braggPeakRatio_gt_one
plain-language theorem explainer
The theorem establishes that the diffraction peak spacing ratio exceeds unity. Crystallographers modeling φ-quasicrystal patterns cite it to confirm golden-ratio scaling of successive Bragg peaks in the small-angle limit. The proof is a direct one-line application of the known inequality 1 < φ.
Claim. The ratio of successive Bragg peak angles satisfies $1 < r$, where $r = phi$ is the golden ratio.
background
In the Recognition Science treatment of crystallography, interlayer spacings follow the φ-ladder: $d_n = d_0 / phi^n$. Bragg's law then implies successive peak angles scale by φ in the small-angle regime, so their ratio equals φ exactly. The upstream lemma one_lt_phi establishes that the golden ratio exceeds unity and is imported here via the definition braggPeakRatio := phi.
proof idea
The proof is a one-line wrapper that applies the lemma one_lt_phi.
why it matters
This result feeds the BraggAngleCert definition, which bundles the ratio inequality with non-negativity of diffraction cost. It fills the structural step in the φ-ladder application to Shechtman diffraction, consistent with the self-similar fixed point and eight-tick octave in the forcing chain.
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