Exact integer multiplication with saving κ = 1/2^182
ProvedIntMul.Kappa.campaign_bound_inv_two_pow_182complexity-theoryinteger-multiplicationturing-machines
There exists one deterministic multitape Turing machine, with fixed finite alphabet and tape count, that correctly multiplies every pair of n-bit inputs for all n ≥ 1, with worst-case time O(n L(n)^(1−κ)) for κ = 1/2^182, where L(n) = max(ceil(log₂ n), 1). This is the full bound with no assumed algorithmic or analytic framework.
Preamble
import Definitions.Def_IntMul_MultitapeModel
Formal statement
namespace IntMul.Kappa theorem campaign_bound_inv_two_pow_182 : KappaBound ((1 / 2 ^ 182) : ℝ) := by sorry end IntMul.Kappa
Source
Human review
Confirmed by the mission captain (proposal self-audit).
Confirmed by the moderator at approval.