{"paper":{"title":"Height functions on the $m \\times n$ Miura-ori flip graph: degree sequence and diameter","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Chakshu Gupta","submitted_at":"2026-06-21T17:40:19Z","abstract_excerpt":"The state space of an origami crease pattern forms a flip graph, whose vertices are the flat-foldable mountain-valley assignments and whose edges join assignments differing by a single face flip. For the $m \\times n$ Miura-ori, the degree sequence and diameter of this graph are known only for two rows. Each assignment maps to an integer height function on the grid, under which a vertex's degree equals its number of local extrema. In this model the vertices of each degree up to five are counted by an explicit polynomial in $m$ and $n$, valid once both exceed a bound that grows with the degree, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.22614","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/2606.22614/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"}