Experimental Proposal for Testing η-Dependent Cherenkov Thresholds in Extreme ENZ Media

This paper proposes a conceptual experimental test of η-dependent Cherenkov thresholds within the Adaptive Constraint Cascade (ACC-APD) framework. The intrinsic parameter η, interpreted phenomenologically as a dimensionless measure of internal binding-energy structure, modifies the effective Cherenkov control parameter according to β_eff = β√(1+η). Using an extreme epsilon-near-zero (ENZ) waveguide with large effective refractive index, the proposal compares proton and alpha-particle beams tuned near the Cherenkov threshold. Due to their slightly different η values, the framework predicts a small but potentially measurable shift in radiation onset and pair-production yield. The expected threshold difference is of order 0.02%. The proposal discusses possible detection strategies based on Cherenkov emission intensity and 511 keV gamma-ray signatures from electron-positron annihilation, together with major experimental challenges including beam precision, ENZ losses, and background suppression. This work is exploratory and phenomenological. It is intended to motivate discussion and possible future collaboration on threshold effects in structured electromagnetic environments.