The Pythagorean Theorem as a Fundamental Law of Mathematical Semantics (version 3)

The article argues that the Pythagorean theorem is not merely a geometric relation but a meta-code that sets the syntax and semantics of all mathematics. It is shown that the isosceles right triangle (legs 1 and 1, hypotenuse √2) is the minimal information cell that generates natural numbers, metric, topology, complex analysis, and group theory. A principle of minimal complexity is formulated, explaining why precisely this figure serves as the “quantum” of mathematical reality. The paper represents an updated version of the concept previously developed within Δ-ontology. In the final part, the discovered regularities receive a rigorous formalization in the language of logical theory: by means of forcing (⊩) and semantic consequence (⊧) it is demonstrated that the infinium ℑ = △₁ₓ₁ forces mathematics to be exactly the way we know it.