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formal statement (Lean)
130theorem C_kernel_band :
131 (0.380 : ℝ) < C_kernel ∧ C_kernel < (0.390 : ℝ) := by
proof body
Term-mode proof.
132 rw [C_kernel_eq_two_minus_phi]
133 have h_lo : 1.61 < phi := phi_gt_onePointSixOne
134 have h_hi : phi < 1.62 := phi_lt_onePointSixTwo
135 refine ⟨?_, ?_⟩ <;> linarith
136
137/-! ## §4. The half-rung budget identity
138
139The crown identity: `J(φ) + C = 1/2`. The penalty for one rung crossing
140plus the kernel-amplitude saving fills exactly the half-rung budget.
141-/
142
143/-- The first-rung J-cost penalty has closed form `φ - 3/2`. -/
used by (3)
From the project-wide theorem graph. These declarations reference this one in their body.
depends on (26)
Lean names referenced from this declaration's body.
-
rung
in IndisputableMonolith.Compat.Constants
decl_use
-
phi_gt_onePointSixOne
in IndisputableMonolith.Constants
decl_use
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phi_lt_onePointSixTwo
in IndisputableMonolith.Constants
decl_use
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kernel
in IndisputableMonolith.Cosmology.BITKernelFamilies
decl_use
-
has
in IndisputableMonolith.Engineering.AsteroidOreSpectroscopy
decl_use
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rung
in IndisputableMonolith.Engineering.AsteroidOreSpectroscopy
decl_use
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one
in IndisputableMonolith.Foundation.IntegersFromLogic
decl_use
-
cost
in IndisputableMonolith.Foundation.MultiplicativeRecognizerL4
decl_use
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cost
in IndisputableMonolith.Foundation.ObserverForcing
decl_use
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identity
in IndisputableMonolith.Foundation.ObserverForcing
decl_use
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one
in IndisputableMonolith.Foundation.RationalsFromLogic
decl_use
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for
in IndisputableMonolith.Foundation.UniversalForcingSelfReference
decl_use
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C_kernel
in IndisputableMonolith.Gravity.ILGSpatialKernel
decl_use
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C_kernel_eq_two_minus_phi
in IndisputableMonolith.Gravity.ILGSpatialKernel
decl_use
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kernel
in IndisputableMonolith.ILG.Kernel
decl_use
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rung
in IndisputableMonolith.Masses.AnchorPolicy
decl_use
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rung
in IndisputableMonolith.Masses.RSBridge.Anchor
decl_use
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amplitude
in IndisputableMonolith.QFT.SMatrixUnitarity
decl_use
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half
in IndisputableMonolith.QFT.SpinStatistics
decl_use
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one
in IndisputableMonolith.QFT.SpinStatistics
decl_use
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amplitude
in IndisputableMonolith.Quantum.DoubleSlit
decl_use
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half
in IndisputableMonolith.RecogSpec.Core
decl_use
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one
in IndisputableMonolith.RecogSpec.Core
decl_use
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identity
in IndisputableMonolith.RRF.Foundation.VantageCategory
decl_use
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rung
in IndisputableMonolith.RSBridge.Anchor
decl_use
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half
in IndisputableMonolith.Support.RungFractions
decl_use