8 Open Problems

1. Derivation of ∥W∥∝M. Theorem 4 assumes the graviton amplitude scales linearly with mass. This should follow from n_bh = log ₂(r_s∕ℓ_P ) = 1 + log ₂M (Planck units), since more bits produce more off-diagonal weight. A rigorous derivation would make Theorem 4 fully self-contained.
2. Continuum limit and Einstein field equations. The discrete toy model uses conformal metric configurations on a finite grid. The Einstein equations should emerge as the large-deviation stationarity condition of the spectral complexity functional over metric configurations in the continuum limit, analogous to how the Euler–Lagrange equations are stationarity conditions of the action.
3. Full tensorial Riemann curvature. The decomposition in Theorem 2 applies to scalar conformal factors, not the full rank-4 Riemann tensor in four dimensions. Extending the codec decomposition to the full tensorial case is required for a complete derivation of GR.
4. Electromagnetic potential. The same flux argument applied to the photon residual of Paper VII should give the Coulomb potential V _EM(r) ∝ 1∕r. The ratio V _EM∕V _grav would then give the ratio of electromagnetic to gravitational coupling, addressing the hierarchy problem from within the framework.
5. Rigorous graviton propagator. The overlap integral in Theorem 4 is a heuristic. A rigorous treatment requires the Green’s function for the graviton propagator in the discrete model, from which the potential would follow without the proof-sketch caveat.