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

==== If you want a formal derivation, the program is clear and doable: ====
# Write a precise microscopic action StotS_{\rm tot}Stot for one shell (spinor field + minimal coupling) and for the bulk EM field — we already sketched it.
# Derive exact local equations (we did: Maxwell with delta sources, boundary Dirac eqn, continuity law).
# Homogenization / multi-scale averaging: apply formal averaging (e.g., two-scale expansion or Wiener averaging) to go from many discrete shells and event rates to macroscopic fields D,H\mathbf{D},\mathbf{H}D,H, polarization P\mathbf{P}P, permittivity ε(ω), etc. This requires specifying distribution functions for event rates and geometry; it is standard in electrodynamics of media.
# Compute effective T^{μν} from averaged fields + matter excitations; insert into weak-field Einstein equations to recover Poisson/Newtonian gravity.
# Compare predictions: dispersion (ε(ω)), fine-structure corrections, predicted small variations of α with geometry/temperature, testable observational/experimental consequences.

I can do any of these next: write the full LaTeX one-page derivation (action → Maxwell with delta sources → jump conditions → continuity → Poynting boundary energy balance), or run a toy homogenization with simple statistical assumptions to produce explicit permittivity formulas, or derive the coarse-grained TμνT^{\mu\nu}Tμν and show the explicit Poisson equation source in terms of microscopic parameters (τ, σ, r). Tell me which you want and I’ll produce it.