{"id":"palomar/PALOMAR-2026-10-22-000030","url":"https://github.com/stalex444/pdt-inflation-model-set-dimension/tree/c41d9d29f9c86fb0f849df79b03e713d3405a5eb","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-10-22-000030-v1.json","repo":"https://github.com/stalex444/pdt-inflation-model-set-dimension","tags":["math.MG","math.DS","math.NT","math-ph","gr-qc","cs.LO","msc:52C23","msc:37D20","msc:11R06","msc:11J71"],"score":0,"title":"The least physical dimension of an inflation-symmetric model set, with the cubic, quartic and degree-12 inflations of x^3 - x - 1 and x^4 - x - 1","trust":"high","domain":"math.MG","source":"palomar","authors":["Stephanie Alexander"],"reviews":0,"subject":"math.MG","summary":"Kernel-checked proofs, in Lean 4 + Mathlib, about cut-and-project schemes on a fixed integer lattice Z^iota invariant under an integer matrix A: splittings R^iota = E + H into A-invariant subspaces with Z^iota meeting H only in 0 and the projection of Z^iota to H dense in H, a window W in H (bounded, containing a relative ball), the model set Lambda(W) = {pi_E g : g in Z^iota, pi_H g in W}, and admissibility, some window with A Lambda(W) contained in Lambda(W) (inflation symmetry in Meyer's inclusion sense). The least physical dimension d(A) is the least dim E over admissible schemes.…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-10-22","reactions":{},"formalized":true}