Bounded consecutive prime gaps

How small can infinitely many gaps between consecutive primes be proved to be?

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Understanding the problem

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How small can infinitely many gaps between consecutive primes be proved to be?

Why it matters

A smaller unconditional upper bound strengthens what is known about how closely primes recur.

What counts as progress

Can an argument prove an unconditional liminf bound for consecutive prime gaps below the previous record?

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