Correlation Decay, Determinant Limits, and Zero Escape in a Nonlinear Spherical Response Model

We study a nonlinear response model on the probability sphere obtained by iterating F(s) = s + s² on squared spatial projections, then centering and normalizing the resulting fields in L². For each fixed dimension d ≥ 2 and amplitude τ > 0, we prove geometric decay of correlations between iterate levels, uniformly over arbitrary choices of spatial axes. Equal averaging with fixed total strength A yields positive finite-rank operators whose trace remains A while their operator norms and squared Hilbert–Schmidt norms are O(1/N). Consequently, det(I + w²C_N) converges locally uniformly to exp(Aw²), with error O(1/N) on compact sets, and all zeros escape at least at order √N. Nonnegative averaging weights with vanishing maximal weight give the same limit. A fourth-order coefficient comparison excludes this specified model as an infinite realization of the Jensen approximants to normalized Riemann ξ. The obstruction is compatible with a rigorously certified common six-stage history in six dimensions. The accompanying materials include reproducible interval certificates and a partial Lean 4 formalization. The formalization covers scalar iteration, conditional correlation and Gram estimates, spectral identities, matrix determinant limits, and conditional Jensen approximation bounds. It does not provide an end-to-end formal verification of the spherical model, the ξ coefficient enclosures, or the six-stage existence certificate. Detailed coverage limitations and build and axiom-audit records are included. The obstruction applies only to the specified model and does not prove or disprove the Riemann hypothesis. The paper distinguishes analytic proofs, finite computer-assisted certificates, and partial formalization; it makes no priority claim.