UEIR Framework: Foundational Revision of Axiom A1 Primitive Recursive Construction of the Boolean Hypercube and Conductance

The original Axiom A1 of the UEIR framework treated the Boolean hypercube Qn = {0, 1}n as a set-theoretically prior object whose coordinates were then given physical interpretation as active or inactive binary constraint generators. This note replaces that single axiom with three primitive recursive definitions (Definitions C1–C3) in which the binary constraint generator g is the undefined primitive and Qn is derived from it. We prove that all five theorems of the existing framework— Attractor Robustness, Bousso Bound, Escape Prevention, Bekenstein–Landauer–Unruh, and the Selection Theorem for k = 181—survive the reordering without modification. Theorem 6.1 (BLU) gains improved physical grounding under the revision: the Landauer erasure cost ΔE = kBT ln 2 per bit is now explicitly the energy cost of a generator state-flip [3]. The foundational order becomes:g −→ Qn −→ Φ = k/n −→ pipeline and theorems.This revision is a genuine deepening of the foundation, not a change to any existing result. Three open problems exposed by the revision are stated formally; each sits at the frontier between quantum mechanics and General Relativity.