INFINITE WHOLE — FINITE FRACTION Infinity as extent, not as division: rewriting the fundamental equations of physics without singularities

Modern physics rests on an implicit postulate: space, time, and physical quantities are infinitely divisible. This postulate, although mathematically convenient, produces aberrations: singularities, divergences, infinities. We propose a fundamental distinction between infinity as extent (possible, as totality) and infinity as division (absurd, as fractioning). The TRUE framework (Théorie Redistributive Universelle Évolutive — Evolutionary Universal Redistributive Theory) introduces a minimal step  h_0  linked to the invariant  \gamma_0 = 0.13648 , below which fractioning no longer has physical meaning. We rewrite the four fundamental equations of physics — Einstein, Schrödinger, Newton-Leibniz — without infinite fractioning, replacing derivatives with finite differences and integrals with finite sums. All verified predictions are preserved; singularities are eliminated. We discuss the implications for quantum gravity, quantum mechanics, and the philosophy of mathematics.