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formal statement (Lean)
64noncomputable def critical_density : ℝ :=
proof body
Definition body.
65 -- H₀ ~ 70 km/s/Mpc ~ 2.3e-18 s⁻¹
66 3 * (2.3e-18)^2 / (8 * Real.pi * G)
67
68/-! ## Why Is Flatness A Problem? -/
69
70/-- The equation for Ω evolution:
71
72 |Ω - 1| ∝ a²(t) in radiation domination
73 |Ω - 1| ∝ a(t) in matter domination
74
75 So deviations from 1 GROW with time!
76 Ω = 1 is an unstable equilibrium (like balancing a pencil). -/
depends on (14)
Lean names referenced from this declaration's body.
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G
in IndisputableMonolith.Constants
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G
in IndisputableMonolith.Constants.Codata
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G
in IndisputableMonolith.Cost.FunctionalEquation
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A
in IndisputableMonolith.Foundation.IntegrationGap
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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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for
in IndisputableMonolith.Foundation.UniversalForcingSelfReference
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is
in IndisputableMonolith.GameTheory.MechanismDesignFromSigma
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G
in IndisputableMonolith.Gravity.JCostInflaton
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A
in IndisputableMonolith.Masses.Anchor
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is
in IndisputableMonolith.Mathematics.RamanujanBridge.MockThetaPhantom
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A
in IndisputableMonolith.Modal.Actualization
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equilibrium
in IndisputableMonolith.Physics.NonlinearDynamicsFromRS
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