Formal Verification of the Frequency Torus Model: Constructive Proof of Quantum Eversion in Lean 4

The paper presents a rigorous mathematical specification and a complete formal proof of quantum eversion within the frequency torus model, implemented in the computer logic language Lean 4. Unlike the classical quantum mechanics approach, where fermion spin is postulated through continuous spinor representations, the proposed frequency mathematics derives discrete quantum properties (4π periodicity) naturally from the geometry of the resonant medium and the requirement of twist continuity. The code has been fully verified by the Lean 4 compiler without any logical placeholders (sorry), confirming the internal consistency and rigor of the developed mathematical framework.