recognition /
Relativity /
Relativity.Geometry.ParallelTransport /
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formal statement (Lean)
177 structure ClosedLoop extends SpacetimeCurve where
178 closed : path 0 = path 1
179
180 /-- The holonomy defect: the difference between a vector and its parallel
181 transport around a closed loop.
182
183 For an infinitesimal loop enclosing area δA^{μν}, the defect is:
184 δV^ρ = R^ρ_{σμν} V^σ δA^{μν}
185
186 This is the geometric meaning of the Riemann tensor. -/
used by (2)
From the project-wide theorem graph. These declarations reference this one in their body.
HolonomyDefect
in IndisputableMonolith.Relativity.Geometry.ParallelTransport
decl_use
no_holonomy_if_flat
in IndisputableMonolith.Relativity.Geometry.ParallelTransport
decl_use
depends on (18)
Lean names referenced from this declaration's body.
of
in IndisputableMonolith.Astrophysics.NucleosynthesisTiers
decl_use
V
in IndisputableMonolith.Cosmology.InflatonPotentialFromJCost
decl_use
of
in IndisputableMonolith.Foundation.DAlembert.LedgerFactorization
decl_use
A
in IndisputableMonolith.Foundation.IntegrationGap
decl_use
defect
in IndisputableMonolith.Foundation.LawOfExistence
decl_use
is
in IndisputableMonolith.Foundation.OptionAEmpiricalProgram
decl_use
of
in IndisputableMonolith.Foundation.PhiForcingDerived
decl_use
is
in IndisputableMonolith.Foundation.SimplicialLedger.EdgeLengthFromPsi
decl_use
of
in IndisputableMonolith.Foundation.SpectralEmergence
decl_use
V
in IndisputableMonolith.Foundation.SpectralEmergence
decl_use
is
in IndisputableMonolith.GameTheory.MechanismDesignFromSigma
decl_use
of
in IndisputableMonolith.Information.PhysicsComplexityStructure
decl_use
A
in IndisputableMonolith.Masses.Anchor
decl_use
is
in IndisputableMonolith.Mathematics.RamanujanBridge.MockThetaPhantom
decl_use
A
in IndisputableMonolith.Modal.Actualization
decl_use
and
in IndisputableMonolith.NumberTheory.CirclePhaseLift
decl_use
SpacetimeCurve
in IndisputableMonolith.Relativity.Geometry.ParallelTransport
decl_use
V
in IndisputableMonolith.RRF.Core.Glossary
decl_use