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Re:OpenAI Withdraws 3 Math Papers by peri-cl on Thursday October 08, 2026 @09:24AM (#50005554)
Surely it's a galactic algorithm that you can't physically run? You wouldn't get a constant as small as 2^{-182} without some other numbers elsewhere being incredibly large.

From the "Introduction" section of that paper: "The constants and thresholds in the construction are extremely large".

(And verifying if the algorithm multiplies correctly or not is the less-interesting part of this, anyway. Gets you no closer to verifying the complexity result).

Re:OpenAI Withdraws 3 Math Papers by hyperbovine on Thursday October 08, 2026 @09:40AM (#50005692)
Isn't it possible that all of the integers that have been or will ever be encountered, anywhere, any time, in human history, number less than 2^182? In which case you could argue that integer multiplication is O(1) via LUT :)
Re:OpenAI Withdraws 3 Math Papers by measurablefunc on Thursday October 08, 2026 @11:45AM (#50007246)
Everything is a lookup table in non-standard arithmetic but that's not useful for someone writing the code b/c they don't have access to non-standard integers & have to write an algorithm to reconstruct it.
Re:OpenAI Withdraws 3 Math Papers by auspiv on Thursday October 08, 2026 @09:44AM (#50005739)
someone else picked up that bit of math and has run with it and has refined it downwards multiple times. believe it is now in the range of 2^-18 or so
Re:OpenAI Withdraws 3 Math Papers by throwaway198846 on Thursday October 08, 2026 @10:28AM (#50006259)
Where?
Re:OpenAI Withdraws 3 Math Papers by auspiv on Thursday October 08, 2026 @11:38AM (#50007152)
@SJ_Swapnil_Jain on X for announcements

repo - https://github.com/swapnil-jain/integer-mult-kappa