fsetZ_rowAddr (KFR: the packed layout of three rows and the row addition as an address map)

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

theorem NLogN.KFR.fsetZ_rowAddr (st : Fin m × Fin f → ℕ) (q : ℕ) (i j : Fin m) (hij : i ≠ j) :
    fsetZ st q (rowAddr i j (fbit st q)) =
      (q : ℤ) + ∑ u ∈ Finset.range f, rowTerm st q i j (f - 1 - u)

Context. The lemma belongs to the part KFR: the packed layout of three rows and the row addition as an address map: For a stride-K row family (pos (r, c) + K (c + f r) = e, f = m^k, AffK2), the rows a < b < c (σ : Fin 3 → Fin m strictly monotone) are the three chunk slots of the rectangle rect N0 N1 N2 N3 (fK) (rectN), with offset ρ' = e mod K: row r occupies the address bits [sR r, sR r + fK) of the record index divided by S₀, its bit f-1-u at sR r + ρ' + uK (pos_eq_sR).

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.