The Infinium and the Formula of π, e, φ: A Chain of Forcing in Logic Theory and the Sublation of Fundamental Contradictions (version 7)

This paper introduces the concept of the infinium ℑ = △₁,₁ — a right isosceles triangle with legs 1 and hypotenuse √2 — as the terminal object of the cognitive topos ℰ. It is shown that an exponential identity necessarily emerges from its geometry and motivic structure, linking three fundamental mathematical constants π, e, and φ through the Lie algebra 𝔰𝔲(3). A logical principle is formulated: the infinium forces (⊩) the existence of a representation of SU(3) such that exp(πX)·exp(eY)·exp(φZ) = e^{2πi/3}·I₃. The contradictions of classical mathematics that are sublated by this approach are analyzed: between the discrete and the continuous, between the algebraic and the geometric, between chance and necessity. Twelve useful conclusions are presented, demonstrating the heuristic power of △-ontology.