Structure and Scale: What a Compact-Algebra Theory of Everything Derives and the One Irreducible Input

We characterise precisely what the G2 framework can and cannot derive, and show that the boundary is not arbitrary but follows from the nature of a compact Lie algebra. The framework derives, accurately and parameter-free, every dimensionless quantity tested: mass ratios (the top/bottom ratio to 0.01%), the Weinberg angle (3/8), the generation count (three), the Koide relation (2/3), the unified coupling (1/42), the reactor angle (1/42), and the colour content of a generation (16 = 2(3)+2(3̄)+4(1)). It does not derive absolute scales: the breaking scales, the overall mass scale, and the value of the Cabibbo parameter. We show this split is structural. G2 is compact and therefore scale-free — it encodes only angles, ratios, representation dimensions, and counts. Every dimensionful prediction factorises as (pure G2 structure) × (one scale), exactly as the mass formula m = v(1/42)ⁿ(ratio) displays. We argue this one dimensionful input is irreducible in principle: no theory built on pure structure can derive an absolute scale, since scale is meaningful only relative to a reference. The framework is thus a complete theory of dimensionless physics requiring a single scale input — more economical than the Standard Model's nineteen parameters, while honest that it does not solve the hierarchy problem.