This technical note reports a falsification-oriented residual audit of a binary-icosahedral (2I=SL (2, 5) ) carrier construction associated with the charged-lepton Koide relation. The study tests whether the empirical orientation residual in the coherent (C₃) carrier can be derived from group-theoretic, projective, or phase-grid mechanisms. The audit verifies that (C₃/C₅) element pairs generate the full binary icosahedral group (SL (2, 5) ), while no elements of order 15 or 30 occur. Thus (/15) is not a direct group-element phase. A simple Pancharatnam phase scan recovers a canonical (/240) scale, but does not derive the observed residual. Bargmann visibility and overlap tests identify standard icosahedral overlap values, but do not explain the contraction factor. A branch/orbit audit shows that the empirical orientation orbit is near a (1/240) phase grid; however, null and look-elsewhere tests show that this grid proximity is only weakly suggestive without an independent mechanism. The main conclusion is negative and deliberately conservative: a structurally motivated (1/240) phase-grid pattern is observed, but no physical or mathematical mechanism deriving the charged-lepton orientation residual is established. The package includes source code, computational outputs, provenance notes, and reproducibility files.
Johny Martin Christiansen (2026) studied this question.