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This is about whether it can actually exist (i.e. is obtainable) in the real universe we are in, not whether it could exist in some other universe that follows most of the same laws. Resolves YES if it's proven that we can create it, or perhaps that it exists as a leftover from the big bang. Resolves NO once we have a theory of everything that says it can't exist. If it can technically be created but decays on the order of a Planck time, I'll also count that as a NO.
Possible clarification from creator (AI generated): Either negative gravitational mass or negative inertial mass would be sufficient for a YES resolution.
February 2nd, 2133. Finally, the AIs have completed the last ever experiment and proven the Theory of Everything. The missing piece has been the decay time of negative mass. The recently completed Transsolar Accelerator used up 99.93% of the Earths mass and was able to create -4.3kg of mass, answering the centuries-old question whether negative mass exists with a clear Yes. Fun fact: The decay time has now been proven to be exactly Pi Plank Times. The famous Manifold question "Can negative mass exist?" just resolved No, accordingly.
Discarding actual experiments able to actually create negative mass, just on the grounds of negative mass not existing long enough seems needlessly strict.