Two-shell icosahedral Heisenberg model: exact spectrum, golden phase window, and parameter-free magnon predictions for i-Au-Ga-Gd and i-Au-In-Eu

Preprint of the main manuscript of the INDYNA program, prepared for journal submission, with supplemental material. The paper presents the conjugate-shell model of icosahedral spin networks: a one-parameter operator family M(g) = A₁ + g·A₂ built from Galois-conjugate distance shells over ℚ(√5), its exactly solvable spectral structure, the golden ladder of level crossings, and experimentally testable predictions for icosahedral magnets and rare-earth quasicrystal approximants (probe hierarchy, first-order transition protocol at the golden coupling, and RKKY tuning of the shell ratio). The supplemental file contains derivations and numerical checks. This record consolidates the results of Research Notes 7–15.