One equation, one ladder, one tower: the uniform core of the golden crossing ladder, its prime-5 exclusivity, and the E6/E8 anchoring INDYNA-STATIK Research Note 15

Research Note 15 of the INDYNA program: the uniform core. This note proves that the associate criterion and the core relation n² + k² = 5 underlying the conjugate-shell construction are field-independent, and works out the McKay-side representation theory (branching of the binary icosahedral group to the binary tetrahedral group). The deposited version includes the corrected branching table: the genuine Galois twin pairs are (2,2′) and (3,3′) only, while (4,4′) are separated by parity — the correction was found by checking the table against the affine E₈ McKay data and is documented in the text. LaTeX source included. Part of the numbered series (Notes 7–15).