Self-Dual SU(3) Geometry and Planck-Scale Boundary Conditions for Near-Critical Standard Model Dynamics

This work investigates a geometric boundary-condition framework for the Standard Model based on a unique self-dual internal structure satisfying \Lambda^2(\mathbb{C}^3) \cong \mathbb{C}^3, which uniquely selects an SU(3) internal geometry. Canonical embedding of SU(2)_L \times U(1)_Y into SU(3) fixes the hypercharge normalization and predicts \sin^2\theta_W = 1/4 at a high symmetry scale \Lambda \sim 10^{18}\,\mathrm{GeV} without invoking grand unification. Assuming classical scale invariance at the fundamental scale forbids a tree-level Higgs quartic coupling. The quartic is generated radiatively as \lambda(\Lambda) \sim \frac{g^4}{16\pi^2}. Comparison with precision three-loop Standard Model renormalization-group analyses shows that the geometric boundary value lies within the experimentally determined Planck-scale band \lambda(\Lambda) \approx 0 \pm 0.01. The framework therefore reproduces the observed near-critical Higgs behaviour and metastable vacuum structure without introducing additional heavy multiplets or gauge unification. Anomaly cancellation is inherited from the parent SU(3) structure, and hypercharge quantization follows from canonical generator normalization. The proposal is formulated as a high-scale boundary-condition model rather than a unification theory. It makes falsifiable predictions regarding weak mixing angle normalization, absence of gauge coupling unification, and near-critical Higgs dynamics.