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COVID-19 vaccines have gone into Californians’ arms at a record rate this week, a promising acceleration that comes even as officials continue to warn of constrained supplies in the near future and as the state stubbornly lags behind many others in how widely the doses are being distributed.

The last six days have seen the six highest single-day totals of shots given out statewide, according to data compiled by The Times. During that stretch, roughly 2.35 million doses were administered statewide — including 344,489 on Thursday and 387,015 on Friday.

The recent torrent of inoculations, however, belies the major challenge that has and will continue to stymie the race to vaccinate as many Californians as quickly as possible, at least in the immediate future: a shortage of supply.

“We don’t have enough vaccines. I could double the capacity today if you got me those vaccines,” Los Angeles Mayor Eric Garcetti said Friday during an interview with Dr. Howard Koh, a professor at the Harvard T.H. Chan School of Public Health.

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