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Why is the difference between adjusted close and close price slightly different between each day?
Prices are adjusted for return and not payout.  So if you take the ratio of the close price and the adjusted close price, it should remain constant. The idea behind a total return (back-)adjustment is to give you a feeling how much money you would have needed back then to reach the price today under the premise that all distributions (dividends, spin-offs, etc.) are reinvested instantly and that reinvestment doesn't cost anything.