canonicalThreshold_pos

RS Physics Module 5 records the structural claim that the one-loop QCD coefficient satisfies $b_0 = 7 = 2^D - 1$, forced by the Count Law once $D = 3$ is in place (T8). The module imports the global constants (including the golden ratio φ) and the cost layer.

The canonical threshold is a real constant defined from φ in this file; positivity of that scale is the elementary fact needed before any comparison or non-negativity argument that treats the threshold as a genuine lower cut. The only upstream lemma used is the tight lower bound φ > 1.5, which follows at once from √5 > 2 and the closed form φ = (1 + √5)/2.

One-line wrapper. Unfold the definition of the canonical threshold, then invoke linarith on the single hypothesis φ > 1.5. No further lemmas or case splits are required; the inequality is pure real arithmetic once the definition is expanded.

Module 5 is marked STRUCTURAL THEOREM (zero sorry, zero axiom) and ties the QCD one-loop coefficient to the eight-tick / D = 3 forcing chain. A strictly positive canonical threshold is the elementary positivity fact that keeps any later domain-cost or threshold comparison well-defined on the positive reals. No downstream consumers are recorded yet; the lemma sits as local infrastructure for the module certificate and for any subsequent comparison that needs 0 < τ_can. It does not itself derive b_0 = 7; it only secures the sign of the threshold scale built from φ.