Dimension-free barriers for matrix interpretations of the Collatz rewriting system, and the maximal one-class weakenings of the modulo-8 conjectures of Yolcu, Aaronson and Heule provable by finite abstractions

Preprint, Part II of two companion papers; it relies on Part I (DOI 10.5281/zenodo.23081447). Yolcu, Aaronson and Heule encoded the Collatz map as an 11-rule string rewriting system and searched for termination proofs by matrix interpretations; four conjectures on the classes 1, 5 and 7 modulo 8 remain open. We prove that if a non-negative affine matrix interpretation of any dimension weakly orients all 11 rules (or those of the reversed system), then a primitive relevant block of maximal growth rate on the canonical binary strings has growth rate at most 0. Hence interpretations with such a block of positive growth cannot be used in the first stage of rule removal or in the relative top-termination argument of Yolcu, Aaronson and Heule, and upper triangular interpretations satisfy (M_f)_ii (M_t)_ii <= 1 at relevant indices. This rests on the value-level barrier of Part I. Analogues hold for a rewriting system for the partial map H of Conjecture 4.14 and, for a truncation of H, for ranking functions additive over local windows of binary digits. We also determine, for each conjecture, the maximal weakenings obtained by adding one residue class that staged valuation certificates prove, for instance 4089 and 10913 modulo 2^14 for Conjecture 4.14. The seven weakenings are checked in Lean 4; their maximality follows from a table of 22 witnesses. The Lean code and checking scripts are on GitHub. Prepared with substantial assistance from generative AI (Anthropic Claude); see the disclosure in the paper. Not yet reviewed by human experts.