Dynamic Dimension, Form Conservation, and Interpenetrating Symmetric Universes: A Geometric Model

Abstract This study presents a geometric model explaining the structure and formation of the universe through exponential form transformation. The concept of “dimension” is defined not as a spatial coordinate but as the instantaneous form state of matter, expressed by a real positive exponent n in xⁿ. Form transforms continuously under pressure and temperature gradients: volumetric (n ≈ 3), areal (n ≈ 2), linear (n ≈ 1), and point-like (n → 0⁺, x⁰ = 1, singularity). The positive and negative (inverse) universes share the same physical field in an interpenetrating structure. The negative universe becomes operative in the same spacetime from the Planck scale onward (n ≈ 2 and below). Form conservation is defined by F (n) = xⁿ − x^ (1/n) ; at n = 1, F (1) = 0, identifying the string phase as the natural equilibrium point. The singularity (n → 0⁺) is the common transition layer of the two form spectra. The Big Bang is the unfolding of the positive form chain in the same field, initiated by a singularity arriving from the negative universe. The model demonstrates strong consistency with the most recent results of Causal Dynamical Triangulations (CDT) — the continuous reduction of the spectral dimension to ~2 at the Planck scale — as well as with the holographic principle, string theory, and the CPT-Symmetric Universe model of Boyle, Finn, and Turok. Keywords: dynamic dimension, form conservation, interpenetrating symmetric universes, exponential form transformation, singularity transition, CDT, CPT symmetry, geometric model.