All Research

Abstract

We certify a complex Mellin invariant of a fixed connected step junction on a ray with negative real part. Positive-axis exponential flatness is propagated through an exterior sector using a classical Phragmén–Lindelöf multiplier, with explicit constants. A left-sector contour then suppresses the reciprocal-Gamma conditioning of the Mellin formula. The application proves that the original fifth logarithmic harmonic of inverse twist speed, invisible to the leading Weyl profile, is detected by the lower heat profile of the same fixed Euclidean tube. The noncommuting DD/DN aperture inverse is enclosed by arbitrary trial columns, complete residuals and infinite input tails. Sixty-seven complex nodes, a tiny endpoint calculation, every infinite quadrature tail and the stated floating arithmetic errors are included. The certified junction Mellin modulus is below 3.198 × 10^(-9), while cancellation requires modulus above 1.18 × 10^(-8); the fifth heat multiplier has modulus greater than 2.16 × 10^(-7). The general propagation mechanism is classical; the contribution is its explicit connected-junction certification and this original-mode separation. A standalone replay suite accompanies the proof.