Treatise on Distinction and the Triangle: A Genetic Reconstruction of Mathematics From a single act of distinction — to numbers, geometry, analysis and topology through the geometric quantum △₁ₓ₁

This work proposes a genetic method for grounding mathematics: all key structures — from natural numbers to topology and algebra — are derived from a single pre-mathematical act of distinction and the principle of minimal complexity. It is shown that this path necessarily yields the right isosceles triangle △₁ₓ₁ (legs 1, hypotenuse √2), which then functions as a universal geometric quantum. From it, logic, number systems, Euclidean metric, Lebesgue measure, homotopical topology and non-abelian symmetries are generated. The thesis is advanced: mathematics is the unfolded economy of the distinction relation through △₁ₓ₁, compactly expressed by the formula Math = Eco(Dist) ⊗ △₁ₓ₁. Philosophical implications (the nature of mathematical necessity, connection to cognitive economy) and mathematical conclusions (structural unity of foundations, natural regularization via the spectral gap) are discussed.