Strong Determinism and Cyclic Time Recurrence: A Geometric Interpretation of Observer Experience from Scale Geometry

This work is the final paper in the 7-part Scale Geometry unified framework series, completing the theoretical closure by addressing the ultimate foundational questions of time, determinism, observer experience, and cyclic recurrence. Building on the core results of preceding papers—including the static closed S³ block universe, compact S¹ scale spectrum topology, Inverse Limit Isomorphism Theorem, and Cyclic Scale Projection Theorem—we rigorously prove four core theorems: the Strong Determinism Ontology Theorem (the universe is an eternally static, uniquely determined geometric structure with no fundamental randomness), the Cyclic Time Recurrence Theorem (periodic modular automorphism flow generates infinite, exact recurrence of observer experience), the Observer Projection Isomorphism Theorem (subjective experience maps to static ontology via scale projection), and the Quantum Probability Determinism Theorem (quantum randomness is emergent from finite scale resolution). As a component of the parent monograph The Scale Geometry Framework: Topology, Projection, and Static Universe (https: //doi. org/10. 5281/zenodo. 19368089), we provide a first-principles geometric interpretation of the arrow of time, illusion of free will, and quantum measurement problem, in homage to Albert Einstein's vision of a deterministic, geometrically unified cosmos. We establish falsifiable predictions including CMB topological signatures of cyclic projection, scale-dependent quantum probability corrections, and absence of fundamental quantum randomness. This work completes the Scale Geometry framework, unifying particle physics, general relativity, cosmology, and observer experience from a single geometric axiom. Author: Xinyu Zheng (郑心宇) ORCID: 0009-0000-3175-1681Correspondence: wxsq1638@outlook. comDOI: To be Assigned by Zenodo