R-layer Mode Theory (RLMT) XLVII: Layered Expansion and the Spectral Structure of the Hubble Constant

This volume develops the layered expansion framework of R-layer Mode Theory and shows that the apparent Hubble tension arises from the spectral structure of a projection‑dependent expansion operator acting on a higher‑layer tension field.Different cosmological probes—TRGB, multiply‑imaged Type Ia supernovae (including SN H0pe), and the CMB—sample distinct projection layers, yielding three ordered Hubble eigenvalues.Using SN H0pe, the mid‑layer eigenvalue is extracted from two time delays and three absolute magnifications, giving Hmid ≈ 72 km s⁻¹ Mpc⁻¹.The framework resolves the Hubble tension without modifying general relativity or introducing new particle species, and predicts observational consistency relations testable with future strong‑lensing supernovae.