Charge as Geometric Orientation: Inside and Outside of the Hyperfactorial Bridge

We propose that electric charge is geometric orientation relative to the hyperfactorial H(3) = 108. The proton exists inside 108 (coupling through its 12 divisor channels), while the electron exists outside 108 (coupling through the 36 coprime channels). This geometric difference explains why proton and electron see different values of the fine structure constant α—vertex α (CODATA 2018) and face α (CODATA 2022) respectively—as demonstrated in our companion paper. The sign of charge emerges from coupling direction: +1 for outward coupling (from inside), −1 for inward coupling (from outside). Opposite charges "attract" because their channels interlock without conflict; same charges repel because their channels point the same direction and compete. Charge conservation follows automatically: creating an "inside" view necessarily creates an "outside" view of the same 108. The exact equality |e_proton| = |e_electron| is geometric: there is only one 108, so inside and outside have the same magnitude. This framework unifies charge with the fine structure constant through the same icosahedral geometry.