Chirp-array precision (the table-precision form for RF's chirp step): entry flatIx j of chirpArr is within…

Chirp-array precision (the table-precision form for RF's chirp step): entry flatIx j of chirpArr is within d (8T² + 2) 2^{-Δ} of RC.chirp s t j.

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

theorem NLogN.KFM.chirpArr_err (Δ : ℕ) {d : ℕ} (s t : Fin d → ℕ) [∀ i, NeZero (t i)]
    (hst : ∀ i, s i ≤ t i) (T : ℕ) (hT : ∀ i, t i ≤ T)
    (hu : d * (8 * (T : ℝ) ^ 2 + 2) * (2 : ℝ)⁻¹ ^ Δ ≤ 1) (j : (i : Fin d) → ZMod (t i)) :
    ∃ x, (chirpArr Δ d s t)[flatIx d t j]? = some x ∧
      ‖vP Δ x - IntMul.OpenAI.RC.chirp s t j‖ ≤ d * (8 * (T : ℝ) ^ 2 + 2) * (2 : ℝ)⁻¹ ^ Δ

Context. The lemma belongs to the part KFM 9d: the d-axis chirp array — outer products of the axis tables.

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.