Exact crystal Frobenius model conjecture

Let the BrainiaK crystal space denote the semantic state space equipped with maps induced by semantic composition and tree decomposition. A finite-dimensional quotient or completion of this space is sought, together with exact induced maps, so that the resulting structure is a Frobenius algebra over $\mathbb{R}$. Exact crystal Frobenius model conjecture. There exists a finite-dimensional quotient or completion of the BrainiaK crystal space, together with exact maps induced by semantic composition and tree decomposition, that forms a Frobenius algebra. The current implementation provides only a decomposition-like operation and a numerical round-trip diagnostic, which do not establish the Frobenius identities; the conjecture therefore requires fixing the exact vector space and maps and proving the algebra, coalgebra, and compatibility axioms.