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theorem proved term proof

poisson_operator_perturbation_kernel_bounded

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formal statement (Lean)

 107theorem poisson_operator_perturbation_kernel_bounded
 108    (P : KernelParams) {k_min : ℝ} (hkmin : 0 < k_min)
 109    {a : ℝ} (ha : 0 < a) (k : ℝ) :
 110    kernel_perturbation P k_min k a
 111      ≤ 1 + P.C * (max 0.01 (a / (k_min * P.tau0))) ^ P.alpha :=

proof body

Term-mode proof.

 112  kernel_perturbation_bounded_above P hkmin ha k
 113
 114/-- **Background-mode invariance.** When the perturbation `δρ = 0` (pure
 115homogeneous configuration), the perturbation operator vanishes and only
 116the standard FRW background remains. This is the operator-level statement
 117that the ILG kernel does not affect the homogeneous mode. -/

depends on (15)

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