Symmetric Nested Dual-Universe Model: Dynamic Dimensionality, Form Conservation, and Zero-Energy Spectral Duality

This work presents a unified geometric model explaining the universe's structure through exponential form transformation and zero-energy spectral duality. We define x ∈ℝ(matter/energy) and n ∈ℝ as the physical entity as the dimensional state index determining the geometric configuration of this entity. In a three-dimensional coordinate universe, the spectrum is bounded: n [-3, +3].∈The Spectral Zero-Boundary Principle posits that the positive universe (+UNIVERSE, n (0, +3]) and ∈∈negative universe (−UNIVERSE, n [-3, 0)) represent opposite states of existence separated by n=0, the singularity boundary serving as a trans-universe gateway. The model is supported by seven theorems with formal proofs. We derive four quantitative predictions:δ1) Hawking spectrum anomaly _H = f(n) - 1 with parameter constraint (n_Pl - 1) [1.74, 2.94] for ±5λ15% range;2) Dark energy density expressed via form excess (3) = |x|^3 + |x|^(-3) - 2;Δ∈3) Time-dependent effective cosmological constant _eff(t) evolution driven by / = 10 asymmetry, Λexplaining Hubble tension;δ ∝β₂ β₁4) CMB power spectrum asymmetry P/P F(n_*) from dimensional state evolution.⁶These predictions are testable via primordial black hole gamma-ray observations, DESI/Euclid dark energy mapping, and CMB-S4 experiments.