A Note on "Quasicrystal Symmetry-Angle Frequencies and Tests of GEIER’s n×6° Rule or GEIER’s nx(2xand,or3)° Rule and Φ-Related Geometry; Part 4.1 of ‘Crystallography and GEIER’s n×6° Rule’"
A Note on "Quasicrystal Symmetry-Angle Frequencies and Tests of GEIER’s n×6° Rule or GEIER’s nx(2x and,or 3)° Rule and Φ-Related Geometry: GEIER’s nx6° Rule ↔ GEIER’s nx(2 x and,or 3)° Rule; GEIER’s nx6° Rule (Crystals C) ↔ (Quasicrystals and C) GEIER’s nx(2 x and,or 3)° Rule; Part 4.1 of ‘Crystallography and GEIER’s n×6° Rule’" From a technical, review-style perspective, the manuscript excels at turning the GEIER grid hypothesis into a clear, falsifiable arithmetic test on an openly documented benchmark (Chang LIU et al. Supplementary Table S1; n = 159; see op.cit.), with the symmetry order n mapped transparently to the fundamental increment θ=360∘/n before evaluating 6°/3°/2° divisibility. The quantitative reporting is unusually disciplined for an angle-regularity claim: beyond the headline coverage rates (e.g. 156/159 on the 6° grid, 159/159 on the 3° grid), GEIER et al. also provide exact CLOPPER–PEARSON binomial confidence intervals and explicitly emphasize the cu...