The Newtonian Gravitational Constant as an Atomic Readout: A Parameter-Free MAT Prediction from Rydberg Spectroscopy and Finite-Support Dirac Boundary Stress

Direct laboratory determinations of the Newtonian gravitational constant G remain mutually inconsistent at the ppm to 10^2 ppm level. Since the revised SI fixes c and h exactly, the mechanical Planck scales inherit this scatter almost entirely from G. This work develops the opposite route within Mittermeier Attractor Theory (MAT): the Planck length is reconstructed from atomic spectroscopy and a single dimensionless finite-support structure before any macroscopic gravitational measurement enters. In this construction, G becomes an output rather than an input. No measured G, Hubble calibration, or pre-existing Planck mass appears in the forward chain. The only non-exact external anchor is the Rydberg wavenumber, known at the part-in-10^12 level. The construction descends from one algebraic seed, the real root of rho^3 = rho + 1. This seed fixes a small transmitted residue, which in turn sets the electron-to-Planck mass ratio through a closed three-term electron aperture, eta_e = pi/4 - alpha_M/e - 27 alpha_M^3. The three terms have fixed interpretations: a geometric quarter bridge, a one-boundary Euler leak, and the symmetric cubic scar (3 alpha_M)^3 of a locked three-channel architecture. Projecting this structure through the exact Rydberg identity yields a single closed value, G^MAT = 6.6742409426 x 10^-11 m^3 kg^-1 s^-2. This value is fitted to no gravitational experiment and lies inside the cluster of the two most precise quasi-static determinations. The aperture is independently auditable: with the MAT spine held fixed, existing G data invert to recover the coefficients pi/4 and 1/e and the cubic integer n_3 = 27.04 +/- 0.22. This excludes the neighbouring integers at more than 4.4 sigma and bounds any quadratic admixture to zero at the relevant resolution. At the microscopic level, the aperture is the normalized trace of a minimal finite-support Dirac-boundary stress operator. The cubic coefficient is therefore not treated as a free number, but as a boundary-algebra invariant. The remaining obligation is the embedding of that finite boundary algebra into a unique continuum ultraviolet completion. The prediction is directly falsifiable: future well-controlled quasi-static source-source measurements below a few ppm should converge to the stated value. The same residue simultaneously fixes the readouts of the fine-structure constant, the electron mass, the Planck- and DESI-facing matter fractions, and the vacuum-energy scale — quantities that the Standard Model and Lambda-CDM ordinarily treat as independent empirical inputs.