Central-Charge Rigidity of Stress Noise at Chronology Horizons

The renormalized mean stress tensor may be finite at a chronology horizon even when the underlying two-point function is singular. We examine whether its connected second cumulant shares this cancellation. For a discrete spacetime quotient with an isolated, nonconjugate self-image null relation, nonvanishing null conormal projections, and a quasifree Hadamard state, the leading symmetrized stress covariance of a free real scalar in every dimension \(D>2\) has the form \( Nₖₖ~{D(D-2)}8 C_D^2|U_γ|^2F_D(ξ){a^2b^2}{|σ_γ|D+2}\), where \(F_D(ξ)=16(D^2-1)(ξ-(D-2)/[4(D-1)])^2+2(D-2)/(D-1)>0\). Thus no real curvature coupling removes the principal singularity. Independent scalar species contribute additively. Orthogonal or unitary internal holonomy enters the isolated noise through a positive Hilbert--Schmidt norm rather than a possibly vanishing character. For unitary conformal field theories obeying the corresponding quotient-image hypothesis, the coefficient is controlled by the positive stress central charge \(C_T\). An explicit Misner-quotient calculation gives a second inverse-square horizon enhancement. We distinguish these point-separated field-theoretic statements and a conditional linearized Einstein--Langevin response from the open problem of nonlinear chronology protection.