def
definition
def or abbrev
CostAlphaLog
show as:
view Lean formalization →
formal statement (Lean)
29def CostAlphaLog (α t : ℝ) : ℝ :=
proof body
Definition body.
30 (1 / α ^ 2) * (cosh (α * t) - 1)
31
32/-- The α-parameterized cost in multiplicative coordinates:
33 F_α(x) = (1/α²)(cosh(α ln x) − 1). -/
used by (18)
-
AlphaCoordinateFixationCert -
alpha_pin_under_high_calibration -
costAlphaLog_fourth_deriv_at_zero -
costAlphaLog_high_calibrated_iff -
deriv_costAlphaLog_eq -
deriv_deriv_costAlphaLog_eq -
deriv_deriv_deriv_costAlphaLog_eq -
hasDerivAt_costAlphaLog_first -
hasDerivAt_costAlphaLog_fourth -
hasDerivAt_costAlphaLog_second -
hasDerivAt_costAlphaLog_third -
J_uniquely_calibrated_via_higher_derivative -
CostAlpha -
costAlphaLog_unit_curvature -
cost_alpha_rescaling -
deriv_costAlphaLog_eq -
hasDerivAt_costAlphaLog -
wlog_alpha_eq_one