A Coherence Field Model of Galactic Halos: Logarithmic Potentials with Exponential Screening from a Memory-Coupled Scalar Field

We study a real scalar field with quartic self-interaction coupled to a causal power-law memory kernel arising from integration over an unresolved microstate bath. The resulting dynamics modify the effective potential and admit finite-energy soliton solutions with an explicit stability criterion.

By coupling the field conformally to matter, we derive an effective gravitational potential of the form Φ(r) = A ln(1 + r/r₀) e^(−r/L), which is regular at the origin, logarithmic at intermediate radii, and exponentially screened at large scales. This reproduces flat galactic rotation curves without infrared divergence and yields testable predictions for gravitational lensing.

The model provides three falsifiable predictions: (i) a universal scaling relation for asymptotic velocity, (ii) a constrained distribution of screening lengths across galaxies, and (iii) consistency between rotation curve and lensing fits using a shared parameter set.

The results are restricted to galactic halo phenomenology and do not attempt to address cosmology or particle physics.