The weak interaction stands apart from other fundamental forces by its maximal violation of parity and its exclusive coupling to left-handed fermions. The Standard Model accommodates this through the SU (2) L gauge group and the Higgs mechanism, but it does not explain why weak interactions exhibit this chiral asymmetry. Energy-Efficiency Theory (EET) offers a graph-theoretic ontological foundation. We propose that the underlying constraint network for weak interactions is characterized by a fundamental topological asymmetry: the vertex set V of all fermions is partitioned into left-handed (VL) and right-handed (VR) subsets, and all weak gauge edges are strictly confined to the VL subgraph. The right-handed set VR is topologically isolated from weak edges. This single topological assumption naturally yields V-A chirality and maximal parity violation: parity maps VL VR, but the image of weak edges lies in VR where no such edges exist. The SU (2) gauge structure emerges from edge coloring of the VL subgraph, with Wilson loops enforcing gauge invariance, non-Abelian vertices arising from plaquette curvature, and anomaly cancellation corresponding to graph Kirchhoff's laws. The GIM mechanism (FCNC suppression) follows algebraically from CKM unitarity. Higgs condensation (1) isotropically stretches the weak edges, endowing W and Z with mass while preserving =1 via custodial symmetry. We present one Level VI falsifiable prediction: the effective neutron lifetime during Big Bang Nucleosynthesis is shortened by a factor ^-4 (> 1), leading to a measurable reduction in the primordial helium-4 abundance Yₚ, which may resolve the longstanding lithium problem. This paper establishes the rigorous graph-theoretic foundations for weak interactions within EET, completing the ontological basis for the electroweak sector.
Hongpu Yang (Fri,) studied this question.