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formal statement (Lean)
541theorem equilibrium_attractive {N : ℕ}
542 (traj : Trajectory N)
543 (h : IsVariationalTrajectory traj) :
544 (∀ t, total_defect (traj (t + 1)) ≤ total_defect (traj t)) ∧
545 (∀ t, 0 ≤ total_defect (traj t)) :=
proof body
Term-mode proof.
546 ⟨trajectory_defect_monotone traj h, fun t => total_defect_nonneg (traj t)⟩
547
548/-! ## The Uniform Minimizer (Explicit Solution) -/
549
550/-- The uniform configuration with charge σ: all entries equal exp(σ/N). -/
depends on (10)
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
-
total_defect
in IndisputableMonolith.Foundation.InitialCondition
decl_use
-
total_defect_nonneg
in IndisputableMonolith.Foundation.InitialCondition
decl_use
-
IsVariationalTrajectory
in IndisputableMonolith.Foundation.VariationalDynamics
decl_use
-
Trajectory
in IndisputableMonolith.Foundation.VariationalDynamics
decl_use
-
trajectory_defect_monotone
in IndisputableMonolith.Foundation.VariationalDynamics
decl_use
-
uniform
in IndisputableMonolith.Information.ShannonEntropy
decl_use
-
all
in IndisputableMonolith.Musicology.ModalPreferenceFromPhi
decl_use