Eternal Expansion: Transcendence of π as Proof of the Inexhaustibility of Reality — Overview
The mechanism of Universe expansion is formalized within the toroidal ODTOE model. The Lindemann theorem (1882) on the transcendence of π proves that the trajec
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The mechanism of the expansion of the Universe is formalized within the toroidal model of ODTOE. Lindemann's theorem (1882) on the transcendence of π proves that a trajectory on the φ-torus does not close after any finite number of revolutions, from which the infinitude and inexhaustibility of the expansion follow. The pressure of potentiality F=(π−3)²·|H|/|C| acts at each cycle of observation. The scale factor a(n)=(1+(π−3)²/(2πφ))ⁿ describes the exponential growth of the effective radius of the φ-torus. The acceleration of the expansion (ä>0) follows from (π−3)⁴>0 without invoking Λ as a free parameter. The dark-energy fraction ΩΛ=68.86% agrees with the Planck 2018 data to within 0.54σ.