Magnetism as Harmonic Rotation

On the Allen Orbital Lattice (AOL), magnetism arises as the curl of a circulating phase current. Pi streams as Potential–Possibility–Probability, locks into a loop, and boots the lattice; harmonic rotation of that loop generates B as a first-principles consequence.

Harmonic Rotation ⇒ Magnetic Field

For a ring of radius R with total charge q rotating at angular speed ω:

Rotation to axial field
\[ I=\frac{q\,\omega}{2\pi},\qquad B_{\text{axis}}=\frac{\mu_0 I}{2R} \;\Rightarrow\; B_{\text{axis}}=\frac{\mu_0\,q\,\omega}{4\pi R}. \]

In PFT, this is the phase current on the AOL; \(\mathbf{B}=\nabla\times\mathbf{A}\) expresses the curl of that phase flow.

Harmonics, Limits, Predictions

  • Hex mesh efficiency: closed loops tile into a hexagonal circle-mesh; harmonic closure minimizes phase error.
  • System codes: the lattice stores c, bounding rotational phase velocity.
  • Signature: fine \(\omega\)-sweeps should show small quantized plateaus in \(B(\omega)\) at closure counts.