Computational Finitism: Discrete Couplings, Geometric Friction, and Radix Invariance

This paper addresses three foundational challenges in the framework of Computational Finitism: the derivation of the discrete beta function (Problem 1), the mechanism of the Tsirelson bound (Problem 3), and the algebraic necessity of Base-10 (Problem 4). We demonstrate that the fine-structure constant runs from a bare value of to the observed via a topological subtraction of 7 vacuum maintenance channels. We prove that this derivation is radix-invariant. Furthermore, we show that the Tsirelson bound () is an emergent limit caused by "Geometric Friction" () damping a bare non-associative correlation of . Finally, we demonstrate that Problem 4 is a category error: the framework is base-independent by construction.