Numerical verification of the IKKT one-loop structure on fuzzy P3 at j = 6

We perform an independent numerical computation of the IKKT matrix modelHessian on the doubled fuzzy sphere at spin j = 6, projected onto the binaryicosahedral invariant sector. All Tier A claims of [1] are verified to machine precision:the Burnside-projected antisymmetric Hessian has eigenvalues exactly (2/3) k(k+2)at the invariant Laplacian degrees k = 12, 20, 24, each with spatial multiplicity 3. Themultiplicative invisibility of the factor 2/3 is confirmed numerically. The obstructiondocumented in [1, Section 4.7] is quantified: the spectral gaps for the A5 irreduciblerepresentations are not proportional, confirming that the spectral correction cannotbe a single universal additive shift.