Hubble tension in the AMC framework

Summary This document is a focused technical note that applies the Alternative Model Cosmology (AMC) framework to the Hubble-tension problem. It formalizes the distinction between a late-time, low-redshift (local-slope) estimator of the Hubble constant and an early-time, CMB-like estimator obtained by fitting a ΛCDM template to early-universe constraints. Within AMC, the early-time ΛCDM fit is interpreted as a projection onto a rigid-template model, yielding an effective parameter H0^(CMB,eff) that generally differs from the late-time AMC value H_alt(τ0). The note provides clean notation, a constants table (including Z, T_alt, and Φ_alt^R as defined in AMC), a compact “projection lemma” statement, and a worked numerical example consistent with the accompanying plots and tables. Communities / subjects Cosmology and Nongalactic Astrophysics (astro-ph.CO), General Relativity and Quantum Cosmology (gr-qc).