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formal statement (Lean)
59 theorem jcost_squared_form (x : ℝ) (hx : x > 0) :
60 Jcost x = (x - 1)^2 / (2 * x) :=
proof body
Term-mode proof.
61 Cost.Jcost_eq_sq hx.ne'
62
63 /-- **THEOREM IC-005.4**: J-cost is strictly positive away from x = 1.
64 The "violation" from the ground state is proportional to (x-1)²/(2x) > 0. -/
used by (7)
From the project-wide theorem graph. These declarations reference this one in their body.
depends on (12)
Lean names referenced from this declaration's body.
Jcost_eq_sq
in IndisputableMonolith.Cost
decl_use
Jcost_eq_sq
in IndisputableMonolith.Cost.JcostCore
decl_use
jcost_squared_form
in IndisputableMonolith.CrossDomain.JConvexityUniversality
decl_use
jcost_squared_form
in IndisputableMonolith.Foundation.JCostGeometry
decl_use
cost
in IndisputableMonolith.Foundation.MultiplicativeRecognizerL4
decl_use
cost
in IndisputableMonolith.Foundation.ObserverForcing
decl_use
is
in IndisputableMonolith.Foundation.OptionAEmpiricalProgram
decl_use
from
in IndisputableMonolith.Foundation.PrimitiveDistinction
decl_use
is
in IndisputableMonolith.Foundation.SimplicialLedger.EdgeLengthFromPsi
decl_use
is
in IndisputableMonolith.GameTheory.MechanismDesignFromSigma
decl_use
is
in IndisputableMonolith.Mathematics.RamanujanBridge.MockThetaPhantom
decl_use
Cost
in IndisputableMonolith.Measurement.RSNative.Core
decl_use