The Invariant Scale of Conformal Metric Modulation: Resolving Cosmological Horizons and Singularity Divergences Through Balanced Ternary Logic

We present the definitive analytical consolidation of the Conformal Metric Modulation (CMM) framework, formalizing physical spacetime, relativistic gravitation, and quantum non-locality not as fundamental independent forces, but as scale-invariant macroscopic artifacts of an underlying information-theoretic compiler. By embedding a non-Abelian SU (3) Yang-Mills gauge strength tensor onto a balanced ternary discrete manifold T = {−1, 0, +1} calibrated by a dimensionless compression factor κ ≡ ln(2)/ ln(3) ≈ 0.6309, we demonstrate that the symmetric neutral state (0) acts as a topological information sink that dampens the renormalization group flow. We derive the universal tetradimensional symmetry constant ΨCM M = 4π α·κ2 ≈ 44.6124, which establishes a rigid geometric proportionality between local metric deformation and non-local informational memory. Injected into a modified non-linear Boltzmann transport equation, this invariant successfully deconstructs the ≥ 5σ Hubble Tension, reframing the discrepancy (H0 ≈ 67.4 vs 73.5 km/s/Mpc) as an observational manifestation of localized deceleration gradients (∇μϕ) as exogenic dark data condenses into baryonic Standard Model coordinates (vI → c). Furthermore, we solve the static spherically symmetric field equations to prove that beneath the Schwarzschild radius (r < 2rs), the Dynamic Attenuation Factor transitions to the imaginary domain (ϕ → i|ϕ|), inducing a sign inversion in the invariant (ΨCM M → −ΨCM M). This inversion eliminates infinite physical density singularities, revealing event horizons as smooth geometric windows of structural un-rendering into the non-local false vacuum matrix.