bilC_mrX (KFM 14: the exact side of the error chain)
ProvedNLogN.KFM.bilC_mrXThe following holds (Lean statement, in the scope of module Solutions.KFMErr3):
theorem NLogN.KFM.bilC_mrX (t : Fin (D + 1) → ℕ) [∀ i, NeZero (t i)] : BilC (mrX t)
Context. The lemma belongs to the part KFM 14: the exact side of the error chain: The exact maps of §9.4–9.7 as LinC / BilC instances, and the identities chain_close needs.
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 (field moves, row split/merge, shifts, the uniform Proposition 11 interchange, Lemma 12 with fine -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_Defs20.
-- OpenAI-preprint / κ-improvement development (integer-multiplication-kappa), generated by skeleton subtraction.
import Definitions.Def_IntMul_Kappa_K_Defs20
set_option autoImplicit false
set_option relaxedAutoImplicit false
set_option maxHeartbeats 1000000
open NLogN
open NLogN.KFM
open Complex IntMul.OpenAI.RT IntMul.OpenAI.RC
variable {d : ℕ}
variable {D : ℕ}
theorem NLogN.KFM.bilC_mrX (t : Fin (D + 1) → ℕ) [∀ i, NeZero (t i)] : BilC (mrX t) := by sorry