Theoretical analysis demonstrates non-perturbative regularization of quantum spacetime geometries, highlighting immediate observational falsification criteria.
This paper constitutes the formal continuation and mathematical refinement of the theoretical framework introduced in Part I regarding the non-perturbative regularization of quantum spacetime geometries. We address and resolve the critical gauge-conservation and dimensionality anomalies inherent in naive quantum-gravitational truncations by enforcing a strictly covariant energy-momentum tensor for the non-commutative vacuum (∇_μ T^μν = 0), driven by an emergent, de Sitter-like backreaction decay into the ambient radiation sector. The historical fine-tuning problem surrounding the primordial spacetime foam variance (σ_Θ ≤ 10⁻³²) is resolved from first principles via localized cosmological UV-IR mixing on compact Connes spectral manifolds, scaling deterministically as (l_P / R_H)¹/². Finally, we provide explicit, non-singular "here-and-now" numerical simulation protocols and strict observational falsification criteria designed for direct deployment within existing Planck/HEALPix analysis pipelines, QuTiP master equation integrators, and cosmic structure N-body solvers (such as Gadget-4 or Arepo), cross-correlated with empirical data from the THINGS / LITTLE THINGS surveys.
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Maxim Sokolov (2026) studied this question.
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