Research note identifies a criterion for quadratic fields supporting conjugate-shell pairs, highlighting implications for magnetic order in quasicrystals.
Research Note 8 of the INDYNA program. This note establishes the "silver bridge": the associate criterion that governs which quadratic fields support conjugate-shell pairs, contrasting the golden tower over ℚ(√5) with a second number-theoretic tower, and identifies a Klein-four structure organizing the sign sectors of icosahedral magnetic order. Part of the numbered series (Notes 7–15) building an exactly solvable spectral theory of icosahedral networks with testable predictions for icosahedral magnets and quasicrystals.
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Arber Gishto (2026) studied this question.
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