Complexity Binding Theory: A Complete Framework for Galaxy Dynamics Without Dark Matter Particles

Complexity Binding Theory (CBT) is an exploratory proposal in which the dynamics usually attributed to dark matter are modeled by a scalar "binding" field with a logarithmic self-interaction potential, rather than by unseen particles. This paper gives the galaxy-rotation formulation and its fit to rotation-curve data. Author's note (revised 2026): The original version called CBT a "zero-parameter" framework with all constants "derived from e and π, no curve-fitting." I no longer stand behind that. On re-analysis, the central constants (β ≈ 2e, the scale a₀ = cH₀/2e, and the interpolation constant C) were selected to match already-known target values rather than derived, and a preregistered blind test on held-out SPARC galaxies does not show CBT outperforming standard MOND — Bayesian evidence favors MOND, and I retired both model versions under my own preregistered stopping rule. CBT should be read as a MOND-class phenomenological model with an information-theoretic motivation, not a validated parameter-free replacement for dark matter.