Minimal Framework for Finite Interaction Capacity

This work explores a minimal foundational framework in which physical structure emerges from a single irreducible assumption: a continuous field with finite interaction capacity. Without presupposing laws, forces, spacetime, particles, information, or observers, the framework examines the structural consequences of bounded interaction, including saturation, boundary formation, closure, minimal length scales, geometry, matter, sensitivity, and observation. The first part presents a conceptual dependency scale from finite capacity to the observer layer, emphasizing non-circular emergence and strict separation between physical structure and symbolic description. The second part provides an exploratory mathematical realization using a constrained scalar field with a hard interaction bound, demonstrating saturated boundaries, phase transitions, and the emergence of a minimal thickness without assuming quantization or discreteness. This work is pre-quantitative and intended as a foundational scaffold rather than a completed physical theory. Its aim is to clarify which structural features may follow necessarily from finite interaction capacity and to identify where standard theoretical approaches encounter limitations under hard constraints.