Loop Quantum Gravity as an Effective Limit of Modal Triplet Theory

We show that the kinematical structure of loop quantum gravity (LQG) arises as an effective shadow of coherent fixed-point dynamics in Modal Triplet Theory (MTT). The real SU(2) Ashtekar–Barbero connection, spin-network kinematics, and discrete spectra of geometric operators emerge as compact holonomy and gap-controlled encodings under noninvertible projection onto the coherent sector. Within the coherent universality class, the Barbero–Immirzi parameter is not a free quantization ambiguity but is fixed by the same spectral and stability bottleneck data that control coherent projection and admissibility. Black hole entropy matching is reinterpreted as a consistency condition on admissible coherent microstate counting rather than parameter fitting. We further show that quantities traditionally treated as independent in LQG are tied together by cross-sector closure, yielding sharp falsifiability criteria. All results are slab-local and admissibility-conditioned, and no claim is made that LQG provides a fundamental microscopic description of spacetime.