Charge Formation in the d2 Phase A geometric model based on d1 boundaries, field-wave, and potential difference

This work treats electric-like charge formation not as a particle property already present at the d0 or d1 level, but as a boundary polarization jointly produced by field, wave, and potential difference in the d2 phase. The basic geometric assumption is that two d1 linear strings establish the two opposite boundaries of an oriented d2 surface. When a potential difference forms on this surface, the field energy produces charges of equal magnitude and opposite sign, conjugate to the boundary potentials.The model consists of two layers. The continuous layer gives a capacitance-like response: Q = CΣ ΔV. The topological layer, when the d2 field-wave phase is compact, allows the charge to be read as n = (1/2π) d∮ φ in stable sectors under the condition Q = ne . Thus the equal-opposite charge pair arises from geometry and energy variation, while the discrete structure of charge comes from the phase-closure condition.ℤ A charged matter particle is defined by the charge pole formed on d2 closing — in boundary, phase, and energy — in the d3 phase, turning into a stable Ω₃ mode. The photon, by contrast, is a balanced fieldwave mode that remains open in d2; since d3 closure does not occur it carries no permanent charge pole and is therefore neutral. This text does not claim to derive the physical electron charge exactly from first principles. Instead, the relative charge structure — fractional quark charges together with the charges of the electron, proton, and neutron, and the neutrality of atoms — is derived geometrically via a three-cell ( ₃) extension and the ∂∂ = 0 closure; the absolute magnitude of charge (e) is left open. Within thePlanckon/ΨD framework 4, a mathematically consistent skeleton for the geometric origin of charge is presented.