recognition /
Foundation /
Foundation.SimplicialLedger.CubicDeficitDischarge /
explainer
No prose has been written for this declaration yet. The Lean source and graph data below render
without it.
generate prose now
formal statement (Lean)
115 def cubicDeficit {n : ℕ} (L : EdgeLengthField n) (h : HingeDatum n) : ℝ :=
proof body
Definition body.
116 match h.edges with
117 | [(i, j)] => (recoverEps L i - recoverEps L j) ^ 2
118 | _ => 0
119
120 /-- Area at a hinge: if the hinge carries a single edge `(i, j)`,
121 return `(κ/2) · (h.weight (i, j))`; otherwise return 0. -/
used by (5)
From the project-wide theorem graph. These declarations reference this one in their body.
cubicArea
in IndisputableMonolith.Foundation.SimplicialLedger.CubicDeficitDischarge
decl_use
cubicDeficitFunctional
in IndisputableMonolith.Foundation.SimplicialLedger.CubicDeficitDischarge
decl_use
cubicDeficit_singleton
in IndisputableMonolith.Foundation.SimplicialLedger.CubicDeficitDischarge
decl_use
regge_sum_cubicHinges
in IndisputableMonolith.Foundation.SimplicialLedger.CubicDeficitDischarge
decl_use
singletonHinge_product
in IndisputableMonolith.Foundation.SimplicialLedger.CubicDeficitDischarge
decl_use
depends on (5)
Lean names referenced from this declaration's body.
recoverEps
in IndisputableMonolith.Foundation.SimplicialLedger.CubicDeficitDischarge
decl_use
EdgeLengthField
in IndisputableMonolith.Foundation.SimplicialLedger.EdgeLengthFromPsi
decl_use
HingeDatum
in IndisputableMonolith.Foundation.SimplicialLedger.EdgeLengthFromPsi
decl_use
L
in IndisputableMonolith.Recognition
decl_use
L
in IndisputableMonolith.Recognition.Cycle3
decl_use