pLP_OK (KFV §21: the generated terms are the paper's exponent table)
ProvedNLogN.KFV.pLP_OKThe following holds (Lean statement, in the scope of module Solutions.KFV17Link):
theorem NLogN.KFV.pLP_OK (hK : 0 < K) (hℓ : 1 ≤ ℓ) : (pLP D ℓ K long).OK
Context. The lemma belongs to the part KFV §21: the generated terms are the paper's exponent table.
Formalization Note. This lemma belongs to layer 5 of the Lean formalization (integer-multiplication-kappa campaign) of the OpenAI preprint Integer multiplication below : the uniform item-language machine (register programs over the NLogN multitape framework) assembling the Proposition 14 / Lemma 13 / Proposition 18 pieces, the resampling and chirp stages and the cost recurrences into one fixed machine, culminating in NLogN.KFTop.kappa_bound : IntMul.KappaBound (1 / 2 ^ 182) (the bound of Def_IntMul_MultitapeModel). All names refer to the definition bundles up to IntMul_Kappa_K_Defs33.
-- OpenAI-preprint / κ-improvement development (integer-multiplication-kappa), generated by skeleton subtraction. import Definitions.Def_IntMul_Kappa_K_Defs33 set_option autoImplicit false set_option relaxedAutoImplicit false set_option maxHeartbeats 1000000 set_option linter.unusedSectionVars false set_option linter.unusedSimpArgs false set_option linter.unusedVariables false open NLogN open NLogN.KFV open Finset Synth GlueLayout GlueP14 GlueError variable (D ℓ K : ℕ) [NeZero D] (long : Fin D → Bool)
theorem NLogN.KFV.pLP_OK (hK : 0 < K) (hℓ : 1 ≤ ℓ) : (pLP D ℓ K long).OK := by sorry