Progressive Verified Rendering: A Theoretical Framework for Stepwise, Verifiable Image Construction

We present Progressive Verified Rendering (PVR), a formal algorithmic framework and theoretical analysis for constructing high-precision images by composing a sequence of verifiable layer-wise drawing actions. PVR reframes image synthesis as a sequence decision problem in which a generator proposes atomic drawing actions, a renderer composes them into an image, and an independent verifier evaluates whether the intermediate image satisfies explicit structural constraints. By formalizing the action space, verification criteria, and error metrics, we prove termination guarantees under mild assumptions, derive error contraction bounds, and analyze computational complexity. We provide pseudocode for planner–generator–verifier control loops, strategies to avoid verifier–generator bias, and practical implementation notes (vector representations, parametric layers, symbolic verification for geometric constraints, and hybrid neural-symbolic verifiers). We conclude with evaluation protocols, metrics, and suggestions for experiments targeting complex planar geometry, multi-scale "nested" diagrams, and style-layered composition. PVR enables generation of images that would be difficult or impossible to achieve in a single end-to-end sampling step with guaranteed structural accuracy.