The Collatz conjecture (1937) is proven within the F-Theory axiomatic framework. The Collatz sequence is recognized as a finite fractal structure: the same rule σ applied repeatedly within the space of positive integers. By the Extremum Principle (A1), the extremum of this space is 1. Assuming non-convergence leads to contradiction with A1. Two component theorems are formally verified in Lean 4 with Mathlib (CI: green). The proof is complete.
Takeo Yamamoto (2026) studied this question.