Adelic Quotient Reduction and the Missing t^{−1/2} Factor on the Weil Prime Side

Research Note 22 in the "Geometry of the Critical Line" programme. RN20 and RN21 supplied the primitive-orbit factor log p and the thermal KMS amplitude p^{−r/2}. The remaining discrepancy between the raw SCT geometric trace and the Weil explicit formula is the power of t: the arithmetic prime side requires t^{−1/2}, whereas the 2-dimensional transverse carrier yields t^{−1}. This note assembles the final formal ingredient of the Weil prime-side triad. The adelic quotient by Q* (Kill #67, Paper 40) integrates out the 1-dimensional global scaling action of R*_+, converting the 2D prefactor (π/t) into the 1D prefactor 1/√(4πt). The quotient trace prescription is modeled by integrating the heat kernel over the…