Locality of Euclid's Theorem

What if Euclid's theorem is logically flawless, yet ontologically local? This paper argues that the classical proof of the infinitude of prime numbers, while formally correct, does not compel belief in an actually infinite set. Within the Mathematics of a Finite Universe (MFU) — where a finite informational horizon Ω_ont bounds all physical realizability — Euclid's construction remains a perfect procedural generator, but its interpretation as a description of absolute reality is an act of faith, not a logical necessity. The work introduces a sharp distinction between procedural unboundedness and actual infinity, and shows that Euclid's own procedure loses operational realizability at the surprisingly low boundary of p = 509 (for Ω_ont = 10^250). A compact contribution to the philosophy of mathematics, physical ontology, and the limits of mathematical realism. Follow my work and related discussions on Facebook: [Facebook]