The results above suggest a coherent picture: quantum mechanics is not a foundational layer of reality but the effective description an observer constructs when observing fermions that are sampled from a compression codec.
The wavefunction is not a physical field propagating through space. It is the codec — the algorithm that selects which fermion configuration an observer experiences, given the constraint that the observed path through the 2n configurations must be the one of minimum description length. Measurement is decompression. The Born rule is Solomonoff induction applied to a complex-valued codec: the probability of outcome j is proportional to the squared amplitude |ψj|2 because |ψj|2 is the spectral weight assigned to that configuration by the minimum-description-length codec.
Bosons, in this picture, are not fundamental. They are the codec’s record of fermion motion, reified into particles by observers who do not know they are watching compressed data. This does not make quantum field theory wrong. It makes it an extraordinarily accurate effective description of compression residuals.
The universal −π∕2 phase of the single-hop boson corresponds to a quarter-turn in the complex plane. Four such hops return the phase to its starting point: 4 × (−π∕2) = −2π. This is the spinor structure of a spin-1∕2 particle: a 2π rotation returns a fermion to its original state only up to a sign, while a 4π rotation is the identity. The π∕2 phase quantisation is not imposed; it follows from the imaginary encoding ψ = f0 + if1 and the definition of the boson matrix.
The framework relies on the complex exponential eiωx as the codec basis. Paper VI [meskanen2026vi] argues that this is the minimum-description-length periodic smooth basis: the algorithm (eiωx) is a fixed one-time cost shared across all wavefunctions, while the per-instance cost is carried entirely by the spectral modes (frequencies), which are unbounded. This is what makes spectral complexity Cs both computable and physically meaningful.
Several existing programs seek to derive quantum mechanics from information theory: reconstructions
based on information-theoretic axioms [hardy2001, chiribella2011], the Bayesian/QBist programme
[fuchs2014], and entropic dynamics [caticha2019]. The present approach differs in two respects. First, it
is constructive: it identifies a specific codec (complex spectral decomposition), a specific complexity
measure (Cs), and derives specific quantitative predictions (the sin(2𝜃)∕
theorem) rather than
axiomatising quantum mechanics from abstract information principles. Second, it is embedded in the
larger cosmological framework of Papers I–V, which derives spacetime geometry, the cosmological
constant, and black hole entropy from the same finite bit budget n. Quantum mechanics is not postulated
at the bottom of this hierarchy; it emerges at the same level as geometry, from the same
codec.
The two-band construction of §8 places the mass question in the same territory as lattice-Dirac and SSH-type condensed-matter models, where a relativistic dispersion relation emerges from a discrete lattice Hamiltonian in the continuum limit. The present contribution is not the lattice-to-continuum result itself, which is standard, but the observation that the pre-existing B-matrix boson-residual formalism attaches to that construction without modification, and assigns a compression-residual interpretation to the resulting mass-dependent coupling.
The present experiments use a one-dimensional chain of discrete sites. The extension to three spatial dimensions, continuous space, and the full Fock space of many-fermion systems requires tensor products of single-fermion wavefunctions and a treatment of indistinguishability that goes beyond the scope of this paper. Additionally, the experiments demonstrate the emergence of a photon-like boson from a scalar codec. Whether the model predicts other bosons, e.g. the massive bosons (W, Z, Higgs) and of the gauge structure of the Standard Model are not yet addressed. The mass term introduced in §8 is imported from standard lattice constructions rather than derived from Cs; deriving the two-band structure and the specific form mσz from the same minimum-description-length principle used elsewhere in the series remains open (§11).