ICC XIV: Spectral Overlap and the Limits of Geometric Flavor Mixing

We investigate fermion flavor mixing within the framework of Information-Copying Cos mology (ICC), where particle properties emerge from the spectral structure of a stochastic copying operator. Building on the mass scaling mf ∝ √ xf derived in ICC XIII, we propose that mixing arises from the overlap of localized eigenstates in spectral space. We introduce a minimal complex overlap ansatz Mij = exp(−dij/ξ)ei(θi−θj), with dij = |ln(xi/xj)|. This construction naturally reproduces the qualitative distinction be tween hierarchical CKM mixing and large PMNS mixing using only three parameters per sector. We demonstrate, however, that any ansatz of the form Mij = f(dij) is structurally incapable of reproducing the full CKM hierarchy quantitatively after unitary projection. This constitutes a no-go constraint on purely geometric overlap models. The framework therefore identifies flavor mixing as a combination of spectral geometry and additional dynamical structure. The ratio ξℓ > ξq is robustly obtained, indicating weaker localization of leptonic eigenstates, consistent with the µ < 0 universality class established in ICC XIII. We outline minimal extensions required for quantitative accuracy, providing a concrete roadmap for future work.