{"paper":{"title":"Tiling decomposition multiplicity predicts stability of GaN(0001) surface reconstructions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.comp-ph"],"primary_cat":"cond-mat.mtrl-sci","authors_text":"Akira Kusaba, Karol Kawka, Pawel Kempisty, Tetsuji Kuboyama","submitted_at":"2026-07-13T05:27:47Z","abstract_excerpt":"The stable adatom configurations of a semiconductor surface have traditionally been sought by sampling: density functional theory (DFT) energies steer a heuristic or Bayesian search through a configuration space far too large to cover. Here we show that, for the GaN(0001)-$(6\\times6)$ surface under the electron counting (EC) rule, the search can instead be posed as a discrete tiling problem and solved exhaustively. Enumerating all rhombus tilings of the surface lattice, together with all EC-compatible adatom arrangements built on them, yields the complete catalog of 416,683 configurations at f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.11105","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/2607.11105/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"}