recognition /
Foundation /
Foundation.VariationalDynamics /
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)
507 def IsEquilibrium {N : ℕ} (c : Configuration N) : Prop :=
proof body
Definition body.
508 IsVariationalSuccessor c c
509
510 /-- **Theorem (Equilibrium Characterization)**:
511 A configuration is at equilibrium iff it minimizes total defect
512 over its feasible set — iff it is the unique minimizer.
513
514 For log-charge = 0, this is the unity configuration (all entries = 1).
515 For general log-charge σ, this is the uniform configuration
516 (all entries = exp(σ/N)). -/
used by (3)
From the project-wide theorem graph. These declarations reference this one in their body.
depends on (20)
Lean names referenced from this declaration's body.
all
in IndisputableMonolith.Aesthetics.NarrativeGeodesic
decl_use
all
in IndisputableMonolith.Anthropology.KinshipGraphCohomology
decl_use
all
in IndisputableMonolith.Engineering.AsteroidOreSpectroscopy
decl_use
Configuration
in IndisputableMonolith.Foundation.InitialCondition
decl_use
A
in IndisputableMonolith.Foundation.IntegrationGap
decl_use
defect
in IndisputableMonolith.Foundation.LawOfExistence
decl_use
is
in IndisputableMonolith.Foundation.OptionAEmpiricalProgram
decl_use
Configuration
in IndisputableMonolith.Foundation.RecognitionForcing
decl_use
is
in IndisputableMonolith.Foundation.SimplicialLedger.EdgeLengthFromPsi
decl_use
IsVariationalSuccessor
in IndisputableMonolith.Foundation.VariationalDynamics
decl_use
is
in IndisputableMonolith.GameTheory.MechanismDesignFromSigma
decl_use
uniform
in IndisputableMonolith.Information.ShannonEntropy
decl_use
A
in IndisputableMonolith.Masses.Anchor
decl_use
is
in IndisputableMonolith.Mathematics.RamanujanBridge.MockThetaPhantom
decl_use
feasible
in IndisputableMonolith.Measurement.RecognitionAngle.TemporalGating
decl_use
A
in IndisputableMonolith.Modal.Actualization
decl_use
all
in IndisputableMonolith.Musicology.ModalPreferenceFromPhi
decl_use
total
in IndisputableMonolith.NavierStokes.DiscreteVorticity
decl_use
total
in IndisputableMonolith.NumberTheory.RiemannHypothesis.ErrorBudget
decl_use
equilibrium
in IndisputableMonolith.Physics.NonlinearDynamicsFromRS
decl_use