{"id":"palomar/PALOMAR-2026-10-20-000014","url":"https://github.com/rwst/Subspace-Theorems/tree/09835cb23557ae5ae0cf55a9c4ab9055f5d60338","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-10-20-000014-v1.json","repo":"https://github.com/rwst/Subspace-Theorems","tags":["math.NT","msc:68R15","msc:11J87","msc:11J54","msc:11J71","msc:37B10","diophantine-approximation","combinatorics-on-words","subword-complexity","lean-formalization"],"score":0,"title":"Stephan 2026: superlinear complexity of the (3/2)^n steering word","trust":"high","domain":"math.NT","source":"palomar","authors":["Ralf Stephan"],"reviews":0,"subject":"math.NT","summary":"A minimal Lean 4 / Mathlib formalization of R. Stephan, Superlinear complexity of the (3/2)^n steering word (arXiv:2607.11648), built on the repository's libraries ArithmeticHeights and DiophantineApproximation, whose p-adic Subspace Theorem it uses. Write (3/2)^n = m_n + ε_n with m_n the nearest integer and t_n = 2 m_{n+1} − 3 m_n. The library Stephan2026a is sorry-free and within Lean's three standard axioms. It proves Theorem 1.1, the subword complexity p_T(k) of the steering word T = (t_n) satisfies p_T(k)/k → ∞, together with the numbered results on its proof path: the repetition…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-10-20","reactions":{},"formalized":true,"formalizes":[{"title":"Superlinear complexity of the (3/2)^n steering word","identifier":"","relationship":"formalizes"}]}