From a High-Symmetry Sector to Testable Observables: An E8-Motivated Projection Program with Proton Decay and Dark Photon Benchmarks

We outline a top-down program in which a “high” structure G⊇E8 is connected to 3+1-dimensional observables via an operational projection Π defined by a unitary dynamics on HG=Hobs ⊗Hhidden and a partial trace. The approach is designed to be falsifiable through a small set of consistency gates (anomaly cancellation, renormalization group closure with thresholds) and phenomenological targets.

As current computed instances we report: (i) a spectrum-driven “Track A” scan in an SU(5)-based breaking scaffold (derived from an in-repo E8 →···→SM embedding) showing that there exist threshold/fragment configurations yielding τp ≳ 1034 y while keeping the α3 mismatch at the α1 = α2 crossing below 5% (1-loop piecewise running and an order-of-magnitude τp estimator), and an MSSM-like reference case reaching µU ≈1.26 ×1016 GeV and τp ≈1040 y, and (ii) a light dark-photon region (mA′ ∼10−4–1 eV, ε ≳ 10−8) illustrated against an order-of-magnitude IAXO-like reach (for orientation only), while in-medium effects can reduce εeff in stellar environments. We emphasize what is already computed and what must be fixed next (anomaly closure, physical mass/threshold mechanisms, and 2-loop/matching improvements) to turn the program into a complete predictive pipeline.