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

=== - The boundary action SbS_{\rm b}Sb with minimal coupling produces a conserved surface current jsurfμj^\mu_{\rm surf}jsurfμ via Noether. That current appears in the Maxwell equations as a thin-shell source δ(r−r0)jsurfμ\delta(r-r_0) j^\mu_{\rm surf}δ(r−r0)jsurfμ. ===
* Absorption is the normal flux of bulk current into the shell: n^ ⁣⋅Jbulk\hat n\!\cdot\mathbf{J}_{\rm bulk}n^⋅Jbulk contributes to ∂tσ\partial_t\sigma∂tσ. Emission is the reverse: surface current radiates into the bulk (encoded by the retarded solution of Maxwell with the surface source). Both are exact consequences of the continuity equation and Maxwell’s equations with delta sources.
* Energy exchange is precisely tracked by the Poynting flux into/out of the shell and work E∥⋅j∥ \mathbf{E}_\parallel\cdot\mathbf{j}_\parallelE∥⋅j∥ done on the boundary degrees. That makes the QAT picture of “photon energy → boundary excitation → emission of new spherical photon” a direct reading of the electromagnetic boundary dynamics.
* Faraday’s induction and the boundary jump rules provide the causal mechanism for how local charge/current changes create global field reconfigurations — the geometric language of lines of force that Faraday used is the same physical content the boundary action describes quantitatively.

If you’d like, next I can:
• produce a short one-page derivation you can paste into your Core Equation document (LaTeX ready), showing the action → jsurfμj^\mu_{\rm surf}jsurfμ → Maxwell with delta source → jump conditions → continuity → Poynting/boundary energy balance; or
• make a compact diagram: 1) spherical shell, 2) normal flux arrow (absorption), 3) tangential current (decoherence), 4) outgoing spherical radiation (emission) with labels of the equations (Gauss jump, Ampère jump, continuity), ready for a slide.

Which would you prefer? (I suggest the LaTeX one-pager first — that gives you a rigorous clip to paste under a video or into the canvas.)