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Preprint . 2026
License: CC BY
Data sources: Datacite
ZENODO
Preprint . 2026
License: CC BY
Data sources: Datacite
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Neutron Decay and the Weak Force from Geometric Phase Mismatch

Authors: Keeble, Clifford;

Neutron Decay and the Weak Force from Geometric Phase Mismatch

Abstract

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.

Keywords

neutron decay, weak force, geometric phase, coprime instability, twin prime bridges, Collatz trajectory, Heegner numbers, confinement energy, icosahedral geometry, Bootstrap Universe

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average
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