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simulate_pi — Estimate pi with seeded Monte Carlo and a 95% Wilson interval; up to 5 million samples. CPU or optional CUDA. Other direct scientific engine

optimize_tasks — Exactly maximize value for up to 32 independent, indivisible tasks within an integer-minute budget. Each task is selected at most once; no p

verify_shadows — Check measured shadows using NOAA solar position, a ground-plane homography from 4–16 controls and Monte Carlo uncertainty. Returns conditio

check_ephemeris — Check a claimed Sun (soleil) or Moon (lune) position for UTC time/location using NOAA/Meeus approximations and lunar parallax. Returns model

audit_statistics — Apply necessary GRIM/GRIMMER checks to rounded means and sample deviations of bounded integer observations. Passing does not prove a dataset

analyze_kinematics — Convert angular speed and candidate distances to minimum transverse speeds; check a claimed speed-distance pair. Distance hypotheses are sup

check_shadow_track — Compare 4–120 measured minute/azimuth pairs with solar motion: residuals, slope, direction and time-lapse speed. Supply measurements, not vi

solve_equilibrium — Solve Kuhn poker with CFR+ self-play, measure exploitability with pure best responses and compare the game value with -1/18. Illustrative ga