Protocol Epistemology of Finiteness: A Cohomological Consistency Criterion for Rule-Matrix Systems (CohoRete, v10.0.0)

Version 10.0.0 introduces: (1) a q-analogue of the correspondence theorem via étale cohomology over F_q (Theorem 2.3bis); (2) a complete classification of Hesse–Munerman pencils over F_q for p ≤ 4 (Theorem 2.7bis), resolving Conjecture 2.21 in this range; (3) a bipersistent module for two thresholds (§2.12bis); (4) a dictionary "Jordan block of A_k monodromy ↔ persistence-bar length" (Theorem 4.5bis); (5) a bipersistent rank invariant for A_k × A_l (§4.6bis), giving a topological observation (not a proof) connected to dense-JOIN complexity at N ≥ 3. Corrections and additions carried from v9.0.0 include verified LFTJ benchmarks (median of 50 runs on AMD Ryzen 7 5825U, up to 210× on triangle queries at d = 50), an honest audit replacing the previously unverified 258× figure, and the introduction of 12 new open questions (§10). Limitations and the full list of what is and is not proven are stated explicitly in §10 rather than implied by framing. Supplementary files accompanying this preprint (uploaded separately via related identifiers): reproducibility report, changelog, source code for numerical verification, and a bibliography extension. 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.