def
definition
def or abbrev
phiCost
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formal statement (Lean)
43noncomputable def phiCost (u : ℝ) : ℝ := Real.cosh (Real.log phi * u) - 1
proof body
Definition body.
44
45/-- phiCost(0) = 0: zero phase increment has zero cost. -/
used by (21)
-
abs_sinh_le_abs_add_sq_of_abs_le_one -
annularCost -
AnnularRingSample -
jensen_ring_bound -
phiCost_add_le_phiCost_add_linear_quadratic -
phiCost_convexOn -
phiCost_eq_Jcost -
phiCostLinearCoeff -
phiCost_nonneg -
phiCost_quadratic_lb -
phiCost_symm -
phiCost_zero -
ring_coercivity -
ringCost -
ringCost_le_topologicalFloor_add_linear_quadratic_error -
topologicalFloor -
topologicalFloor_pos_of_charge_ne_zero -
realizedRingPerturbationError -
zetaDerivedPhaseFamily_excess_zero -
defectPhasePureIncrement -
regular_factor_increment_decomposition