Isocurvature spectral index from holographic tensor networks on cubic honeycombs

This paper derives a parameter-free prediction for the isocurvature spectral index from a holographic tensor network model of quantum gravity. The 4, 3, r family of regular cubic honeycombs tiles three-dimensional space with cubes for positive, zero, and negative cosmological constant. The disorder-averaged boundary theory is SYK₆ with conformal dimension Δ = 1/6, fixed by the six faces of the cube. Under two stated physical hypotheses — that the standard holographic mass-dimension relation applies with d = 3 and that the Bunch-Davies spectral formula applies to the emergent de Sitter geometry — the bulk scalar mass m²R² = −17/36 determines the isocurvature spectral index nᵢso = (12 − 7√2) /3 ≈ 0. 700. This exact algebraic number, together with the Starobinsky predictions nₛ ≈ 0. 965 and rT ≈ 0. 004, will be tested by the CMB-S4 and LiteBIRD experiments. The hypotheses are physically motivated but not derived within the model; the remaining links in the derivation chain are theorems or standard results.