Neutron Decay and the Weak Force from Geometric Phase Mismatch

The neutron is shown to be inherently unstable because its internal structure involves two coprime bridges (33 and 43) whose geometric phases cannot synchronise. The proton uses bridge 41 (the nucleation prime) with electron bridge 33, giving GCD(41, 33) = 1, but survives because its single vortex structure allows phase averaging. The neutron adds a second vortex via bridge 43 (the partnership prime), and GCD(33, 43) = 1 creates an irreconcilable phase mismatch between the two vortices — the dual coprime condition that makes the neutron unstable. The bridges 41 and 43 form a twin prime pair straddling 42 = 2 × 3 × 7, connecting the three smallest primes. The Collatz trajectory from bridge 43 has length 29 steps, visiting every icosahedral coupling constant (V = 12, coordination 5, topology χ = 2) on its descent to ground state — providing the rebuilding sequence by which the electron vortex reconstitutes after neutron decay. A confinement energy formula is derived: E_conf = (α/2π) × (m_n − m_p − m_e)c² ≈ 0.594 keV, where α is the fine structure constant. This represents the geometric phase mismatch energy that must be overcome for decay to proceed. The neutron lifetime is proportional to 1/E_conf⁵ through Fermi's golden rule. The nine Heegner numbers (1, 2, 3, 7, 11, 19, 43, 67, 163) appear as bridge parameters, with 43 being the neutron's partnership prime and the unique class-number-one discriminant that creates instability. Version 1.2: Addresses all adversarial review issues. Adds Collatz null hypothesis (p < 10⁻⁴ for trajectory visiting all five coupling constants). Corrects immutable vortex distinction (single coprime = stable averaging; dual coprime = unstable interference). Adds Heegner number connection. Strengthens confinement energy derivation with status boxes throughout.