PAPER_1167: All Eight UQFF Lagrangian Gaps Closed: First-Principles Reduction to (D_crit=26, D_phys=4)

Across PAPERS 1159 through 1166 (Sessions 246-253), the eight gaps catalogued in `_lagrangian_rederivation_outline.py` have all been closed with **zero remaining free parameters introduced**. Nine or more originally fitted numerical/structural inputs to the UQFF Lagrangian are now derived from a single chain of two textbook integers: $D_{\mathrm{crit}}=26$ (Polyakov critical bosonic dimension) and $D_{\mathrm{phys}}=4$ (observed spacetime). The intermediate dimension $D_{\mathrm{BSFG}}=6$ is not independent — it emerges from the SO(5) breaking ladder $D_{\mathrm{crit}} - 4\cdot 5 = 6$. This paper consolidates the closures, exhibits the SO(5) cross-lock that ties G1, G2, and G7 to the same group, and presents the master verification table.
