Editing Openai/6897769e-4ee4-800f-aba5-69cca34f701c (section)

=== - The boundary Dirac action lives on the 2-D electron sphere: that is exactly the QAT “manifold for division of charge” and the place where photon ↔ electron energy exchange happens. ===
* Using h/2πh/2\pih/2π explicitly in the action ties the phase quantum to the spherical circumference (2π factors visible). The half-radius reff=r/2r_{\rm eff}=r/2reff=r/2 becomes the microscopic loop that sets the fundamental phase domain.
* Antiperiodicity (spinor behavior) emerges naturally either as the spin-bundle property of a boundary spinor or as the elementary-loop vs geometric-loop mismatch. This provides a clean mathematical route from QAT geometry → half-spin → half-integer angular spectrum.
* The same boundary fields can be coupled to the electromagnetic field living in the bulk (or to the incoming/outgoing photon fields) via surface currents; those couplings are how absorption/emission events change boundary occupation and produce the dynamical “flow of time” you described.