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formal statement (Lean)
108structure EnergyProcessingEquivalence where
109 /-- J-cost at balance is zero (existence is free) -/
110 balance_zero_cost : Jcost 1 = 0
111 /-- J-cost away from balance is positive (deviation costs) -/
112 deviation_positive_cost : ∀ x : ℝ, 0 < x → x ≠ 1 → 0 < Jcost x
113 /-- J-cost matches kinetic energy in weak field: J(1+ε) = ε²/(2(1+ε)) -/
114 quadratic_energy_bridge : ∀ ε : ℝ, -1 < ε →
115 Jcost (1 + ε) = ε ^ 2 / (2 * (1 + ε))
116 /-- Energy creates processing field -/
117 energy_sources_processing : ∀ (e : EnergyDistribution) (G : ℝ),
118 ∃ pf : ProcessingField, pf = energy_to_processing_field e G
119
120/-- The energy-processing bridge is proved from RS first principles. -/
used by (2)
From the project-wide theorem graph. These declarations reference this one in their body.
depends on (16)
Lean names referenced from this declaration's body.
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bridge
in IndisputableMonolith.ClassicalBridge.Fluids.CPM2D
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G
in IndisputableMonolith.Constants
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G
in IndisputableMonolith.Constants.Codata
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Energy
in IndisputableMonolith.Constants.RSNativeUnits
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G
in IndisputableMonolith.Cost.FunctionalEquation
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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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from
in IndisputableMonolith.Foundation.PrimitiveDistinction
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is
in IndisputableMonolith.Foundation.SimplicialLedger.EdgeLengthFromPsi
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is
in IndisputableMonolith.GameTheory.MechanismDesignFromSigma
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ProcessingField
in IndisputableMonolith.Gravity.CoherenceFall
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EnergyDistribution
in IndisputableMonolith.Gravity.EnergyProcessingBridge
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energy_to_processing_field
in IndisputableMonolith.Gravity.EnergyProcessingBridge
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G
in IndisputableMonolith.Gravity.JCostInflaton
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is
in IndisputableMonolith.Mathematics.RamanujanBridge.MockThetaPhantom
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