Busy Beaver
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Hardness as an Information Constraint: A Unifying Meta-Complexity Assumption
Announce Type: new Abstract: Monroe (2026) shows that the nonexistence of an optimal proof system can be read as an information constraint regarding canonical hard instances: no sound arithmetic theory simulates the extensions adjoining sufficiently large, unprovable Busy Beaver values. Furthermore, if the best-known route to simulation is also necessary -- that is, if simulation requires a relative-consistency explanation over a weak base theory -- then the same constraint holds for...
Puffins, dolphins and bumblebees in running to feature on new UK banknotes
Bank of England says updated imagery will celebrate native wildlife while bolstering anti-counterfeit featuresPuffins, dolphins and bumblebees are among the wildlife that could feature on new banknotes in the UK as the Bank of England announces its shortlist. There has been controversy over the decision, with figures including Nigel Farage criticising the Bank for, he claimed, wanting to replace Winston Churchill with a beaver. The Conservative leader, Kemi Badenoch, said it was “a silly...