Icosahedrite Al₆₃Cu₂₄Fe₁₃ as Bootstrap Quasi-Crystal: Composition Theorem, Phason Modulation, and the Pre-Commitment Fossil

Icosahedrite (Al₆₃Cu₂₄Fe₁₃), the first natural quasi-crystal, was discovered in the Khatyrka meteorite and recently studied by high-resolution synchrotron X-ray diffraction (Takakura et al. 2025). We show that its satellite diffraction structure, lattice geometry, and phason modulation properties follow from the Bootstrap Universe framework without free parameters. Its composition maps onto icosahedral invariants through six independent routes, though the mechanism linking topology to site occupation remains open. The composition decomposes as: Al₆₃ = V + E + F + 1 (complete icosahedral skeleton plus origin), Cu₂₄ = three-phase Eisenstein motor period, Fe₁₃ = V + 1 = F₇ (first coordination shell, seventh Fibonacci number), with total atom count 100 = (V − χ)². The 12 satellite reflections per Bragg peak equal χ × D! = 2 × 6. The six cosine modulation waves correspond to the D! = 6 colour domains propagating along the six five-fold axes. The 108° rhombohedral angle is the interior angle of the regular pentagon. The aperiodicity of the lattice is a consequence of the Abel–Ruffini theorem (1824): A₅ is simple, therefore φ's irrationality is algebraically protected. The observed QC → modulated → rhombohedral transition sequence maps directly to the Bootstrap crystallisation narrative. Icosahedrite is a 4.5-billion-year-old fossil of the pre-commitment state, frozen mid-crystallisation by meteorite impact. Six falsifiable predictions are presented.