{"paper":{"title":"Forman--Ricci Curvature for Irregular Convex Mosaics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"cond-mat.soft","authors_text":"Abhyudaya Gupta, Kuldeep Saha, Sayak Mukherjee","submitted_at":"2026-05-28T11:47:55Z","abstract_excerpt":"Forman has defined a discrete version of the Ricci curvature on Riemannian manifolds, known as the Forman--Ricci curvature. The Forman--Ricci curvature has found significant applications in several pattern recognition problems occurring in natural sciences. Domokos and Langi, on the other hand, have defined a notion of irregularity for convex mosaics, which has also found remarkable applications to the geological problem of fractures in rocks. We define a modification of the classical Forman--Ricci curvature for irregular convex mosaics and demonstrate how they can be used to distinguish betwe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.04007","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/2606.04007/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"}