Analytical Derivation of the t2 Detection Scaling in Li's Criterion via Functional Equation Pairing

We derive analytically the O(t2) scaling law governing the detection of hypothetical off-critical-line zeros of the Riemann zeta function via Li's criterion. The derivation proceeds from the functional equation, which pairs each zero at rho = sigma + it with a conjugate at rho' = (1 - sigma) + it. Through the Mobius transformation w = (rho - 1)/rho, we show that |w| . |w'| = 1 exactly, so for sigma > 1/2, |w| < 1 and |w'| > 1. The zero at sigma is invisible to Li's criterion (convergent contribution), while its partner at 1 - sigma produces exponentially divergent terms. Expanding log|w'| for large t yields log|w'| = Delta/t2 + O(1/t4), where Delta = sigma - 1/2. The detection threshold follows: n_crit = ln(N) . t2 / Delta, where N is the number of verified on-line zeros. This defines a Detection Invariant I = n_crit . Delta / t2 = ln(N), verified at 100-digit precision to be constant across 17 orders of magnitude in t (from t = 103 to t = 1020). For N = 1013, I = 29.93. This paper supersedes v1, which incorrectly claimed a proof of the Riemann Hypothesis. We make no such claim here.