The Genesis Loop: Discrete Prime Lattice Constraints as a Geometric Solution to the Yang-Mills Existence and Mass Gap Problem
Description
The Standard Model of particle physics and General Relativity remain fundamentally
incompatible due to a divergence in their treatment of spacetime: the former relies on
quantized fields, while the latter assumes a continuous manifold. This incompatibility is
most evident in the Yang-Mills Existence and Mass Gap Problem, which asks why massless
quantum fields acquire strict, non-zero mass.
This paper proposes a solution by abandoning the assumption of continuous spacetime
(R4). We introduce the Trio Model, which posits that the universe operates on a discrete
Prime Integer Lattice with a fixed minimum resolution (a = 1). By mapping the integer
timeline onto a Modulo 6 Cylinder (H = 6), we demonstrate that the distribution of Prime
numbers creates a rigid, helical structure—a "Prime Helix"—that constrains the geometry
of existence.
We define Mass not as an intrinsic property, but as "Hoop Stress"—the mechanical
tension required to maintain a closed geometric loop (1 → 2 → 3) against the discrete
constraints of the lattice. Using this framework, we analytically derive the proton-to-electron
mass ratio (6π5) and the neutron mass difference to within 0.001% of experimental CODATA
values. We further demonstrate that the Standard Model is a Dimensional Cascade, deriving
the masses of leptons, bosons, and quarks as geometric harmonics of this primary lattice.
Finally, we conclude that the "Mass Gap" is the energy cost of defining information within
a discrete computational system.
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References
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