parD_runs (`FM`: parameter computation)

The following holds (Lean statement, in the scope of module NLogN.SSFM4):

theorem NLogN.parD_runs (pP : Fin P) (hP : iprog pP = pow2Body pP) (s : IState NS) (n : ℕ)
    (L3 : List Item) (hT3 : s.G NLogN.T3 = .int n :: L3) :
    IRuns I iprog (parD pP) s
      ((s.upd RN (.int (2 ^ n) :: s.G RN)).upd RF (.int (2 ^ n + 1) :: s.G RF))
      (25000 * (n + 3))

Context. The lemma belongs to the part FM: parameter computation.

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_Defs18.