Spectral Theory of the Five-Class Consonantal Subshift and a Composite [[7,1,3]]_22 Qudit Code

Paper II of the Trifurcation series (October 2026). First public version. It replaces unpublished drafts of 29–30 September 2026, which are withdrawn. Their class table summed to 20 letters, entropy was given in the wrong units, the Dixmier-trace constant was wrong, and the composite code was ill-defined and violated the quantum Singleton bound. The 22 letters of the Semitic alphabet fall into five articulatory classes of sizes 4, 4, 4, 5, 5 in the grouping of Sefer Yetzirah. Forbidding two consecutive letters from the same class defines a subshift of finite type on the complete multipartite graph K4,4,4,5,5. Its characteristic polynomial is λ17(λ+4)²(λ+5)(λ²−13λ−80). The Perron root is (13+√489)/2 ≈ 17.5567, with its eigen-relation checked in Lean 4. The topological entropy is 2.8654 nats = 4.1339 bits per symbol. The paper also gives the Parry measure, word counts, the symmetry group, and the spectral dimension 0.92701 and Dixmier trace 0.43709 of the exponential word-length operator on the Cuntz–Krieger algebra. On the coding side, a self-orthogonal MDS [7,3] code over F11 gives a quantum MDS [[7,1,4]]11 code. Through Z22 ≅ F2 × F11 it combines with the Steane code into a [[7,1,3]]22 qudit code, verified by exhaustive search. No binary CSS [[6,1,3]] code exists (exhaustive search), and no generalized Reed–Solomon [7,3] code over F11 with finite evaluation points is self-orthogonal. Files. 1_…_alien-codex.pdf: dark display edition. 2_…_journal.pdf: light journal edition, same content. …_source.zip: LaTeX source and style file. …_code.zip: subshift_spectrum.py, qudit_codes.py, their JSON outputs, and ConsonantalSubshift.lean, checked inside the 05_lean_formalization project of the public Res-Nova repository (commit c3ff5f3). Epistemic labels used in the text: [P] proved in Lean 4; [D] derived, including computation; [C] cited result; [E] empirical; [conj] conjecture; [O] open; [X] withdrawn or excluded. AI systems assisted with derivations, code, numerical runs and drafting under the author's direction. The author reviewed every claim against the files in this deposit and takes full responsibility for the content.