Eleven Primitives and Three Gates: The Universal Structure of Computational Imaging

Computational imaging systems routinely underperform because the assumed forward model diverges from the true physics. Here we prove two results. First, the Finite Primitive Basis Theorem: every linear, shift-variant imaging forward model admits an epsilon-approximate representation as a typed directed acyclic graph over exactly 11 canonical primitives. Second, the Triad Decomposition: every reconstruction failure decomposes into three root causes (Gate 1: Recoverability, Gate 2: Carrier Budget, Gate 3: Operator Mismatch) with mismatch dominant across all validated modalities. Together these results yield a modality-agnostic diagnostic and correction framework. We validate across 168 modalities spanning 5 carrier families (photons, X-ray, electron, acoustic, particle) and 19 categories of computational imaging. Autonomous operator correction recovers +0.8 to +10.7 dB of mismatch-induced degradation without retraining the solver. Phase 2 multi-phantom results demonstrate consistent performance across diverse imaging systems. Hardware validation on real instruments confirms mismatch dominance and validates the Physics Fidelity Ladder framework.