selOpF_Pm (KFR: `permRecs` realises the row operator `Pm i j`, and the statement `Lem13ILP`)

The following holds (Lean statement, in the scope of module Solutions.KFRPerm):

theorem NLogN.KFR.selOpF_Pm {m r : ℕ} {κ : Type} [Fintype κ] [DecidableEq κ] (st : Fin m × κ → ℕ) (n : ℕ)
    (i j : Fin m) (xs : List (Fin r → ℂ)) :
    selOpF st n (Pm i j : Butterfly.Op (Fin m × κ)) xs =
      (List.range n).map fun q => xs.getD (fset st q (rowAddr i j (fbit st q))) 0

Context. The lemma belongs to the part KFR: permRecs realises the row operator Pm i j, and the statement Lem13ILP.

Formalization Note. This lemma belongs to the item-language (IL) layer of the integer-multiplication-kappa campaign: tape-level programs (register programs over 64 item stacks of the NLogN multitape framework, definition bundles IntMul_HvdH_M_Defs1–IntMul_HvdH_M_Defs8) that implement the data-movement primitives of the OpenAI preprint Integer multiplication below $n\log n$ (field moves, row split/merge, shifts, the uniform Proposition 11 interchange, Lemma 12 with fine $O(1)$-per-element costs, Gaussian record primitives, Proposition 14 pieces) with exact list denotations from the array-model bundles IntMul_Kappa_K_Defs* and explicit cost bounds. All names refer to the definition bundles up to IntMul_Kappa_K_Defs22.