The Assembled Weil Kernel: From Carrier Geometry to the Explicit Formula

Paper 47 in the "Geometry of the Critical Line" programme. TITANIUM (T6). This paper assembles all five factors of the Weil prime-side kernel from the spectral geometry of the SCT 5-manifold into a single self-contained theorem. The Gaussian profile comes from the flat torus parametrix (Paper 39). The t^{−1/2} exponent comes from the distributional quotient trace evaluated at the geometric carrier pole s = 1 (RN44). The orbit length log p comes from the centraliser volume of the prime translations (RN20). The arithmetic weight p^{−r/2} comes from the KMS state at β = 1/2 descending through the quotient dictionary (RN21, RN43). The normalisation (4πt)^{−1/2} comes from the torus volume division 2π² (RN45). The seven-step proof chains these standing results. The prime-side component of the Transverse Trace Conjecture of Paper 8 is structurally resolved; the remaining work is functional-analytic packaging of the residue prescription and the identity-side completion. The paper does not prove the Riemann Hypothesis.