The Prediction

The realised gravitational coupling is α_G∗ = α_em²¹ × (1 + 1/π) / (1 + α_em), and the realised constant is:

G = α_em²¹ × (1 + 1/π) / (1 + α_em) × ℏc / m_e²

Using the CODATA inputs, as AP28 uses them:

α_em²¹ = 1.338 × 10⁻⁴⁵
1 + 1/π = 1.31831
1 / (1 + α_em) = 0.992756
Structural value (AP28): G = 6.7206 × 10⁻¹¹ N·m²/kg²
Realised value: G = 6.6719 × 10⁻¹¹ N·m²/kg²
Measured (CODATA 2018, unchanged 2022): G = 6.6743 × 10⁻¹¹ N·m²/kg²

Residual: −0.036%.

Read against the landscape rather than against a single number. AP28’s structural value stands 0.69% above the recommended value — thirteen times the roughly 500 ppm spread between independent laboratory determinations, outside every experiment ever performed. The realised value stands about 360 ppm below the recommended value — inside that spread, within one standard uncertainty of the lowest published determination and below others. The commitment closes about ninety-five per cent of the discrepancy and moves the prediction from outside the experimental landscape to its low edge. That is what the correction does. And stated against individual experiments, as a hostile reader will state it first: the realised value sits twenty-nine standard deviations below HUST-T-18 and twenty-five below UWash-00 in those experiments’ own uncertainties, and sixteen below the CODATA recommendation at its formal 22 ppm. The commitment moved the exclusion from roughly six hundred standard deviations to twenty-nine — a twenty-fold improvement that is still exclusion, not agreement, and is claimed as nothing more.

And here is what the landing is, exactly: non-exclusion, not evidence. By §10’s own argument the target is soft — an admissible window seven and a half per cent of ε wide against a 22 ppm formal uncertainty — and a realised value sitting essentially on top of the lowest modern determination is precisely the kind of agreement this paper declines to lean on. The prediction earns its keep from the fork it creates and the switches that guard it, not from where it happens to land today.

The sign flip, stated plainly. Under AP28 alone, the gap ran prediction-above-measurement, the direction downward apparatus leakage can explain — Ø Predictions Part II says exactly this. Under the commitment, the residual runs prediction-below-measurement, and the same leakage mechanism cannot absorb it: leakage lowers what laboratories read; it cannot raise it. Adopting this paper therefore trades a large residual with a comfortable story for a small residual with no story yet. The residual is reported open and unattributed (§0.7): laboratory convergence toward the low determinations, a higher-order term in ε, or a refinement not yet forced. Which of these, the data will say — under the switches of §12 — and this paper will not say first.