We list the primary open problems in order of foundational priority.
- Continuum limit. The fullEinstein field equations should emerge as the large-deviation
stationarity conditions of CG over metric configurations in the continuum limit of the discrete
model of Paper VIII. This requires a treatment of the limit that is beyond the scope of the
current toy models.
- Emergence of energy. The spectral cost Cψ is an information-theoretic quantity. Its
identification with physical energy (E ∝ℏω) requires a derivation of the unit conversion from
Planck units to SI, analogous to the treatment of G in Paper VIII.
- The Multi-fermion Machinery. The single-fermion results already establish the essential
structure. Extending to tensor products is a technical programme, not a conceptual one.
- The topology question. Why is the observer’s boundary a 3-sphere? The spherical topology
emerges naturally from the minimal boundary extension of the 1D encoding, but a proof that
no other topology can dominate the measure has not been given.
- The saddle-point equation. Solving equation (6) requires an explicit model of ZO(n). A
tractable approximation to the observer partition function, even in a toy model, would be a
significant step.
- Derivation of the D-ψ-G decomposition. Equation (5) is conjectured, not derived. A
proof that the boundary structure of any self-describing observer forces this three-way split
would convert the conjecture into a theorem.