P-S1: Spatial Uniqueness and the Geometric Boundaries of Quantum Information — The Many-Body Correlation Reduction Theorem and Its Seven Corollaries

Abstract: Since its birth, the mathematical framework of quantum mechanics — Hilbert space, state superposition, unitary evolution — has been treated as the fundamental postulates of mainstream physics. This has led to a situation lasting nearly a century: quantum mechanics yields extraordinarily precise computational results, but no one truly understands "why" quantum mechanics must take this form rather than any other. Physicists wryly call it "shut up and calculate. " Based on Space Ontology, we prove that "shut up and calculate" works because the entire mathematical structure of quantum mechanics is rooted in a geometric soil deeper than Hilbert space — the nonlinear dynamics of space itself. From the simple postulate that "space is the only entity, " its direct mathematical consequence — the Many-Body Correlation Reduction Theorem CABC = (CAB) ² — sets geometric boundaries for quantum information in seven independent directions: the upper limit of entanglement capacity, the speed of entanglement establishment, the specific form of the uncertainty principle, the inevitability of decoherence, the natural emergence of the Born probability rule, the dimension of the optimal computational primitive, and the criterion for the quantum-to-classical transition. These seven corollaries transform quantum mechanics from a mathematically "axiomatised input" into a physically "geometrically necessitated output. " All core conclusions are anchored in rigorously proven theorems from previously finalised papers in this series. Finally, we point out that these geometric boundaries not only explain "why quantum mechanics works, " but also indicate strategic directions for overcoming current bottlenecks in quantum technology — shifting from manipulating quantum gates to modulating geometric shapes. This series has proposed over a hundred testable predictions, covering a wide range from particle physics to cosmology, many of which have received preliminary or indirect verification. This paper is the first in the third series (Strategic Syntheses) of Space Ontology, synthesising the core principles derived from the first two series.