Innovation Necessity from Density-Based Collapse in a Discrete Resolution Framework

We formalize a discrete resolution view of control, learning, and innovation in which each observation or decision is a binary resolution act: coherent (C) if it confirms the current model and requires no forced re-resolution, or decoherence (D) if it forces re-resolution (rework, redesign, exception handling, escalation, workaround). Leaving the control of time-domain statistical processes, we define collapse as exceeding an allowable decoherence density threshold in resolution depth. We prove that driving density based collapse risk to zero requires the expected cumulative decoherence mass to grow slower than the allowable budget, which in turn necessitates persistent constraint creation. In this framework, innovation is not an organizational preference but a mathematical requirement for asymptotic coherence.