The Golden Gate: The Galois Automorphism as the Passage Between Physical and Perpendicular Space of the Icosahedral Quasicrystal (Research Note 7)

Research Note 7 of the INDYNA program on icosahedral spectral structures. This note develops the conjugate-shell construction on icosahedral vertex networks, in which two Galois-conjugate distance shells define a one-parameter operator family M(g) = A₁ + g·A₂ over ℚ(√5), and establishes the golden-ratio structure of its level crossings. The included corrigendum documents a correction to the original text. This deposit is part of a numbered series (Notes 7–15) building on Notes 1–6; the series culminates in an exactly solvable spectral theory with experimentally testable predictions for icosahedral magnets and quasicrystals.