Fpp_conj (KFL §17: `permRecs (rowAddAddr …)` as a triple map on the bit array)

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

theorem NLogN.KFL.Fpp_conj (K ρ f : ℕ) (px py : Fin 3) (hne : px ≠ py) (c : Tr) :
    Fpp K ρ f px py c = (compL (preL px py) ∘ RAc K ρ f ∘ compL (preL px py).reverse) c

Context. The lemma belongs to the part KFL §17: permRecs (rowAddAddr …) as a triple map on the bit array: The Gaussian records (R entries, 2 (w+1) bits per entry after toBitsI) of the rectangle rect N0 N1 N2 N3 L form the bit array of the geometry geoB (Q = 2^L, B = 2 R (w+1)). bits_permRecs: converting permRecs rect (rowAddAddr px py) R zs to bits gives rixT (geoB …) (Fpp px py) of the bits of zs, where Fpp px py replaces slot py by y ⊕ (x ∧ selM f) (x = slot px). Fpp_conj: Fpp px py is the canonical row addition RAc conjugated by at most two slot swaps.

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.