Abstract

We sketch a programme in which both quantum mechanics and general relativity emerge from a single principle: observers exist, and their probability of existence is determined by the compressibility of their description. The central object is a Boltzmann-like probability measure over histories γ compatible with an observer O:

where 𝒞_O[γ] is the total description cost of history γ given observer O.

Rather than deriving this from first principles — a task left for future work — we collect here the evidence that it is the correct organising equation. Papers VII and VIII of this series establish exact, analytically verified results: the off-diagonal density matrix of a purely fermionic system yields a photon-like boson with amplitude ∥B(𝜃)∥ = sin(2𝜃)∕; the identical decomposition applied to metric configurations yields the Ricci/Weyl split, gravitational wave polarisations, and a Newtonian potential V (r) = −Mm∕(8πr) in Planck units. These results share a single structure: ρdiag(ρ)+(ρ−diag(ρ)), the local/non-local split of any compressed configuration. We conjecture that this structure forces the cost functional to decompose into three regimes — discrete (D), spectral (ψ), and geometric (G) — corresponding to quantised spacetime, quantum mechanics, and general relativity respectively. The value n ≈ 184 bits for the universe’s information content, derived independently from inflationary cosmology and black hole thermodynamics in Papers IV and V, is expected to emerge as the saddle point of the observer’s own existence probability, though the explicit computation remains open. This paper is a progress report and a research agenda, not a completed derivation.