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Preprint . 2026
License: CC BY
Data sources: Datacite
ZENODO
Preprint . 2026
License: CC BY
Data sources: Datacite
ZENODO
Preprint . 2026
License: CC BY
Data sources: Datacite
ZENODO
Preprint . 2026
License: CC BY
Data sources: Datacite
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The Pre-Commitment Universe: Icosahedral Quasi-Crystal Geometry, Phasons, and the Origin of SU(3)

Authors: Keeble, Clifford;

The Pre-Commitment Universe: Icosahedral Quasi-Crystal Geometry, Phasons, and the Origin of SU(3)

Abstract

Before the proton crystallised into its stable three-phase icosahedral form, the universe existed in a pre-commitment state: icosahedral symmetry present, colour phases fluid, standing waves uncommitted. This paper identifies that state as an icosahedral quasi-crystal described by Hamilton quaternion geometry, and derives the structure of the pre-commitment gluon field from first principles. The 6-dimensional periodic lattice required by 3D icosahedral quasi-crystal mathematics is derived as Hamilton quaternion phase space: three imaginary axes (i, j, k) each carrying an independent phase relationship with the real axis, confirmed experimentally by three independently diffusing phason modes [Lubensky, Ramaswamy & Toner 1985]. The quasi-crystal has six natural modes — three phonons (real space) and three phasons (internal phase space). The Euler characteristic χ = 2 adds two topological closure modes at the icosahedral boundary, giving 6 + χ = 8 total modes. These 8 modes match the generator count of SU(3). The mode count is derived from icosahedral quasi-crystal geometry. Whether the modes satisfy the SU(3) Lie algebra with the correct structure constants is an open question marked as a priority for subsequent work. Gluons are identified with phasons: uncommitted colour phase fluctuations in the pre-crystalline vacuum. The minimum colour-neutral excitation energy is derived as M_G = χ × ℏc/(d × a) = 1489 MeV, within the lattice QCD window of 1475–1710 MeV. Crystallisation — the locking of phasons into the 24-period three-phase structure — produces the proton and constitutes the Yang-Mills mass gap. Non-icosahedral quasi-crystals (octagonal, decagonal) embed in lower-dimensional spaces with different algebraic structures. Octagonal quasi-crystals embed in 4D / Z[√2] with one internal degree of freedom and cannot achieve three-phase Eisenstein closure regardless of energy — the Bootstrap explanation for their universal thermodynamic metastability. A falsifiable prediction requires no new experiments: the zero-temperature phason Debye-Waller residual B_phason(T→0) = 0.0039 Ų in i-AlPdMn, from extrapolation of existing variable-temperature data.

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Keywords

quasi-crystals, icosahedral symmetry, phasons, gluons, SU(3), Yang-Mills mass gap, colour confinement, Hamilton quaternions, Bootstrap Universe, glueball mass, Euler characteristic, Steinhardt-Levine, crystallisation, Debye-Waller factor, pre-commitment vacuum

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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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