Geometric Resolution of Diophantine Invariants in Equal-Scale Lattice Spaces and the Verification Asymmetry Proving P = NP via Lean 4

This paper provides a unified geometric foundation that resolves three monumental challenges in number theory—the ABCConjecture, Fermat’s Last Theorem, and the structural correction of Srinivasa Ramanujan’s infinite scaling paradigm—byanchoring arithmetic operations within a rigid “Equal-Scale Lattice Space” with fixed physical dimensions. Furthermore,the resulting algebraic identities are fully formalized and certified using the Lean 4 theorem prover. Based on theabsolute computational cost asymmetry between the discovery of these new geometric invariants by human intelligence andtheir instantaneous mechanical validation by an automated prover, we provide a definitive real-world demonstrationestablishing that P ̸= NP is true.