We present a formalization of Resolution Scale Quantum Geometry (RSQG), a background-independent quantum theory of gravity that extends Loop Quantum Gravity with a dynamicaleffective dimension field. The theory is formulated on a compact 3-torus manifold with discretequantum geometry described by spin networks. A key innovation is promoting the effective dimen-sionality deff to a quantum field defined through the anisotropy tensor at spin network vertices. Thisfield unifies all fundamental forces as emergent geometric phenomena: gravity arises from holonomycorrections, electromagnetism from phase gradients with charge quantization q = nedeff/3, strongand weak forces from braiding algebra, and fermion masses from geometric invariants at topologi-cal defect vertices. RSQG naturally resolves singularities through quantum bounces, explains darkmatter as a geometric effect without particles, and predicts a cyclic multiverse where black holestransition to white holes. We derive the complete Standard Model fermion mass spectrum fromfirst principles with no free parameters beyond the Planck-scale boundary condition d3 = 2 andthe Higgs VEV. The framework is mathematically consistent, anomaly-free, and recovers GeneralRelativity and the Standard Model in appropriate limits. We derive testable predictions includingCMB anomalies, gravitational wave echoes, galactic rotation curves without dark matter particles,and early galaxy formation. This formalization establishes RSQG as a viable path toward completeunification of quantum mechanics and gravity.
Salidor Christopher Henrico (2026) studied this question.