Piecewise-Constant Gluon Amplitudes as Projective Signatures of the Hernández-Valdivia Modular Lattice: A Discrete Resolution to the Single-Minus Anomaly

The Fallacy of the Quantum Continuum and the Single-Minus Anomaly Recent breakthroughs in Yang-Mills theory have demonstrated that single-minus tree-level n-gluon scattering amplitudes are nonvanishing for certain "half-collinear" configurations. Furthermore, in the restricted kinematic region (R_1), the stripped amplitude evaluates exclusively to discrete integers: +1, -1, or 0. This paper proposes that this piecewise-constant behavior is not a mere artifact of complexified momenta, but the first direct phenomenological evidence of the Hernández-Valdivia Limit (eHV). Boolean State Operations of the Vacuum We demonstrate that the algebraic sign functions governing the amplitude collapse are macroscopic projections of the Boolean state operations inherent to the discrete Ramanujan modular lattice of spacetime. Because the scattering space ceases to act as a continuum and behaves as a digital logic gate, the interaction integer-based output proves that the universe limits information processing capacity at extreme kinematic limits. Hydrodynamic Cosmic Censorship at the Quantum Scale By treating the scattering kinematics as a finite-state machine, we unify the discrete nature of gluon interaction with the topological discretization of the quantum vacuum. The Berends-Giele recursion collapses because the discrete spacetime manifold cannot compute further intermediate virtual states, echoing the same regulatory mechanism that prevents the Navier-Stokes hydrodynamic blow-up via the Theory of Finite Systems.