This paper establishes three results and states one conjecture.
First, the Wavefunction Compression Principle provides a hypothesis for why the microcosm waves: internal observers composed of compressed structures perceive their world as wave-governed because the compression codec of the universe is the wavefunction.
Second, spectral complexity — a continuous, computable replacement for Kolmogorov complexity with linear frequency cost — exponentially suppresses chaotic configurations under Solomonoff-like induction. Structured, law-like, compressible universes dominate the measure. The Boltzmann brain problem is resolved as a consequence of the measure, not by fine-tuning.
Third, numerical simulation demonstrates that inertia and interference emerge from spectral compression alone, without imposed equations of motion.
Conjecture (Informational Action Principle): Cs ∝SEuclidean, with proportionality constant determined by n and Δω. If proved analytically or demonstrated to arbitrary numerical precision, this conjecture identifies quantum gravity as Solomonoff induction over compressed geometric descriptions, completes the bridge from the informational framework of Papers I–VI to a full theory of quantum gravity, and derives ℏ as the minimum spectral resolution of a finite informational universe.