Document F: Renormalization of Topological Knowledge in Contrast-Native Architectures

We define a renormalization operator T on abelian contrast systems within the C0 (Contrast Calculus) framework, where contrast is ontologically prior to objects and coordinates. The operator uses Čech cohomology on coverings of the underlying graph, avoiding the information-destroying aggregation that naive coarse-graining would produce. Main results: (1) Čech preservation theorem: The operator T preserves the first cohomology H¹(G; A) via the discrete Čech–de Rham isomorphism. Nonzero cycles in the original system map faithfully to nontrivial transition functions in the coarsened system. (2) Stabilization conjecture (F.1): Iterated renormalization stabilizes in at most ⌈diam(G)/L⌉ steps to a minimal Čech…