A Technical Note on Causal Capacity κ and Horizon Structure

This paper presents a focused technical development of the causal capacity κ introduced within a causality-first approach to gravity. An operational definition of κ with physical dimensions is provided, together with a local balance law and a causal (non-geometric) criterion for horizon formation. A simple toy model is analyzed explicitly, demonstrating that bounded κ-dynamics admit smooth, non-singular solutions under sustained stress, with causal horizons emerging naturally at the κ-saturation surface without reference to spacetime geometry. This work serves as a technical companion to “BEEMOLOGY – Causality as the Foundation of Gravity and Spacetime” (Zenodo DOI: [10.5281/zenodo.18204204]), which introduces the broader conceptual framework.