Abstract

Paper VI [meskanen2026v] presented the hypothesis that the quantum mechanical wavefunction is the compression signature of nature: the universe is a finite, static bitstring of n bits, and the path an internal observer experiences is the one that compresses best under a complex-valued spectral codec. The present paper supports this hypothesis with seven experiments implemented in Python and included as supplementary material. We show that a photon-like boson emerges as the compression residual of a purely fermionic system, without any interaction term introduced by hand. All essential features of quantum mechanics are recovered: Born rule, Pauli exclusion, particle–antiparticle pairing, and the virtual propagator. The central result is an analytically exact theorem: for a single fermion in superposition between two sites, the off-diagonal (boson) amplitude is ∥B(𝜃)∥ = sin(2𝜃)∕, independent of system size, site separation, and encoding. This equals , the interference term of the Born rule, made visible as a matrix norm. We further report an exploratory extension in which the same B-matrix formalism is applied, unchanged, to a two-band lattice Hamiltonian H(k) = mσ_z + tsin(k)σ_x, giving a boson-residual amplitude ∥B(k)∥ = |tsink|∕(E(k)) with E(k) = , which recovers the relativistic dispersion relation E² = (pc)² + (m₀c²)² as its continuum limit. This result is numerically verified but not yet derived from the spectral complexity functional C_s, and is reported as a genuinely open problem rather than a closed theorem. These results suggest that quantum mechanics is not a foundational layer of reality but an emergent description — the story an observer tells about fermions sampled from a compression codec.