Two independent programs converge on the same structure. A random-matrix (RMT) account of neural networks finds that structure forms when symmetry sectors are forced to cooperate: an architecture with weakly-coupled sectors, a coupling, and a selector (a gate) exhibits the level-repulsion and effective-rank signatures of random-matrix universality. A sibling formal program, lenguage, proposes a specific algebra for meaning — the integer Clifford algebra Cl(4,0;Z) (16 blades, grades 0-4) — with a selector (the "k") and a Coq-verified coloured operad whose operations compose meaning. We show these are not an analogy but one artifact: instantiating the RMT model with lenguage's actual grades (as sectors), kernels (as coupling = the operad's operations), and gate (as the selector), the RMT signatures survive, the operad-verifier leg is satisfied by construction and re-checked at runtime against the machine-checked proof, and the full functor M on real language data already lives in the coupled (GOE) regime. The actual trained 7B model of lenguage (Qwen2.5-7B + LoRA + a discrete Cl(4,0;Z) head) carries the spectral-support signature in its weights, its live activations, and over training. A trained unified model works (matches a dense head) at no accuracy cost; the operad's value is verifiability and bit-exactness — and, on a genuinely non-commutative (compositional) task, the decisive inductive bias where a structure-blind model and a generic order-aware model both fail. The functor M is quantitatively homomorphic (graded bound 1-d = 98.0% for the algebra, 97.1% for the best functoriality-trained 7B checkpoint). A residual bound — the real signatures are atom-additive, losing argument order — is resolved (Section 7): a dual-channel TYPE|ORDER re-encoding with a data-driven codebook lets the trained 7B recover argument order (role-swap discrimination 10.8% to 34.4%, against a 75.2% encoding-level ceiling), and the signature head's stable rank tracks its emergence (corr = -0.81; n = 6 checkpoints, single run). Tier-2: a structural-algebraic instantiation, not a physical identity.
J. Arturo Ornelas Brand (Sat,) studied this question.