GTUD Rotation as Josephson Phase: Calibrating G = E² (Δθ)² in Macroscopic Quantum‑Tunneling Circuits

We operationalize the GTUD relation G = E² (Δθ)² by identifying Δθ with the Josephson phase excursion Δφ in macroscopic quantum‑tunneling (MQT) circuits. Using the washboard potential U(φ) = −E_J cos φ − (ħ/2e) I φ with effective mass M_φ = C (ħ/2e)² and plasma frequency ω_p(I) = √(2e I_c / ħ C) (1 − I/I_c)^{1/4}, we derive: (i) harmonic small‑angle energy shifts ΔE ≈ ½ M_φ ω_p² (Δφ)²; (ii) an MQT action S_B = (36/5) ΔU/(ħ ω_p) yielding Γ ≈ a ω_p exp(−S_B/ħ) and the sensitivity δ ln Γ ∝ −(Δφ)²; (iii) a SQUID/array additivity criterion based on orthogonality and a Gram‑matrix/Gershgorin bound; and (iv) preregisterable experimental protocols with OU/1/f noise models and uncertainty budgets. We include annotated analytic figures (washboard geometry, ln Γ vs G scaling, additivity envelope, ω_p vs bias) and a JSON prereg schema. This provides a falsifiable metrological embedding of GTUD in the Nobel‑recognized Josephson tunneling framework (Martinis et al., 1985; Devoret et al., 1984–1985).