This paper presents a corrected and extended version of PDL-D20 (version 1), which established a structural connection between Newton's gravitational constant G and the fine-structure constant α within the Projective Dynamic Logo (PDL) framework. Version 1 contained two numerical errors and a structurally unjustified bridge formula. The corrected values are εG = 0.0075194 (not 0.0073891) and Δrval = 0.047960 (not 0.049751). The original bridge formula is replaced by a structurally derived expression whose three factors encode the hierarchical amplification of the proton architecture, the golden-ratio surface projection, and the no-self-loop coherence constraint on the up-core. Inverting this formula yields the parameter-free prediction GPDL = 6.67448 × 10−11 m³ kg−1 s−2, in agreement with the CODATA 2022 recommended value to 27 ppm and consistent with all current experimental determinations of G. No free parameters are introduced. The prediction is falsifiable and will constitute a decisive test of the PDL architecture when next-generation measurements of G reach the 1 ppm level. Version 3 — March 2026. This version supersedes version 2. Two numerical errors have been corrected (εG and Δrval), and the bridge formula has been replaced by a structurally derived expression with no free parameters. Version 1 is archived for reference but should not be cited for numerical results. And golden ratio study.
Cédric Laubscher (Mon,) studied this question.