structure
definition
def or abbrev
DeficitAngleFunctional
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formal statement (Lean)
136structure DeficitAngleFunctional (n : ℕ) where
137 deficit : EdgeLengthField n → HingeDatum n → ℝ
138 area : EdgeLengthField n → HingeDatum n → ℝ
139 area_pos : ∀ L h, 0 ≤ area L h
140
141/-- The Regge action on a list of hinges, as defined by the functional:
142 `S_Regge = Σ_h A_h · δ_h`. -/
used by (24)
-
cubicDeficitFunctional -
CubicSimplicialInvarianceCert -
HingeTrivial -
regge_sum_append -
regge_sum_append_trivial -
regge_sum_nil -
regge_sum_refinement_invariant -
SimplicialRefinement -
SimplicialRefinement -
trivial_hinge_contribution -
EdgeLengthFromPsiCert -
field_curvature_identity_under_linearization -
ReggeDeficitLinearizationHypothesis -
regge_sum -
regge_sum_flat_under_linearization -
exact_flat_agrees_with_linearized -
NonlinearDeficitFunctional -
CalibratedAgainstGraph -
calibrated_iff_hypothesis -
cubic_calibrated_against_graph -
field_curvature_identity_simplicial -
field_curvature_identity_simplicial_einstein -
SimplicialFieldCurvatureCert -
simplicial_linearization_discharge