Rigorous Proof of the Necessity of Abandoning the Point as a Primitive of Mathematics (Double-Entry Verification and Step‑by‑Step Balance Analysis)

This work presents a rigorous meta‑mathematical proof that the point cannot serve as a consistent primitive of mathematics. Based on five independent levels of analysis (physical, mathematical, geometric, computational, and philosophical), six fundamental defects of point‑based ontology are identified: unobservability, indistinguishability, zero measure, non‑computability, redundancy of axiomatics, and the gap between the discrete and the continuous. As an alternative, the right isosceles triangle (RIT) with leg 1 and hypotenuse √2 (the Infinitum) is proposed, which eliminates all of the above problems. The method of proof is double‑entry bookkeeping, where each statement about the shortcomings of the point is matched with a corresponding advantage of the RIT. The final balance is struck on all six positions. The proof is constructive and can be verified independently.