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formal statement (Lean)
26noncomputable def Upsilon (P : ILG.KernelParams) (a : ℝ) : ℝ :=
proof body
Definition body.
27 if a ≤ 0 then 1 else 1 + P.C * a ^ P.alpha
28
29/-- The modified Sachs focusing equation (Target G).
30 For angular diameter distance D_A along an affine parameter λ:
31 d²D_A/dλ² + (1/2) * Upsilon(a) * R_μν k^μ k^ν * D_A = 0
32 where Ricci focusing is rescaled by Upsilon. -/
used by (6)
From the project-wide theorem graph. These declarations reference this one in their body.
depends on (10)
Lean names referenced from this declaration's body.
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G
in IndisputableMonolith.Constants
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alpha
in IndisputableMonolith.Constants.Alpha
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G
in IndisputableMonolith.Constants.Codata
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G
in IndisputableMonolith.Cost.FunctionalEquation
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is
in IndisputableMonolith.Foundation.OptionAEmpiricalProgram
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is
in IndisputableMonolith.Foundation.SimplicialLedger.EdgeLengthFromPsi
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is
in IndisputableMonolith.GameTheory.MechanismDesignFromSigma
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G
in IndisputableMonolith.Gravity.JCostInflaton
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KernelParams
in IndisputableMonolith.ILG.Kernel
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is
in IndisputableMonolith.Mathematics.RamanujanBridge.MockThetaPhantom
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