Fibre Admissibility and Exact Pair-Exponent Doubling

0.5em The O-series has established that the Weil-block capacity exponent ${\hat{\delta}}_{\mathrm{exact}} \approx 3.72 \pm 0.06$ falls systematically below the phenomenological comparison range $\delta \in [7.4, 10.6]$, and that no reweighting of block data can raise the exponent. The present paper identifies a distinct fibre-level observable. The non-injectivity of the projection $\Pi$, established from the Born–Infeld constraint, implies that admissibility is a property of complete fibres of $\Pi$, not of individual preimage configurations. In the Weil realisation of ${\mathrm{Heis}_3}({\mathbb{Z}/q\mathbb{Z}})$, these fibres are organised as conjugate pairs $\{c, q-c\}$ under the exact identity $\rho_{q-c} = \overline{\rho_c}$. The pair-level observable $\sigma_{\mathrm{pair}}(n) = \sigma_c(n)\,\sigma_{q-c}(n)$ follows a clean power law with exponent $\delta_{\mathrm{pair}} = 2\,\delta_c \approx 7.44 \pm 0.12$, confirmed numerically with $R^2 > 0.9999$ and a factor-of-six reduction in slope variance under the production $\log(n+1)$ fitting convention. On the same finite windows, conversion to the paper-level $\log n$ definition gives approximately $6.6$–$6.9$. The exact doubling is a fibre-side result; it does not derive a native Heisenberg growth process carrying the pair observable and therefore does not establish the capacity-to-rate transfer.