Direct laboratory determinations of the Newtonian gravitational constant G remain mutually inconsistent at the ppm to 10² 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-10¹2 level. The construction descends from one algebraic seed, the real root of rho³ = 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, etaₑ = pi/4 - alphaM/e - 27 alphaM³. The three terms have fixed interpretations: a geometric quarter bridge, a one-boundary Euler leak, and the symmetric cubic scar (3 alphaM) ³ of a locked three-channel architecture. Projecting this structure through the exact Rydberg identity yields a single closed value, GMAT = 6. 6742409426 x 10^-11 m³ 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 n₃ = 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.
Rainer Andreas Mittermeier (Fri,) studied this question.