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formal statement (Lean)
19class ConeEntropyFacts : Prop where
20 cone_entropy_bound :
21 ∀ {α : Type _} (cone : LightCone α) (area : ℝ),
22 entropy cone ≤ area / (4 * λ_rec^2)
23
24section
25
26variable {α : Type _}
27variable (K : Causality.Kinematics α)
28variable (U : Constants.RSUnits)
29variable (time rad : α → ℝ)
30
31/-- Verification-level cone bound: if per-step bounds hold, any `n`-step reach obeys
32 `rad y - rad x ≤ U.c * (time y - time x)` with no `n` in the statement. -/
used by (2)
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.
-
Kinematics
in IndisputableMonolith.Causality.Basic
decl_use
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Kinematics
in IndisputableMonolith.Causality.ConeBound
decl_use
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Kinematics
in IndisputableMonolith.Causality.Reach
decl_use
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step
in IndisputableMonolith.Complexity.CellularAutomata
decl_use
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cone_entropy_bound
in IndisputableMonolith.ConeExport.Theorem
decl_use
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K
in IndisputableMonolith.Constants
decl_use
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RSUnits
in IndisputableMonolith.Constants
decl_use
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K
in IndisputableMonolith.Constants.LambdaRecDerivation
decl_use
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U
in IndisputableMonolith.Constants.RSNativeUnits
decl_use
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Constants
in IndisputableMonolith.CPM.LawOfExistence
decl_use
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entropy
in IndisputableMonolith.Foundation.InitialCondition
decl_use
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Kinematics
in IndisputableMonolith.LedgerUniqueness
decl_use
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Kinematics
in IndisputableMonolith.LightCone.StepBounds
decl_use
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U
in IndisputableMonolith.Recognition
decl_use
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entropy
in IndisputableMonolith.Thermodynamics.BoltzmannDistribution
decl_use
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entropy
in IndisputableMonolith.Thermodynamics.PartitionFunction
decl_use
-
RSUnits
in IndisputableMonolith.TruthCore.Display
decl_use