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theorem proved term proof

kernel_background_independent_of_params

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formal statement (Lean)

 357theorem kernel_background_independent_of_params (P : KernelParams) :
 358    kernel_background = 1 := rfl

proof body

Term-mode proof.

 359
 360/-- **The mode partition.** For a density field `ρ = ρ̄ + δρ` with
 361homogeneous mean `ρ̄` and zero-mean fluctuation `δρ`, the ILG-modified
 362Poisson source decomposes as
 363\[ \rho_{\rm eff}(k,a) = \bar\rho \cdot k_{\rm bg} + \delta\rho(k) \cdot
 364  w_{\rm pert}(k_{\min}, k, a), \]
 365with the background factor `k_bg = 1` and the perturbation factor
 366saturated at `kernel_perturbation P k_min k_min a`. -/

depends on (7)

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