Building upon the structural foundations established in Papers I–X of the Unified Field Theory Framework (UFT-F), Paper XI extends the renormalization program to the Riemann Hypothesis (RH). This work interprets critical-line stability not as an isolated arithmetic conjecture, but as compatibility data for a spectral-dissipative master flow. The Riemann Admissibility Hypotheses are formulated as trace-class and spectral-gap constraints, ensuring that the zeta zeros correspond to the eigenvalues of a unique self-adjoint operator. Within a heat-trace renormalization framework, any deviation from the critical line is identified as a non-normalizable state that violates the Anti-Collision Identity (ACI) and index rigidity. By demonstrating that the distribution of primes is governed by the fixed-point stability of the universal spectral-RG flow, RH is reduced to a requirement of Spectral Admissibility within the UFT-F manifold. What is Renormalization in this Context? Renormalization is the mathematical process of filtering infinities and instabilities to extract stable, physically (or geometrically) meaningful quantities. In this series, it is applied to the full UFT-F corpus: the earlier 4,000+ pages of results on particle masses, geometric structures, and closures are re-expressed in standard mathematical language so that their stability and logical soundness can be directly verified by the broader community using conventional tools and nomenclature. Boxing In the Millennium Problems Papers VIII–XVIII represent the categorical audit and standardization phase of the UFT-F program. Rather than claiming standalone unconditional proofs, these papers demonstrate that each Millennium Prize problem (Riemann Hypothesis, P vs NP, Hodge, BSD, Navier–Stokes regularity, Yang–Mills mass gap, and others) reduces functorially to a question of spectral admissibility inside Spectral Figurate Geometry. The problems are rigorously “boxed in” within ordinary mathematical structures: any violation would necessarily break the global spectral stability, L1-integrability, index rigidity, and Redundancy Cliff (chi ≈ 763.55827) already established in Papers I–VII. In short, these conjectures are not arbitrary independent mysteries ... they emerge as structural requirements of the very geometry that permits stable mathematical objects to exist in the first place. In the case of Paper XI, we prove that if the Riemann Hypothesis were false, the "vibrational floor" of the number line would collapse, creating an unstable geometry that contradicts the observed laws of physics. We have boxed in the primes by showing they must follow the critical line to maintain the internal consistency of the UFT-F manifold. This series does not replace the core UFT-F results; it makes their consequences legible, auditable, and verifiable in standard mathematical terms.