Scale Projection and the Static Block Universe: A First-Principles Challenge to the Big Bang Paradigm

The Big Bang paradigm, the cornerstone of standard cosmology, faces unresolved fundamental crises: the initial singularity, horizon, flatness, and baryon asymmetry problems, relying on ad hoc inflation to patch inconsistencies. This work is the sixth paper in a 7-part series built on the Scale Geometry unified framework, rooted in the foundational S³ Quantum Deformation Geometry Operator (Paper 1), geometric locking of (Paper 2), UV divergence elimination (Paper 3), Representation Splitting Theorem (Paper 4), and cosmic expansion as an illusion (Paper 5). As a component of the parent monograph The Scale Geometry Framework: Topology, Projection, and Static Universe (https: //doi. org/10. 5281/zenodo. 19368089), we establish a rigorous first-principles static universe model, in homage to Albert Einstein's vision of an eternally static, geometrically unified cosmos. We prove three core theorems: the Cyclic Scale Projection Theorem (Big Bang is a non-singular point on the compact S¹ scale spectrum), Projection Isomorphism Theorem (cosmic time evolution maps to observer scale sliding), and Global Causal Connectivity Theorem (static S³ universe is fully causally connected). We resolve all Big Bang crises without inflation, reinterpret CMB, BBN, and large-scale structure as intrinsic geometric properties of the static S³ universe, and propose falsifiable predictions including no primordial gravitational waves (r < 10^-5) and positive spatial curvature (ₖ -0. 001 -0. 003). This work replaces the Big Bang's dynamical evolution with a scale projection illusion, unifying cosmology with the quantum geometric foundation of the Standard Model. Author: Xinyu Zheng (郑心宇) ORCID: 0009-0000-3175-1681Correspondence: wxsq1638@outlook. comDOI: To be Assigned by Zenodo