1 Introduction

The codec framework of Papers I–VII treats the universe as a finite static bitstring of n ≈ 2¹84 bits. Fermions are localised excitations — pixels — encoded as normalised complex wavefunctions. Bosons are compression residuals: the off-diagonal entries of the density matrix ρ = |ψ⟩⟨ψ| that remain after the per-site fermionic diagonal is removed.

Paper VII showed that a two-site fermion hop produces a compression residual B with ∥B∥ = sin(2𝜃)∕, purely antisymmetric structure, and a universal −π∕2 phase encoding the Born rule exactly. That result is about the fermion’s motion — the boson is what the codec records when a fermion moves, not a separate particle that mediates the motion.

The present paper asks: what is the universal structure of the fermionic content itself, and how does it organise into the particle spectrum we observe?

The answer has two parts. First, three exact theorems establish the norm structure of any n-site fermion, culminating in a conservation law that subsumes all previous results. Second, the pair (n,m) — sites and winding number — classifies the fermion complexity classes. The classification is purely fermionic: no interaction terms, coupling constants, or gauge symmetries are introduced. What Standard Model language calls bosons are derived labels for correlations between fermion events, not independent objects.

A note on scope: gravity was derived in Papers IV–V at the geometric layer, independently of the wavefunction codec. That derivation is not revisited here. The relationship between the geometric and codec layers is addressed in the Discussion.