recognition /
Information /
Information.InformationIsLedger /
explainer
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formal statement (Lean)
98 theorem balanced_has_minimum_cost (e : RecognitionEvent) :
99 infoCost balancedEvent ≤ infoCost e := by
proof body
Term-mode proof.
100 unfold infoCost balancedEvent
101 rw [Jcost_unit0]
102 exact Jcost_nonneg e.ratio_pos
103
104 /-- **THEOREM IC-001.6**: The balanced state is the unique minimum.
105 It is the only state where no additional information is encoded. -/
used by (1)
From the project-wide theorem graph. These declarations reference this one in their body.
depends on (17)
Lean names referenced from this declaration's body.
Jcost_nonneg
in IndisputableMonolith.Cost
decl_use
Jcost_unit0
in IndisputableMonolith.Cost
decl_use
Jcost_nonneg
in IndisputableMonolith.Cost.JcostCore
decl_use
Jcost_unit0
in IndisputableMonolith.Cost.JcostCore
decl_use
balanced
in IndisputableMonolith.Foundation.LedgerForcing
decl_use
RecognitionEvent
in IndisputableMonolith.Foundation.LedgerForcing
decl_use
RecognitionEvent
in IndisputableMonolith.Foundation.ObserverForcing
decl_use
is
in IndisputableMonolith.Foundation.OptionAEmpiricalProgram
decl_use
is
in IndisputableMonolith.Foundation.SimplicialLedger.EdgeLengthFromPsi
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
balancedEvent
in IndisputableMonolith.Information.InformationIsLedger
decl_use
infoCost
in IndisputableMonolith.Information.InformationIsLedger
decl_use
RecognitionEvent
in IndisputableMonolith.Information.InformationIsLedger
decl_use
is
in IndisputableMonolith.Mathematics.RamanujanBridge.MockThetaPhantom
decl_use
Jcost_nonneg
in IndisputableMonolith.NavierStokes.PhiLadderCutoff
decl_use