Observable-Class Derivation Mismatch and the Exact Growth Equation: From Proxy Capacity to Block-Level Dynamics

The O3–O7 derivation chain establishes the structural relation β* = 1/(δ + 1/2) linking the capacity decay exponent δ to the cascade growth exponent β* governing charged-lepton mass ratios. Papers O12–O14 demonstrated that the exact Weil-block capacity exponent δ̂exact(q) ∈ [3.6, 4.8] is incompatible with the target window δ ∈ [7.4, 10.6], and that this tension is structural rather than a finite-size artefact. The present paper identifies the precise origin of the mismatch: the O6 growth equation dp/dn Rₙ \, cBI √p(n) derives β* from a scalar global redundancy functional Rₙ, whereas the exact observable measured in O12–O13 is a block-averaged capacity over $(q-1)$ Weil representations of internal dimension q. We prove a non-equivalence theorem establishing that the block-averaged exponent δ̂exact does not, in general, coincide with the scalar exponent α entering the growth equation. We define the effective dynamical redundancy Rₙᵉᶠᶠ as the observable that genuinely governs the valence growth in the exact-block setting, and re-derive the growth equation with this observable as input. The re-derivation yields two structural scenarios: (C1) the functional form β* = 1/(δeff + 1/2) survives with a corrected exponent δeff that differs from δ̂exact by an aggregation bias; (C2) the functional form itself is modified by a representation-dimension correction, β* = 1/(δeff + 1/2 + σ(q)), where σ(q) → 0 as q → ∞. Scenario discrimination requires a block-level redundancy measurement not yet available from the O12 pipeline, identified as the central open direction of this paper.