Observable-Class Derivation Mismatch and the Heisenberg Transfer No-Go: From Proxy Capacity to Block-Level Span Dynamics

The O3–O7 derivation chain proposes, on a changing-degree LPS family, the relation ${\beta^{*}} = 1/(\delta + 1/2)$ linking the capacity decay exponent $\delta$ to the cascade growth exponent ${\beta^{*}}$ governing charged-lepton mass ratios. Papers O12–O14 demonstrated that the exact Weil-block capacity exponent ${\hat{\delta}_{\mathrm{exact}}}(q) \in [3.6, 4.8]$ is incompatible with the target window $\delta \in [7.4, 10.6]$, and that this tension is structural rather than a finite-size artefact. The present paper identifies the precise origin of the mismatch and proves a non-transferability result: the O6 growth equation $\mathrm{d}p/\mathrm{d}n \lesssim {R_n} \, c_{\mathrm{BI}} \sqrt{p(n)}$ derives ${\beta^{*}}$ from a scalar global redundancy functional ${R_n}$, 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 ${\hat{\delta}_{\mathrm{exact}}}$ does not, in general, coincide with the scalar exponent $\alpha$ entering the growth equation. We define an effective block-weighted redundancy ${R_n^{\mathrm{eff}}}$ and show that its exponent cannot repair the gap by aggregation alone. The native identity is instead $\Delta r_n=|S_n|\Sigma_n\asymp \Sigma_n n^{D-1}$. Neither the Born–Infeld factor $c_{\mathrm{BI}}\sqrt{p}$ nor the changing LPS valence has a native carrier on the fixed-degree Heisenberg cascade. Moreover, a constant factor $q^{-\eta}$ cannot alter an intra-$q$ slope, and direct exponent matching in the transplanted equation does not yield the legacy reciprocal formula. The former C1/C2 outputs are therefore retained only as phenomenological diagnostics. Block-level redundancy measurement remains useful for the aggregation question, not as a test of a native capacity-to-rate transfer.