GUP/BEB correspondence

We develop a fully expectation–value formulation of the GUP/Bekenstein–bound (BEB) correspondence, building on \cite{Ali:2024tbd,Ali:2022ckm,Ali:2022ulp}. Using Dirac’s commutator–Poisson equivalence, the BEB supplies an information backreaction on the GUP–deformed bracket; at saturation the residual uncertainty in a sector cancels, enabling \emph{operational} simultaneity of conjugate expectations and resolving the EPR tension without hidden variables. A single self-consistency then fixes intrinsic confinement scales: the full (linear$+$quadratic) GUP reproduces the hydrogen Bohr radius (electron) and the proton charge radius (hydrogen nucleus). The same correspondence predicts an information–controlled crossover from a short–distance complex (evanescent) regime to an emergent real (Lorentzian) regime, with a symmetry flow from complex $SU(4)$ frames to $SO(1,3)$; under scale transmutation the short–distance $SU(4)$ is repurposed as the Pati–Salam $SU(4{)}_c$. Incorporating exterior–field entropy at horizons defines an effective Planck constant consistent with generalized–entropy extremality, tying entropy–area physics directly to the GUP at the expectation level.