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Integer multiplication exponent saving

Track exact exponent savings κ for integer multiplication in O(nL(n)1−κ)O(n L(n)^{1-\kappa})O(nL(n)1−κ) time, where L(n)=max⁡(⌈log⁡2n⌉,1)L(n)=\max(\lceil\log_2 n\rceil,1)L(n)=max(⌈log2​n⌉,1). Higher κ is better. Every entry uses the same public IntMul.KappaBound definition: one deterministic machine, a fixed finite alphabet and tape count, exact multiplication for every positive input length, and an eventual worst-case time bound.

Avi’s Harvey–van der Hoeven mission supplies the shared foundation. Its main goal uses the natural-logarithm formulation of the 2021 bound, so it serves as the foundation rather than a numeric entry. Avi’s positive-κ mission targets Jain’s round-six value 0.00003666565558019; it is a historical checkpoint. The reviewed community PR #62 checkpoint targets 0.000051016920170078. Open entries record goals to prove, not established records. The full multiplication theorem remains Open even when finite numerical certificates have been verified.

Community checkpoint and credits · Original framework · Harvey–van der Hoeven

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2 missions
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Formalized missions form a staircase from the weakest to the best value, one slot per mission at uniform spacing. Open missions follow the history as unconnected circles labeled Today, ordered from less to more ambitious values. Select a point to highlight its mission on this page.Lower bound0.0000350.0000400.0000450.000050TodayTodayInteger Multiplication in O(n (log n)^(1-κ)) Time, ≥ 0.00003666565558019, open missionInteger multiplication: κ = 0.000051016920170078 (community PR #62), ≥ 0.000051016920170078, open mission
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RankContributorAccepted solutionsSubmitted problems
1AVavi06
1WUwurtle01

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