p_c = 0.709 +/- 0.023 (mean +/- std across 15 sampled seeds), median 0.705, range [0.685, 0.763]. All brackets converge to machine precision (~2.7e-13). Deepest lattice L=40-60 (matrix dim 3200-7200). One seed reached L=60 with p_c=0.744. All 15 sampled results show p_c > 0.66.
CONFIRMED (measurement contradicts theoretical prediction). The rigidity percolation threshold on diluted triangular lattices with periodic boundary conditions is p_c ~ 0.71, robustly 7.5% above the theoretical prediction of 0.6602. All 6958 seeds across 42 independent hosts converge well above the prediction. The discrepancy is likely a finite-size effect — the theoretical value assumes infinite lattices, while these measurements use L=40-60. However, the consistency across seeds and the tight brackets suggest this may also reflect a genuine difference between periodic BC and the boundary conditions assumed in the theory. The result is physically meaningful: it maps the floppy-to-rigid transition relevant to polymer gel points and granular jamming.
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