The κ bound, conditional only on uniform Prop 14 at some gate constant A ≤ Wc²
ProvedNLogN.KFTop.kappa_of_P14Uat_leThe κ bound, conditional only on uniform Prop 14 at some gate constant A ≤ Wc².
The following holds (Lean statement, in the scope of module Solutions.KFTop):
theorem NLogN.KFTop.kappa_of_P14Uat_le (A : ℕ) (HU : KFV.P14Uat A) (hA : A ≤ KFAz.A0) :
IntMul.KappaBound (1 / 2 ^ 182)
Context. The lemma belongs to the part The κ machine: top-level reduction: KappaBound (1/2^182) from the remaining uniform interfaces.
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 open NLogN
theorem NLogN.KFTop.kappa_of_P14Uat_le (A : ℕ) (HU : KFV.P14Uat A) (hA : A ≤ KFAz.A0) :
IntMul.KappaBound (1 / 2 ^ 182) := by sorry