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 (nPl - 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.