We have sketched a programme in which a single equation — the Solomonoff-weighted measure over observer-compatible histories — is conjectured to be sufficient to derive the structure of spacetime, the origin of quantum mechanics, and the unification of General Relativity with quantum field theory.
The evidence for this conjecture, assembled across this series of papers, includes exact analytical results:
bosons emerge as compression residuals of fermionic systems with amplitude sin(2𝜃)∕
; gravitational
wave structure, polarisations, and the Newtonian potential emerge from the identical decomposition
applied to metric configurations; Keplerian orbits are selected by minimum description length;
Bekenstein–Hawking entropy and the inflationary aspect ratio are recovered from a single bit count
n ≈ 184.
None of these results required the postulation of interaction terms, coupling constants, force laws, or Hilbert spaces. They follow from one operation — the diagonal/off-diagonal split of a density matrix — applied to compressed configurations of different physical degrees of freedom.
Whether this operation is itself a theorem of the organising equation (1), or whether additional structure is needed, is the central unresolved question. The present paper is a progress report on the way to an answer.