What survives of the lattice hypothesis when the lattice is replaced by a quasicrystal?

Fibonacci chain by substitution, cross-checked against cut-and-project, structure factor by non-uniform FFT.

Every clause of the prediction holds. Six peaks indexed as q₀(m + n/τ) to better than 4×10⁻⁵. Intensities follow sinc²(c·(m − nτ)) — the perpendicular index being the Galois conjugate — with rms residual 1.7×10⁻⁴ across 23 peaks. The Bragg discriminator |Σ|²/N² gives 0.49280, 0.11272, 0.77263, invariant to five decimals over a 47-fold range in N. Peak counts above successive thresholds: 3, 15, 59.

And the control is what makes it a measurement. The Thue–Morse comb has |Σ|²/N² falling by 0.5625 per fourfold in N against a predicted 0.5625. Aperiodicity alone does not diffract; the extra condition is what separates them.

Four implementation bugs surfaced, each producing a plausible wrong answer: a spurious fftshift scrambling the q axis; a q = 0 forward-scattering peak read as Bragg; a q-window shrinking as N grew so a different peak was maximal each time; and FFT scalloping mistaken for decay. They surfaced only because the prediction named the numbers. A vaguer claim would have been confirmed by all four.