{"paper":{"title":"Minimal Posets Realizing \\texorpdfstring{$\\mathbb{Z}_2 \\times \\mathbb{Z}_4$} as Automorphism Group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ponaki Das, Sainkupar Marwein Mawiong","submitted_at":"2026-06-05T17:32:13Z","abstract_excerpt":"We prove $\\beta(\\mathbb{Z}_2 \\times \\mathbb{Z}_4) = 14$, where $\\beta(G)$ denotes the minimum cardinality $|P|$ among finite posets $P$ with $\\Aut(P) \\cong G$. The lower bound is established by a complete case analysis of orbit decompositions of $P$ under faithful $G$-actions, organized by the largest orbit size. The upper bound is realized by an explicit $14$-element poset whose automorphism group is computed by a height-function argument together with a rigidity analysis of its covering relations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.07478","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/2606.07478/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"}