Empirical Testing Protocols — E(C) = mc²·e^(kC)

Empirical protocols for falsifying the chameleon scalar-tensor framework E(C) = mc²·e^(kC). SKA-Mid null tests, TIRF+AFM biological measurements, and torsion balance propulsion experiments.

Torsion Balance Propulsion Protocol (Paper XII)

Target: δF/F ~ 10⁵ at 10⁸ Torr vacuum. Asymmetry factor A = 3 between two facing plates. Coherence gradient ∇C = 2.4×10³ m¹ at x_m = 0.026. Predicted force F_prop = 0.74–0.95 N (1 kg test mass). Pressure onset at 10⁴ Torr — atmospheric screening quenches the signal below this threshold. Protocol: SOF-certified operator, fibre torsion balance, ≥10⁸ Torr vacuum, A = 3 asymmetric mass geometry, 100 second integration windows.

Biological TIRF + AFM Protocol (Papers VIII, IX)

Measure kinesin motor velocity v as a function of ECM density ρ_ECM in collagen gel matrices. Prediction: Pe = 2.02 at r = 75 nm (templating regime). Pe crosses 1 at r ≈ 107 nm. Protocol: TIRF microscopy for single-molecule motor tracking, AFM for ECM stiffness mapping, coherence field index C calculated from SHG imaging (SHG-C threshold ≥ 0.70).

SKA-Mid Null Tests (Paper VI)

Four pre-registered null predictions for the chameleon scalar-tensor framework, all falsifiable with SKA-Mid Band 1–5:

  • γ₁ = 0 — circular polarisation null (Stokes V = 0)
  • EVPA Δθ = 0 — no anomalous rotation measure gradient
  • Group delay τ = 0 — no dispersive delay above ISM baseline
  • Δα/α ~ 0.003–0.03 — fine structure constant drift bonus prediction

NANOGrav Pulsar Timing (Paper LII)

Using fully public NANOGrav 15yr + IPTA DR2 post-GWB residuals. Chameleon void-fraction correlation: slope = k·x_m = 1.92·0.026 = 0.050 yr/pc per unit |δ|. High-void vs low-void differential = 2.12 yr across 20 millisecond pulsars. J1713+0747 and J1909-3744 carry strongest signal (Δt ~ 4.3–4.7 yr). Analysis time: ~2 weeks. GWB correlation is orthogonal to void-fraction correlation.