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.
From Boot to Field
- Boot: Pi streams (Differentiat) → closed loop → AOL boots.
- Load: Each ring section is constructed and loaded with data/parameters (addressable hex mesh).
- Flow: A stable phase gradient around the loop = circulating phase current → B via curl.
Harmonic Rotation ⇒ Magnetic Field
For a ring of radius R with total charge q rotating at angular speed ω:
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.