Protocol Epistemology of Finiteness: A Cohomological Consistency Criterion for Rule-Matrix Systems (CohoRete, v8.0.0)

This preprint develops a cohomological consistency criterion for rule-matrix systems: an algebraic isomorphism of a rule-matrix model to its canonical acyclic form exists if and only if the first non-abelian Čech cohomology group Ȟ¹(X,G) is trivial (Correspondence Theorem, both directions, explicit global-section construction). Version 8.0.0 adds a C++ implementation of Leapfrog Triejoin with correctness tests and benchmarks (up to 258× speedup on triangle queries; an order-sensitivity bug found and fixed during benchmarking is documented in the text), and formalizes negation in production rules via balance of signed graphs (Ȟ¹ with ℤ₂ coefficients) with an explicit non-abelian extension for finite groups. The framework draws on Sokolov's polyadic matrix algebra, Munerman's algebraic data-processing models, and Amari's information geometry; where results are proved only for restricted cases (the normal family, finite groups) rather than in general, this is stated explicitly in Section "Limitations" rather than implied by the framing — e.g. β₄ > 0 is proved for the normal family only; the antisymmetric drift term is a geometrically motivated derivation with one open step, not a closed proof; dense JOIN at N≥3 remains an open algorithmic problem. This is a student preprint (Applied Mathematics and Computer Science, Smolensk State University), intended for eventual development into a Bachelor's thesis. Shared under CC BY-NC-ND 4.0; any commercial use requires a separate written license agreement with the author.