The Koide phase cos(δ) = −19/28 is derived from the complete closure condition of the 600-cell spectrum. The binary icosahedral group 2I has 9 irreducible representations. The closure condition — that all 9 eigenspaces must contribute to the lepton mass sum in exact balance — uniquely selects cos(δ) = −19/28. This is a full-length paper providing the complete derivation, compared to the earlier Selecting the Koide Phase paper which presented the result. Four theorems are proved, zero free parameters remain.