The Mathematical-Physical Unity Principle: An Analytic Bridge Between L-Functions and Quantum Systems

Abstract This paper introduces the Zero-Point Existence Criterion (ZPEC), an analytic bridge based on the Mathematical-Physical Unity Principle (MPUP) that rigorously equates the stable existence of a physical entity to the spectrum of the zeros of its corresponding L function. Starting from quantum mechanical first principles, we provide a constructive proof that the total quantum perturbation of a system is strictly mapped to the analytic structure of L-functions. This mapping allows the Structural Rigidity Constraint Axiom (SRC) of physics to impose a direct ontological requirement on mathematical zero struc tures. We demonstrate this via a Physical Rigidity Proof of the Riemann Hypothesis (RH): any zero deviating from the critical line Re(s) = 1/2 would necessitate the corre sponding physical system to violate quantum mechanical unitarity, thereby excluding its existence. Furthermore, we establish the bi-directional nature of this bridge: by assuming the mathematical validity of the Generalized Riemann Hypothesis (GRH), we inversely derive quantum unitarity as an algebraic necessity, revealing that the fundamental conser vation laws of physics are formal projections of the critical symmetry of L-function zero distributions. Algebraic Locking of a Non-Trivial Prediction: As a definitive experimental test, we construct the L-function Ln(s) describing the geometric residuals of the neutron capture interface. We derive an algebraic locking relationship between the anomalous periodicity Pexp and the first zero γ1 of Ln(s), mediated by a Universal Characteristic Constant κn. This constant is locked to a pure algebraic value A, independent of specific nuclides, marking a first-principles arithmetic derivation of a physical constant: κn ≡ γ1 · Pexp ln(2) = A