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The curve might be skewed to the left. Humanity might be so addicted to oil that it invests every last dollar in beating the logistic bottleneck and develops every remaining 10 barrel/day puddle simultaneously to keep the economic growth cycle going, followed by catastrophic collapse. Time will tell.
That is an alternative hypothesis, and time will tell. However, the extent of investment in new projects is not presently consistent with your hypothesis. It is more consistent with the hypothesis that as new oil becomes more costly to find and develop, the investments will become fewer and farther between, thus delaying the onset of new flows to < the flows lost to depletion.
Even without some sort of hyper development regime, it is not at all self-evident that the global, all-time production distribution is going to be symmetric around the peak. After all, in the past the world GDP and demand was significantly lower at the same time as big finds were easy. Now we are going to have to shrink demand by force, while no more large fields are available. World population and demand are not going to reverse in the future in a mirror image of the past. More likely is that there will be massive inertia trying to keep the status quo, leading to a catastrophic transition. Who knows, maybe magical new power sources will show up and save the day but until then, oil, gas and coal are going to be exploited (gas and coal will delay the crash).