Rigorous Rearrangement Tensor Renormalization in Four Dimensions

Version 3.0 is a proof-audit revision of the four-dimensional high-temperature tensor-renormalization manuscript. It makes the O/D primitive decomposition and Src/NSrc dichotomy explicit, strengthens the occurrence-decorated tagged-cluster cancellation bookkeeping, records the 17/16 overlap gain and the 32/31 RG exponent, clarifies normalization and finite-volume iteration conditions, and provides updated supplementary and reproducibility materials. The accompanying computations are adversarial finite consistency checks of combinatorial and geometric components. They are not premises of the theorem and do not constitute a computer-assisted proof of the complete analytic result. The scope remains a local high-temperature/infrared tensor-RG theorem; no continuum Yang–Mills construction or Yang–Mills mass-gap proof is claimed.