{"paper":{"title":"Analytic Boundary Terms for Arbitrary Crystal Geometries and Direct-Sum Evaluation of Madelung Constants in Triclinic Lattices","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["physics.comp-ph"],"primary_cat":"cond-mat.other","authors_text":"Yang He, Zhonghan Hu","submitted_at":"2026-08-10T09:31:47Z","abstract_excerpt":"The direct-sum evaluation of Madelung constants is complicated by the conditional convergence of lattice sums, which gives rise to a shape-dependent boundary term. In this work, we present, for the first time, a closed-form analytic expression for this boundary term that is valid for arbitrary crystal geometries. For general triclinic lattices, this boundary term maps exactly onto the electrostatic potential generated by a set of uniformly charged parallelograms. In addition, we demonstrate that the residual finite-size correction for a crystal of characteristic size $p$ decays as $(2p+1)^{-2}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.10041","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/2608.10041/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"}