3x3 Speedcubing: The Ultimate Limits Forecast

GEV Extreme Value Theory

WR single = sample minimum of N attempts. Gumbel asymptotic:

log T_min ≈ μ − σ · √(2 ln N) + σ · (ln ln N + ln 4π) / (2√(2 ln N))

或粗略:
T_min ≈ μ · exp(−σ_log · √(2 ln N))

代入 μ_log = log(4.5) = 1.50, σ_log = 0.12, N = 10^7:
T_min ≈ 4.5 × exp(−0.12 × √(2 × 16.12))
      = 4.5 × exp(−0.68) ≈ 2.27 s

Three failure modes: (1) lower tail truncated by physical floor; (2) non-iid (hardware era / cohort non-stationary); (3) Gumbel extrapolates to 0 as N→∞ vs cube20.org 16-STM floor. Rigorous modeling uses reverse-Weibull (ξ < 0) giving finite endpoint τ ≈ 2.0 s, matching physical floor.