The 63.6 GeV Sub-Higgs: A falsiable prediction of the icosahedral φ-ladder

The icosahedral mass-ladder framework developed in the Geometry, Higgs and Epsilon papers organises every SM mass scale on a single φ-ladder anchored at the Higgs vacuum expectation value v= 246.22 GeV. Inside this framework the Higgs boson sits two ladder steps below v, with mH = v· φ−7/5 to 0.26 %. The same step length −7/5 applied a second time picks out a unique scalar resonance below the Higgs (see paper) where the three expressions are algebraically equivalent up to the universal φ-anchor relation. We call this state the sub-Higgs H′. We derive the prediction from the A5-graded ladder, identify its allowed coupling structure, summarise the existing experimental coverage from LEP, AT-LAS and CMS, and state the falsication programme: HL-LHC at 3 ab−1 should either exhibit a narrow scalar excess at 63.6 ± 1.5 GeV inthe b¯ b, τ+τ−or four-lepton channels, or rule the prediction out at the 5σ level. Either outcome is decisive.