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

==== Below are incremental calculations / models that give sharp, testable outputs. I recommend starting with the simplest. ====

===== 1. Model: Bulk action (AdS4_44) with metric gMNg_{MN}gMN, U(1) gauge field AMA_MAM, and minimal Einstein–Maxwell action. Boundary is S2^22×time (your spherical shells). =====
# Boundary data: Turn on a time-dependent boundary source Aa(0)(t,Ω)A^{(0)}_a(t,\Omega)Aa(0)(t,Ω) modelling the QAT photon field hitting the shell and a boundary current Ja(t,Ω)J^a(t,\Omega)Ja(t,Ω) with dissipative spectral density.
# Compute: Use linear response / GKPW to compute the bulk field solution and the backreaction on the bulk metric to leading order (compute metric perturbation hMNh_{MN}hMN from boundary stress TabT_{ab}Tab built from the current correlator).
# Question answered: Does a plausible boundary spectral density produce a bulk metric perturbation with Newtonian 1/r behaviour in the near-boundary limit? How does the induced bulk stress scale with boundary parameters?

This is the minimum to see whether boundary dissipative processes can seed metric perturbations of the right qualitative form.

===== 1. Start with a boundary effective action for many fermion and boson modes on S2^22, with action Sbdry[Ψ,A]S_{\rm bdry}[\Psi,A]Sbdry[Ψ,A]. =====
# Integrate out the boundary fields at one loop to compute the effective action Seff[hab,A]S_{\rm eff}[h_{ab},A]Seff[hab,A] including a term ∝Λ2∫d3x −h R(h)\propto \Lambda^2 \int d^3x\,\sqrt{-h}\,R(h)∝Λ2∫d3x−hR(h) (a boundary curvature term).
# Map that induced boundary curvature to an emergent bulk gravitation constant via holographic dictionary (central charge ↔ 1/GN1/G_N1/GN).
# Estimate the scale: is a reasonable UV cutoff and density of modes enough to give realistic GNG_NGN?

This can test whether a QAT microphysics can produce the magnitude of gravitational coupling or shows the need for new scales.

===== 1. Represent concentric spherical shells by layers of a tensor network (MERA-like) with link structure encoding photon exchange rates (bond dimensions related to local event rates). =====
# Modify the boundary tensors to represent local absorption/emission events (changes in entanglement) and track how minimal surfaces (entanglement cuts) and an emergent discrete geometry respond.
# This is numerically tractable and will illustrate how local boundary operations (photon events) change emergent spatial geometry and perhaps produce curvature.

===== Model a single shell as a 2D dissipative fluid (conductivity, surface tension, surface stress tensor). Couple it to bulk Maxwell and compute Poynting flux → surface stress → bulk metric perturbation. Use membrane paradigm equations as a template. =====