The Flat Transverse Parametrix and the Gaussian Heat-Kernel Asymptotic on the SCT Critical Sector

Paper 39 in the "Geometry of the Critical Line" programme. We prove that the flat transverse block of the SCT critical slice contributes a Gaussian twisted heat parametrix to all algebraic orders in the heat parameter t, with all Minakshisundaram–Pleijel curvature corrections vanishing identically. The only surviving deviations are exponentially small Poisson lattice corrections. We show that the exact Gaussian heat-kernel identity is false (the corrections are p-dependent and uncancellable), and replace it with a sharply formulated asymptotic conjecture. The paper establishes the sectorwise trace factorization, the longitudinal MP universality (u₀ = 1, independent of winding number), and reduces the remaining arithmetic gap to two inputs: the primitive-length normalization log(p) and the critical-line amplitude p^{-r/2}. This paper does not prove the Riemann Hypothesis.