ATPEW – From the Pioneer Anomaly to a Universal Structural Constant: The 4.854 Coupling Across Scales

This paper presents a key predictive milestone of the ATPEW (Aldon Theory of a Primordial Energy Wave) framework: the identification and cross-scale validation of a universal structural coupling constant, K = 4.854. Initially derived from the Pioneer anomaly (a residual acceleration of ~8.74 × 10⁻¹⁰ m/s²), this constant is interpreted within ATPEW as the coupling ratio between the primordial energy wave and local phase propagation. The transition from earlier adjustable models (V8) to the fully predictive V9 formulation is described. In this version, the Pioneer-derived constant is imposed universally, transforming ATPEW from an optimization-based model into a falsifiable physical theory. Applied to the SPARC galaxy rotation curve catalogue (175 galaxies), the fixed constant preserves and improves predictive accuracy, reducing global RMS deviations relative to MOND while stabilizing dynamics in massive systems. The same constant naturally predicts a decline in rotational velocity in the outer Milky Way, in agreement with Gaia DR3 observations, contrasting with the asymptotic flat profiles expected from MOND. These results suggest that the 4.854 ratio represents a scale-invariant structural parameter linking local gravitational anomalies and galactic dynamics within a unified flux-based description of space-time. The work establishes a clear falsifiability pathway for ATPEW and positions the constant as a potential bridge between solar-system-scale measurements and large-scale astrophysical structure.Note added March 2026: The 4.854 coupling constant identified in this work may reflect a numerical coincidence rather than a fundamental structural constant. A rigorous derivation from the PEW Lagrangian parameters is required before this result can be considered established. The document is maintained for transparency of the research process.