Rigorous Rearrangement Tensor Renormalization in Four Dimensions

Version 2.0 is a substantial presentation and proof-clarification revision. The main theorem and intended scope remain the same. The manuscript has been rewritten to make the argument easier to audit, with an explicit Type-0 gauge calculation, a more detailed construction of the four-dimensional tagged-cluster cancellation, an explicit treatment of the one-vertex conflict case, clarification that the finite combinatorial recursion acts on whole Hilbert–Schmidt tensor terms rather than an infinite component expansion, and a more explicit normalization and iteration argument. The supplementary material has been revised to match these clarifications. The reproducibility scripts and their reported finite audit results are unchanged; package metadata and checksums are updated for v2.0.