recognition /
Gravity /
Gravity.ReggeCalculus /
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)
125 theorem flat_deficit_zero (h : HingeData)
126 (h_flat : h.dihedral_angles.sum = 2 * Real.pi) :
127 deficit_angle h = 0 := by
proof body
Term-mode proof.
128 unfold deficit_angle; linarith
129
130 /-- On the flat cubic lattice Z^3, each edge is shared by 4 cubes.
131 Each cube contributes dihedral angle pi/2.
132 Sum = 4 * pi/2 = 2*pi, so deficit = 0. -/
used by (2)
From the project-wide theorem graph. These declarations reference this one in their body.
depends on (11)
Lean names referenced from this declaration's body.
is
in IndisputableMonolith.Foundation.OptionAEmpiricalProgram
decl_use
is
in IndisputableMonolith.Foundation.SimplicialLedger.EdgeLengthFromPsi
decl_use
is
in IndisputableMonolith.GameTheory.MechanismDesignFromSigma
decl_use
deficit
in IndisputableMonolith.Geometry.DihedralAngle
decl_use
deficit
in IndisputableMonolith.Geometry.Schlaefli
decl_use
flat_deficit_zero
in IndisputableMonolith.Gravity.DiscreteCurvature
decl_use
deficit_angle
in IndisputableMonolith.Gravity.ReggeCalculus
decl_use
HingeData
in IndisputableMonolith.Gravity.ReggeCalculus
decl_use
Z
in IndisputableMonolith.Masses.Anchor
decl_use
is
in IndisputableMonolith.Mathematics.RamanujanBridge.MockThetaPhantom
decl_use
Z
in IndisputableMonolith.Physics.AnchorPolicyCertified
decl_use