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Foundation /
Foundation.VariationalDynamics /
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formal statement (Lean)
343 theorem variational_step_reduces_defect {N : ℕ}
344 (c next : Configuration N)
345 (h : IsVariationalSuccessor c next) :
346 total_defect next ≤ total_defect c :=
proof body
Term-mode proof.
347 h.2 c (self_feasible c)
348
349 /-! ## Deterministic Evolution -/
350
351 /-- **Definition**: A ledger trajectory is a sequence of configurations
352 indexed by tick count. -/
used by (3)
From the project-wide theorem graph. These declarations reference this one in their body.
depends on (21)
Lean names referenced from this declaration's body.
of
in IndisputableMonolith.Astrophysics.NucleosynthesisTiers
decl_use
tick
in IndisputableMonolith.Constants
decl_use
tick
in IndisputableMonolith.Constants.RSNativeUnits
decl_use
of
in IndisputableMonolith.Foundation.DAlembert.LedgerFactorization
decl_use
Configuration
in IndisputableMonolith.Foundation.InitialCondition
decl_use
total_defect
in IndisputableMonolith.Foundation.InitialCondition
decl_use
A
in IndisputableMonolith.Foundation.IntegrationGap
decl_use
is
in IndisputableMonolith.Foundation.OptionAEmpiricalProgram
decl_use
of
in IndisputableMonolith.Foundation.PhiForcingDerived
decl_use
Configuration
in IndisputableMonolith.Foundation.RecognitionForcing
decl_use
is
in IndisputableMonolith.Foundation.SimplicialLedger.EdgeLengthFromPsi
decl_use
of
in IndisputableMonolith.Foundation.SpectralEmergence
decl_use
IsVariationalSuccessor
in IndisputableMonolith.Foundation.VariationalDynamics
decl_use
self_feasible
in IndisputableMonolith.Foundation.VariationalDynamics
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
trajectory
in IndisputableMonolith.Robotics.PIDStabilityFromJCost
decl_use
next
in IndisputableMonolith.RRF.Hypotheses.EightTick
decl_use