The Cohesion UFT Rotation-Curve Law, Global Suppression, and the Radial Acceleration Relation

The Canon Continuance operator predicts a torsion-based surplus acceleration whose
amplitude is regulated by both local baryonic structure and a global surface-brightness
suppression factor. In this work, the global suppression constant β is derived analytically
from the coherence-collapse condition, yielding β ≈ 0.235 kpc/(km/s)2
, in agreement
with empirical fits to SPARC rotation curves. Using this result, the full Canon
rotation-curve law is written in closed form, including the weak-field limit, the highacceleration suppressed limit, and the transition function between them. The Canon
radial acceleration relation (RAR) is then derived, and its slope, curvature, and scatter
properties are analyzed. The Canon RAR is shown to be exactly linear in log-log space
with slope unity and negligible curvature, in contrast to MOND’s curved RAR. The
predicted intrinsic scatter (∼ 0.05–0.10 dex) matches the observed SPARC RAR. This
work provides the first complete analytic formulation of the Canon rotation-curve law
and its observational consequences.