost inequality and contractivity properties of the semigroup are studied, and a strong enough Gaussian concentration implying the log-Sobolev inequality is also shown as a generalization of the one on the smooth Riemannian manifold.","authors_text":"Huaiqian Li","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-08-28T11:15:17Z","title":"Dimension free Harnack inequalities on $\\RCD(K, \\infty)$ spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.6129","kind":"arxiv","version":5},"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":"sha256:3a7a53d02a07c75410fd19840cf0f1979e0855ab7da0fbd3de4f30d04c3915a6","target":"record","created_at":"2026-05-18T02:07:32Z","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":"9b9b768d4830b400551d86dbf3ea4d2bef380de893ad6ddbf619ece17c66e996","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-08-28T11:15:17Z","title_canon_sha256":"37a2279aee5c2c8911e2d9f0e56a5834e50f52f9e5b21be0c99555ff81213be7"},"schema_version":"1.0","source":{"id":"1308.6129","kind":"arxiv","version":5}},"canonical_sha256":"816abb13dd4a248f1c96e3ff84e2b9f9a64a68a7e638b4654f9ebbe4653f3e84","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"816abb13dd4a248f1c96e3ff84e2b9f9a64a68a7e638b4654f9ebbe4653f3e84","first_computed_at":"2026-05-18T02:07:32.173920Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:07:32.173920Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GMQ2m9ntlTH/8H/ysfg36VdC9cJ4fnjgnhtmLE8XdgkP1GYIL6gV406mvsbURFxkynvm7nwDaHZk5U9sPHHXAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:07:32.174579Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.6129","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3a7a53d02a07c75410fd19840cf0f1979e0855ab7da0fbd3de4f30d04c3915a6","sha256:707c211d5e5252ad3cbcf08030c8819dc0049c95f6c5ebf5fde6117ecf8e4dca"],"state_sha256":"e98c086faa1a2d67c3ae6efe8da3dd6c873d825e1788ad06e329b91489aa3ee6"}