Supplementary Material

Python experiments:

• wavefunction.py — Wavefunction class with spectral complexity C_s and Solomonoff weight 2^−C_s.
• minimal_video.py — Minimal 2 × 2, 2-frame video: enumerate all 256 configurations, compute C_s and boson signal.
• boson_structure.py, boson_structure_2.py — Symmetry, propagation, and quantisation analysis of the off-diagonal density matrix.
• scaling_1.py, scaling_2.py — Longer chains (L = 4–16), more frames; momentum quantisation test.
• two_fermion_hop.py — Two-fermion hops; phase universality, path independence, Pauli exclusion.
• pauli_as_zero_residual.py — Encoding scope and analytical proof of B = 0 for stationary fermions.
• theta_scaling.py — Numerical and analytical verification of ∥B(𝜃)∥ = sin(2𝜃)∕ across all L.
• dispersion_poc.py — Two-band lattice Hamiltonian H(k) = mσ_z + tsin(k)σ_x; numerical diagonalisation; verification of ∥B(k)∥ = |tsink|∕(E(k)) and of the continuum-limit recovery of E² = (pc)² + (m₀c²)².
• exclusion_poc.py — Tests whether the same overlap/exclusion cost that produces Pauli exclusion for spatial sites in Experiment 4 also operates on the internal band degree of freedom of Experiment 7. Finds that Solomonoff/MDL weighting over the band-mixing angle Δ between two fermions’ internal states, using only the exclusion cost (no Hamiltonian, no imported mass parameter), is maximized at Δ = π∕2 – full orthogonality between the two fermions’ band occupations – reproducing the standard antisymmetric one-fermion-per-band ground state from pure MDL reasoning. Does not yet yield an energy scale.
• exclusion_poc_3level.py — Follow-up testing whether ≥ 3 internal bands admit a residual boson coherence, in the fixed band basis, that a 2-band system cannot have even in principle (since Λ²(ℂ²) is one-dimensional). Finds a nonzero, continuously tunable residual ∥B₁∥ (up to 1∕(2) ≈ 0.354 at maximal tilt) once the occupied two-fermion subspace is tilted relative to the band axes – a new continuous degree of freedom absent in the 2-band case, though not yet tied to a specific mass value.