La Profilée (LP) establishes a necessary persistence condition IR = R / (F · I · C) ≤ 1 that has been established across domains ranging from quantum decoherence to cosmological structure, spanning approximately sixty orders of magnitude in physical scale. This paper establishes why this condition holds identically across all structural levels without modification, scaling, or domain-specific adjustment. The result follows from structural minimality. The two assumptions from which LP derives the persistence condition — determinability and real transformation — contain no metric, no length scale, and no energy scale. The canonical decomposition into Frame, Module, and Coupling is forced by the reachability structure of the state space, which is defined independently of any scale parameter. IR is therefore scale-free by construction, not by coincidence. This paper provides the formal grounding for this claim. It defines admissible scale transformations as a subclass of the admissible representations already established in LP, proves that IR threshold structure is invariant under this class, and qualifies precisely where the non-trivial condition — AR5, preservation of flux-relevant structure under coarse-graining — must be independently verified for each domain instantiation. This paper does not introduce scale invariance as an additional symmetry assumption. It shows that scale invariance is a necessary consequence of structural minimality: a persistence condition derived without scale parameters cannot acquire scale dependence through application.
Marc Maibom (Mon,) studied this question.
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