The Mittermeier kappa-alpha-pi Bridge: A Planck-Boundary Constant from the Mittermeier RG Attractor and Its Gravity-Electromagnetism Resonance

A persistent obstacle for "world-formula" programs is that key dimensionless couplings—most notably the fine-structure constant alpha—are measured but not derived. This paper isolates one number that IS derived in closed form from the SSOT-hard nucleus of the Mittermeier RG Attractor: kappaM: = lambda (0) = e^- (2 + ln (rho) ) = e^-2 / rho, where rho is the plastic constant (rho³ = rho + 1). Numerically, kappaM = 0. 102162. Equivalently, the rescaled constant x: = e² * kappaM = 1/rho is the unique positive root of x³ + x² - 1 = 0, making the plastic-constant lock explicit. The defining point is structural: kappaM is locked at the UV boundary u = 0 with no fit freedom, as a consequence of a closed parameter lock in the attractor's two-threshold normal form. We then show that this purely attractor-derived constant sits in a tight web of near-resonances with electromagnetism and geometry: kappaM approx 14 * alpha, kappaM approx 1 / (pi² - 11 * alpha), 14 * alpha * (pi² - 11 * alpha) approx 1, where the first relation holds at the level of -13. 245 ppm when alpha is taken at the CODATA-2022 recommended value. We interpret this as evidence for a Mittermeier kappa-alpha-pi Bridge Relation: a simple, integer-structured coupling law linking the fine-structure constant to (pi, rho, e) via kappaM, with controlled residual corrections. The present work is intentionally "step one": it does not attempt a full quantum-gravity construction. Instead, it isolates a concrete, falsifiable bridge between a gravity-side boundary constant and precision metrology, with enough structure to support sharp follow-up tests (scheme robustness on the attractor side; scale matching and running on the QED side).