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formal statement (Lean)
122theorem cost_descent_step {f : ℝ → ℝ} (hf : RecognitionDescent f)
123 {r : ℝ} (hr : 0 < r) (hne : r ≠ 1) :
124 Cost.Jcost (f r) < Cost.Jcost r :=
proof body
Term-mode proof.
125 hf.strict_descent_off r hr hne
126
127/-! ## §5. Equilibrium is the unique zero of the J-cost -/
128
used by (1)
From the project-wide theorem graph. These declarations reference this one in their body.
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pidStabilityCert
in IndisputableMonolith.Robotics.PIDStabilityFromJCost
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depends on (13)
Lean names referenced from this declaration's body.
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of
in IndisputableMonolith.Astrophysics.NucleosynthesisTiers
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of
in IndisputableMonolith.Foundation.DAlembert.LedgerFactorization
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cost
in IndisputableMonolith.Foundation.MultiplicativeRecognizerL4
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cost
in IndisputableMonolith.Foundation.ObserverForcing
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is
in IndisputableMonolith.Foundation.OptionAEmpiricalProgram
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of
in IndisputableMonolith.Foundation.PhiForcingDerived
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is
in IndisputableMonolith.Foundation.SimplicialLedger.EdgeLengthFromPsi
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of
in IndisputableMonolith.Foundation.SpectralEmergence
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is
in IndisputableMonolith.GameTheory.MechanismDesignFromSigma
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of
in IndisputableMonolith.Information.PhysicsComplexityStructure
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is
in IndisputableMonolith.Mathematics.RamanujanBridge.MockThetaPhantom
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Cost
in IndisputableMonolith.Measurement.RSNative.Core
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RecognitionDescent
in IndisputableMonolith.Robotics.PIDStabilityFromJCost
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