GUP/BEB correspondence

In this paper, we develop a fully expectation-value formulation of the GUP/Bekenstein-bound (BEB) correspondence, building on Refs. 1 – 3 . 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 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[Formula: see text]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 [Formula: see text] frames to [Formula: see text]; under scale transmutation the short-distance [Formula: see text] is repurposed as the Pati–Salam [Formula: see text]. 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.