This paper demonstrates that the three-generation structure of the Standard Model fermion spectrum follows from three-dimensional geometry within Informational Field Theory (IFT). In IFT's pre-metric configuration space, stability conditions select a three-dimensional effective manifold on which topologically nontrivial field configurations reside. Shape tensors constructed from log-gradients of the informational density field and the coherence functional are symmetric traceless 3x3 matrices with exactly three eigenvalues. These eigenvalues correspond to variational excitation energies within topologically classified sectors, providing a structural explanation for exactly three fermion generations without numerical mass fitting. The mass operator is constructed from shape tensor polynomials with explicit dimensional analysis. Fermion mixing arises geometrically from eigenbasis misalignment between the two independent shape tensors, and CP violation requires nontrivial holonomy of the propagation 1-form around topological defects. A universal prolate shape-chirality parameter is found empirically consistent across all fermion sectors within 2% of the theoretical bound. The framework yields falsifiable predictions: a shape-chirality bound distinguishing it from generic flavor models, anticorrelation between mass hierarchy strength and mixing angles, CP-topology correlation, and the absence of a fourth generation below the perturbative unitarity bound. The dimensionality constraint (three spatial dimensions) is supported by the Derrick theorem and hyperbolicity conditions but is not fully derived from Layer-0 axioms alone; this limitation is explicitly acknowledged. Part of the Informational Field Theory program. All primitives trace to the IFT spine document. High Energy Physics – Theory, Mathematical Physics, Quantum Field Theory, Particle Physics Phenomenology, Foundations of Physics
Ilja Schots (Sun,) studied this question.