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

===== Objective: propose and test a concrete toy model linking event rate (photon-electron interactions) to cosmological-scale numbers such as MU∼t2M_U\sim t^2MU∼t2 or Dirac’s hypotheses. =====

Two complementary lines:
A. Local-to-cosmological scaling: suppose a characteristic per-atom event rate RRR and a characteristic shell radius rrr; integrate/sum over all matter to produce an effective energy density; relate that to curvature (left-hand side of Einstein eq.). Try to match the scale of G or Dirac numbers by choosing physically plausible rates. This is a parametric numerical experiment and can produce an order-of-magnitude check.

B. Conformal geometry: explore whether conformal (scale invariant) mapping of spherical shells could naturally produce power-law relations like M∼t2M\sim t^2M∼t2. Provide mathematical sketch.

Deliverable: numerical survey (order-of-magnitude) and narrative of plausibility.