[27]Connectivity Geometry: A Falsifiable 1.391 Prediction for Lattice QCD in a k=3 Network

Traditional discrete physical models typically assume that the underlying spacetime is a smooth nearest-neighbor connected grid (step size k=1). Based on the framework of connectivity geometry, this paper investigates a non-local jumping spin network (step size k=3), and proposes two logically independent propositions. Proposition A (Mathematical Conclusion): The iterative commutator closure of the initial operators in this k=3 network generates an 8-dimensional traceless Lie algebra su(3); after explicitly introducing a central generator, it is extended to a 9-dimensional u(3) = su(3) ⊕ u(1). Proposition B (Phenomenological Prediction): Under the frozen discrete mode counting convention N=16 and the phenomenological matching assumption g_SW=1/2, we predict the effective clover coefficient at the reference lattice spacing c_sw_eff(k=3)=1.391. Its statistical test window is ±0.029, and the parameter sensitivity band is [1.34, 1.46]. Due to differences among lattice QCD collaborations in beta, gauge action, fermion improvement schemes, and c_sw normalization conventions, existing numerical values are not directly comparable across different baselines; therefore, this paper does not cite a single measured value, and the quantitative verdict is deferred to future independent non-perturbative determinations strictly corresponding to a* ≈ 0.08 fm and beta* ≈ 6.0. It must be explicitly stated that even if Proposition B is falsified, Proposition A still stands independently.