Universe Internal Indistinguishability Theory (NGV-Prime-zeta)
Year: 2025
Type: article
Abstract: \textbf{Axiomatizing Randomness as No-God-View Indistinguishability, with Prime-Driven Constructions and $\zeta$-Triadic Geometry} This paper establishes a complete mathematical framework that redefines "randomness" as indistinguishability internal to observers, and implements this principle through prime-driven constructions. We employ full-period linear congruential permutation functions that strictly satisfy Hull-Dobell conditions, achieving completely deterministic block rearrangement, strictly following the No-God-View (NGV) principle: randomness is not an ontological property, but an emergent property relative to finite observational capabilities. Through introducing Riemann $\zeta$ function's triadic information conservation theory, we establish a geometric coordinate system for visible information, where the wave component $i_0$ precisely characterizes the visibility of quantum phase coupling. Core contributions include: (1) Proved that prime-driven deterministic block-permutation construction is $(m,\epsilon)$-indistinguishable from ideal Bernoulli sources at arbitrary fixed observation scale $m$; (2) Provided explicit exponential decay rate of error under Riemann Hypothesis (RH); (3) Established measure-preserving transformation theorem from Bernoulli to quantum statistics; (4) Revealed deep connections between statistical formulas on critical line $s=1/2+it$ and GUE conjecture. This theory unifies fundamental concepts in number theory, information theory, and quantum physics, providing an operational mathematical definition for understanding the essence of "randomness".
Authors: Ma, Haobo, Zhang, Wenlin
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7091626299
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