Protocol Epistemology of Finiteness: A Cohomological Consistency Criterion for Rule-Matrix Systems (CohoRete, v14.0.0)

Version 14.0.0 is an exploratory investigation, not a completed theory, of possible connections between the Correspondence Theorem's non-abelian Čech cohomology and braid groups / R-matrices (§ "Braid groups and R-matrices"). Rigorous definitions are given (the Artin presentation of B_n, the Yang–Baxter equation, the reduced Burau representation), together with explicit computations verified symbolically for B_2 and B_3. Two of three conjectures from the working plan are shown, on inspection, to be category errors rather than open theorems: the Čech cocycle condition (a triple-overlap condition valid for any structure group) and the Artin braid relation (a defining relation specific to B_n's own presentation) are objects of different logical kinds, so no equivalence can hold by construction; separately, the transfer matrix H_τ (a non-linear entrywise threshold function on a single matrix) cannot be a tropical limit of an R-matrix (a linear operator on V⊗V satisfying the Yang–Baxter equation) — a type mismatch between the two objects, not a missing computation. Both findings are documented explicitly in the text rather than concealed. A third, genuinely open conjecture — whether Yang–Baxter cohomology and H¹(X,G) coincide for graph nerves — is left as the section's only substantive open question. Starting with version 12.0.0, the preprint accumulates exploratory directions for future development (algebraic probability theory, infinitesimal deformation theory, braid groups) alongside the core results. Only the results through version 11.0.0 (the Correspondence Theorem and its extension to the Bockstein homomorphism) are intended for the author's Bachelor's thesis defense; later sections are shared for transparency and future reference rather than as defended thesis content. This is a student preprint (Applied Mathematics and Computer Science, Smolensk State University). Shared under CC BY-NC-ND 4.0; any commercial use requires a separate written license agreement with the author.