The Perfect Factorisation of the Completed Zeta Function: Six Structural Dimensions Applied to xi(s) = 0

A substitution transforms the completed zeta function xi(s) into a function with real Taylor coefficients. From this, a perfect factorisation of the imaginary part follows algebraically: V = 2 alpha beta P. The Hessian matrix at every zero is isotropic with the universal coupling constant kappa = 1, verified at 30 zeros by independent finite difference computation. A flow proof shows: V is continuous along every U=0 curve, starts at nonzero, maintains its sign throughout, and grows monotonically in the ratio V/alpha. This has been verified at 10 zeros (gamma 1 through gamma 50), with 0 sign changes in 100 measurement points. Three natural laws are presented. We invite falsification.