What sets the connectivity threshold of a correlated point pattern?

The percolation threshold of a random geometric graph is studied across a one-parameter family of two-dimensional point patterns interpolating between clustered, uncorrelated and repulsive arrangements. At fixed density the threshold mean degree varies by a factor of 6.3 across the family. Neither the long-wavelength limit of the structure factor, nor the transitivity of the graph, nor the moments of the degree distribution predicts it. The covered area fraction at threshold does: over twenty models it gives 0.6768 ± 0.0332, matching the classical Boolean value 0.6763 to within 0.07 standard errors, a fourteen-fold collapse of the variation. The residual deviation peaks where the correlation distance matches the connection range, with opposite sign for repulsion and clustering. The critical exponent ν = 1.312 ± 0.088 is consistent with the exact two-dimensional value 4/3, so the correlations displace the transition without altering its universality class. The archive contains the simulation and analysis code together with an automated validation suite checking every module against independently known results.