{"paper":{"title":"(2+1) Regge Calculus: Discrete Curvatures, Bianchi Identity, and Gauss-Codazzi Equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"gr-qc","authors_text":"Freddy P. Zen, Seramika Ariwahjoedi","submitted_at":"2017-09-25T08:38:29Z","abstract_excerpt":"The first results presented in our article are the clear definitions of both intrinsic and extrinsic discrete curvatures in terms of holonomy and plane-angle representation, a clear relation with their deficit angles, and their clear geometrical interpretations in the first order discrete geometry. The second results are the discrete version of Bianchi identity and Gauss-Codazzi equation, together with their geometrical interpretations. It turns out that the discrete Bianchi identity and Gauss-Codazzi equation, at least in 3-dimension, could be derived from the dihedral angle formula of a tetr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.08373","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":""},"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"}