Protocol Epistemology of Finiteness: A Cohomological Consistency Criterion for Rule-Matrix Systems (CohoRete, v11.0.0)

Version 11.0.0 closes three previously open questions from v10.0.0 (§10, appendix on the three walls), collectively referred to as "Line I": (1) a full proof, with explicit computation on the minimal 6-vertex triangulation of ℝP², that the connecting map δ¹ of non-abelian Čech cohomology coincides with the Bockstein homomorphism for 1→ℤ₂→ℤ₄→ℤ₂→1, together with a direct algorithm for δ¹ on arbitrary finite 2-complexes (the Lyndon–Hochschild–Serre spectral sequence was found inapplicable to this problem) and a generalization to arbitrary central extensions verified on the non-split extension Dic₃→S₃; (2) a proved obstruction: the almost complex structure J=M⁻¹Ω underlying the T₂-class construction of Milijević (2024) exists only for n=2 and does not generalize to any n≥3, via two independent arguments (degeneracy of odd-order antisymmetric matrices; Cartan's classification of Hermitian symmetric spaces); (3) a table of moduli dimensions for p-ary forms of degree p under GL(p), identified with classical objects — the j-line (p=3), the 19-dimensional K3 moduli (p=4), the 101-dimensional quintic Calabi–Yau moduli (p=5) — the exact discriminant degree (deg Δ=108) for quaternary quartics, and the explicit degenerate fibres (t⁴=256) of the Fermat pencil. A related question on lower-bounding CP-rank via H₁ of a tensor's support is answered negatively: the governing combinatorial invariant is the matching number (N-dimensional matching at order N≥3, an NP-complete problem), not H₁. The interpretation of the p-ary form equivalence group is fixed to the symmetric version (a single GL(p), consistent with §2.9 of v10.0.0); the general (non-symmetric, independent GL(F)^p) version's TI-hardness is unaffected and remains unresolved. One new open question is introduced (§10(Д)): a constructive alternative for the T₂-class obstruction at dim>4 via Hermitian covariance families on the Siegel series Sp(n,ℝ)/U(n), Hermitian symmetric for every n — proposed but not developed in this version. 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.