The Neutron Lifetime Discrepancy and Topological Selection Rules

The neutron lifetime discrepancy — a persistent ~ 4σ tension between beam experiments (τ_beam ≈ 887.7 ± 2.2 s) and bottle experiments (τ_bottle ≈ 878.4 ± 0.5 s) — has motivated proposals for exotic neutron decay channels involving dark sector particles. We analyse this discrepancy within the Hopf soliton framework, where baryons are multi-sector solitons on the flag manifold F₂ = SU(3)/[U(1) × U(1)] and dark matter is a vacuum knotting condensate with no stable compact particles (Paper LXVII). We identify three independent topological obstructions to neutron dark decay: (i) the absence of any stable dark particle — compact H = 0 knots dissolve in ~ 10⁻²² s, and the vacuum condensate cannot absorb decay products; (ii) conservation of π₂(F₂) = ℤ ⊕ ℤ sector charges that cannot be carried by CP¹ configurations; and (iii) exponential suppression of topology-changing tunneling. We then investigate the sole remaining loophole — oscillation to a Weyl-conjugate "dark neutron" — and show that the electromagnetic mass splitting (~ 161 keV) exceeds the required δ m ~ 10⁻²⁰ eV by 26 orders of magnitude. All dark decay channels are closed. The framework predicts τ_n = 882 s from the weak matrix element (Paper XIX), consistent with the bottle world average. The J-PARC electron-beam result (877.2 ± 4.4 s), the first beam experiment to agree with bottles, supports the prediction that the discrepancy is a proton-counting systematic, not new physics.