Phason Coherence Length in Icosahedral Quasi-Crystals: A Prediction from Bootstrap Universe Geometry

The Bootstrap Universe framework derives fundamental constants from icosahedral geometry, beginning with the axiom I AM I. Here we show that the same constants governing nuclear confinement — the vertex degree d = 5 and the equatorial count (V − χ) = 10 — predict the phason coherence length in atomic icosahedral quasi-crystals via Lφ = (V − χ) × d × aR = 50aR, where aR is the quasi-lattice constant. The derivation follows from the 6D→3D cut-and-project geometry and the standing-wave mutual visibility rule: every equatorial phason vertex must see every spatial connection point for coherence to be maintained. The two polar vertices are excluded — pinned as phonon anchors by the projection direction — leaving V − χ = 10 free vertices forming a complete bipartite visibility graph K₁₀,₅ with d = 5 spatial steps, giving 50 independent coherence conditions. Two published measurements exist and neither falsifies the prediction: i-AlCuFe shows a phasonic modulation wavelength of 20 nm (predicted 25.8 nm, 22% discrepancy) and i-AlPdMn shows a phason correlation length of ~30 nm (predicted 32.4 nm, 7% agreement). The two measured quantities are physically related but not identical. Five further predictions are made for systems where the real-space coherence length has not been published. The result links nuclear geometry to condensed matter physics across seven orders of magnitude using no free parameters.