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The open price is the price of the first order in that timespan -- the time start/end are just aggregation limits for orders. Technically a bar doesn't have a price until the first order executes in that time window.

As only the orders matter, the time is just how we break up the order into buckets. So there is no price at "10:01:00.000000" unless an order executed at "10:01:00.000000". If the first order after the clock strikes "10:01:00.000000" happens at "10:01:02.473829" that is the open price for the bar we lump the orders from 10:01:00.0000 and 10:01:59.9999999 together for and call "10:01".

Same for the close price -- its the last order in the time period. It can happen at any time within the time window, and might come before "10:00.59.99999".

Order #1 @ "10:00.58.435321": $5.00
Order #2 @ "10:01:02.473829": $5.02 you...

10:00: Close $5.00
10:01: Open $5.02

Open and close prices are only ever the same if those two sequenced orders on either side of a time threshold happen to execute for the same price.

In other words, bars don't exist. Only orders exist.

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