The Boltzmann Cosmological Model: Emergent Spectrum (0,1,e,π²)

We propose a structural cosmological model arising from the Minimal Discrete Épure G■=(Z²,d■). The single fully derived ingredient is the volume of the cost-asymmetric Fourier-transposed Brillouin zone, vol(BZ■)=2π²=2E_γ; the remaining structure is a conjecture, fitted to data and marked as such throughout. The model rests on a four-level energy spectrum (0,1,e,π²) — of which only E_γ=π² is currently derived — a Boltzmann inverse temperature β=23/24 with a rigorous combinatorial interpretation, and an explicit tight-binding Hamiltonian. Under these inputs the model reproduces the four Planck 2018 fractions to better than 4%. Epistemic status: the Boltzmann model itself is a structural conjecture; the Brillouin volume formula and the combinatorial interpretation of β are theorems; the cosmological match is a numerical observation. The derivation of the levels (0,1,e) from first principles is the central open problem.