{"paper":{"title":"Lower Bound for Weighted Intermediate Ricci Curvature and Tensorial Entropy Convexity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Chao-Ming Lin, Kai-Hsiang Wang","submitted_at":"2026-08-04T09:58:57Z","abstract_excerpt":"We introduce a weighted version of intermediate Ricci curvature and establish several equivalent characterizations of its lower bound. As an application, we generalize the results of Aishwarya--Rotem--Shenfeld [arXiv:2509.23399v1] by deriving intrinsic-dimensional evolution variational inequalities and the corresponding Wasserstein contraction estimates for the heat flow. We also compare our characterization with that of Ketterer--Mondino [arXiv:1610.03339v3] via lower-dimensional optimal transport."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.03405","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2608.03405/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}