PAPER_1162: Kaluza-Klein Tower Suppression: Mode-by-Mode 1/26! Bound from BH26 Spectrum (G5 Closure)

We close gap **G5** of the Lagrangian re-derivation outline by computing, mode-by-mode, the Kaluza-Klein tower contribution to the 4D effective Newton constant when the 26D BSFG action is integrated over the 22-torus $T^{22}$ at the bosonic critical dimension. Using the canonical BH26 spectral ladder $\lambda_k = k(k+25)$ on $S^{25}$ ([CondensedPhysics4.py L46442](CondensedPhysics4.py#L46442)), the contribution of the $n\geq 1$ KK modes after the 26-fold radial derivative required by the $G$ closure (PAPER_1161) is bounded by $\sum_{n\geq 1}\lambda_n^{-26} = 1.624\times 10^{-37}$, which is **$10^{10}$ times smaller** than the $1/26! \approx 2.48\times10^{-27}$ factorial-barrier bound assumed (but not previously computed) in the outline. The dominant $n=1$ mode contributes $1/26^{26}$, in exact duality with G8: the same Pochhammer machinery that **extracts** $26!$ from the zero mode (G8) **inverse-projects** higher modes by $1/\lambda_n^{26}$. ---
