def
definition
def or abbrev
gradient
show as:
view Lean formalization →
formal statement (Lean)
72noncomputable def gradient (φ : ScalarField) (x : Fin 4 → ℝ) : Fin 4 → ℝ :=
proof body
Definition body.
73 fun μ => directional_deriv φ μ x
74
75/-- Squared gradient g^{μν} (∂_μ ψ)(∂_ν ψ) with inverse metric. -/
used by (40)
-
const_one_is_geodesic -
PotentialFunction -
potential_implies_exact -
circuitSeparation -
SpectralTuringBridgeHypothesis -
alpha_t_lt_half -
love_eliminates_all_waste -
restoring_force_negative -
applyCourage -
courage_enables_high_gradient_action -
Vec3 -
antiGravField -
baseline_gravitational_coupling -
ExternalPhaseField -
ExternalPhaseField -
modified_falling_condition -
energy_processing_bridge -
energy_to_processing_field -
WeakFieldPair -
alpha_from_self_similarity -
kernel_perturbation -
poisson_coercive -
fibonacci_ratio_recursion -
phi_hierarchy_is_unique_fixed_point -
ic005_certificate -
jcost_deriv -
jcost_deriv_pos_of_gt_one -
jcost_deriv_zero_at_one -
of -
phi_rung_complexity_unbounded