Quantum Interference Projector Theory and Universal Polyhedral Geometry: A New Paradigm of Cosmic Structure with a Self-Regulation Mechanism

10.5281/zenodo.18525075 A novel theory is presented, explaining the large-scale structure of the Universe asan interference pattern generated by a 12-ray quantum projector based on icosa-hedral symmetry. The theory postulates that observed space is a projection froman 8-dimensional space through 12 channels corresponding to the vertices of anicosahedron. Key predictions are: (1) A characteristic scale L∗ = 210 Mpc, (2) Ahierarchy of scales Ln = L∗ × κn with κ = 8/9, (3) A global density enhancementΠ = 4/3, (4) Exponentially decaying tolerances with an initial value ε0 = 1/3,correlated between levels according to the law εn+1 ≈ −κεn. The theory providesa unified explanation for the BAO scale (≈ 105 Mpc), observed icosahedral sym-metry, and CMB anisotropies. A complete mathematical framework is presented,including an autoregressive model for tolerance dynamics, and a comprehensivestatistical framework for falsifying the theory based on data from SDSS, eBOSS,and SPARC. The obtained empirical correspondences have a combined statisticalsignificance exceeding 8σ. Keywords: cosmology, large-scale structure, quantum interference, geometric cos-mology, icosahedral symmetry, autoregressive process, falsifiability, SDSS, eBOSS,SPARC.