Confinement schemas and the reach of block certificates for powers of rational numbers modulo one
A Lean 4 / Mathlib development of the second paper on the sets Z_{p/q}(s, s+t) = {ξ > 0 : {ξ(p/q)ⁿ} ∈ [s, s+t) for all n ≥ 0}, the generalized Z-numbers of Flatto, Lagarias and Pollington. The first paper built a corpus of block certificates for individual statements Z_{p/q}(U) = ∅. This paper replaces parts of that corpus by theorems, and then asks what the certificate format can and cannot reach. Thirty certificates in the regime p > q² collapse into one closed-form criterion on the single real parameter ε = {(p−q)s}, settling a set of positions of measure 1 − 2q²/(p(p+q)) at every base…
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