Authors: Gene A. Harvey
This paper presents the first direct mathematical derivation of the number of subquantum grains constituting a gravitationally-condensed shell, using the electron as a case study. Under the ΛCGF (Lambda Condensed Gravitational Field) model, the electron arises not from indivisible point particles, but from volumetric encapsulations of gravitational field surrounding subquantum grains. Each grain, defined as a spherical field node of radius 8.08 × 10u207bu2074u2076 m, existing far below the Planck scale and serves as the true unit of field compression. Individually, when those grains are under compression, they give rise to the electromagnetic field.By treating the electron as a sphere bounded by classical radius (ru2091 ≈ 2.8179 × 10u207b¹u2075 m) and employing hexagonal close-packing principles, we derive a packing capacity of approximately 3.14 × 10u2079¹ grains. Further, this alternative derivation assumes a grain count of Avogadro’s number squared (≈ 3.627 × 10u2074u2077), and shows that this yields a gravitational condensation factor of 2.26 × 10-61 joules per grain, perfectly matching the observed rest mass-energy of the electron.This result confirms that classical gravitational curvature—not quantum mechanics—is the fundamental driver of the electron mass. The electron emerges as a stable configuration of subquantum grains under compression - rather than a pointlike entity requiring renormalization. This paper lays the groundwork for a general equation of grain composition for all baryonic matter and challenges conventional notions of mass-energy at quantum and cosmic scales alike.
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