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Does the time-lagged correlation between CO2$\ce{CO2}$ and ocean temperature have a shorter timelag than the one between CO2$\ce{CO2}$ and air temperature?

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Does the time-lagged correlation between CO2 and ocean temperature have a shorter timelag than the one between CO2 and air temperature?

I'm talking about evidence from both proxy records in the last 50,000 years (if possible) and the recent past (if also possible)