Encrypted Cloning via Icosahedral Coset Structure: A Binary Polyhedral Correspondence

We show that the structural primitives of encrypted quantum cloning [Yamaguchi and Kempf, PRL 136, 010801 (2026)]—index-5 copies, one-time key exclusivity, and encrypted-state opacity — emerge from the coset decomposition [2I : 2T] = 5 of the binary icosahedral group. At θ = π/3 the opacity shifts from the local state (|r| = 0.937) to the decryption frame, realizing a public-parameter / hidden-frame (label-hiding) structure. IBM Quantum data are consistent with the predicted sector hierarchy at > 3.9σ per gap.