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formal statement (Lean)
46 theorem jcost_nonneg (x : ℝ) (hx : x > 0) : Jcost x ≥ 0 :=
proof body
Term-mode proof.
47 Cost.Jcost_nonneg hx
48
49 /-- **THEOREM IC-005.2**: J-cost has a unique minimum at x = 1.
50 This proves that the "ground state" of RS is uniquely determined
51 and can be verified in constant time. -/
used by (6)
From the project-wide theorem graph. These declarations reference this one in their body.
measureTheoryCert
in IndisputableMonolith.Mathematics.MeasureTheoryFromRS
decl_use
MeasureTheoryCert
in IndisputableMonolith.Mathematics.MeasureTheoryFromRS
decl_use
entropyArrowCert
in IndisputableMonolith.Physics.EntropyArrowFromJCost
decl_use
jcost_nonneg
in IndisputableMonolith.Physics.EntropyArrowFromJCost
decl_use
jcost_nonneg
in IndisputableMonolith.Physics.TachyonFreeTachyonFromRS
decl_use
tachyonFreeCert
in IndisputableMonolith.Physics.TachyonFreeTachyonFromRS
decl_use
depends on (23)
Lean names referenced from this declaration's body.
of
in IndisputableMonolith.Astrophysics.NucleosynthesisTiers
decl_use
Jcost_nonneg
in IndisputableMonolith.Cost
decl_use
Jcost_nonneg
in IndisputableMonolith.Cost.JcostCore
decl_use
has
in IndisputableMonolith.Engineering.AsteroidOreSpectroscopy
decl_use
of
in IndisputableMonolith.Foundation.DAlembert.LedgerFactorization
decl_use
cost
in IndisputableMonolith.Foundation.MultiplicativeRecognizerL4
decl_use
cost
in IndisputableMonolith.Foundation.ObserverForcing
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
is
in IndisputableMonolith.GameTheory.MechanismDesignFromSigma
decl_use
Jcost_nonneg
in IndisputableMonolith.Gravity.CoherenceCollapse
decl_use
Jcost_nonneg
in IndisputableMonolith.Gravity.EnergyProcessingBridge
decl_use
of
in IndisputableMonolith.Information.PhysicsComplexityStructure
decl_use
is
in IndisputableMonolith.Mathematics.RamanujanBridge.MockThetaPhantom
decl_use
Cost
in IndisputableMonolith.Measurement.RSNative.Core
decl_use
Jcost_nonneg
in IndisputableMonolith.NavierStokes.PhiLadderCutoff
decl_use
and
in IndisputableMonolith.NumberTheory.CirclePhaseLift
decl_use
that
in IndisputableMonolith.NumberTheory.PhiLadderLattice
decl_use
jcost_nonneg
in IndisputableMonolith.Physics.EntropyArrowFromJCost
decl_use
jcost_nonneg
in IndisputableMonolith.Physics.TachyonFreeTachyonFromRS
decl_use
constant
in IndisputableMonolith.Relativity.Fields.Scalar
decl_use