The bridge equation: a 0.16% match A number-line visualization showing the measured cell occupancy 0.5657 (from the bridge equation applied to particle physics and cosmology) and the predicted value 0.5666 (from 4π divided by K times square root of 2), with the gap between them labeled 0.16 percent. Both values fall well inside the plus-or-minus 1 percent Planck uncertainty band on the dark matter density, which spans 0.5605 to 0.5719. ±1% Planck uncertainty on ρDM 0.16% 0.5605 0.5719 0.5657 Measured ρDM · c · ξ⁴ / ℏ particle physics × cosmology 0.5666 Predicted 4π / (K√2) geometric constants The gap is roughly 12× smaller than the Planck uncertainty on ρDM.