Candle memory seems to exist! However, it only happens when the “hole” in the candle is larger than 3/4" and smaller than 2" diameter. However, there are other effects which masquerated as candle memory. Also, my testing was done on cast paraffin candles with a small string wicks in a 70degF environment, so maybe things will different under other conditions.
Here’s the most interesting part.
With a very wide candle, if I artifically force the melt-pool diameter to become larger than two inches, it will be unstable, and the size contracts to approximately 2" and then stops shrinking.
On the other hand, if I dig out a narrow hole surrounding the wick in order to force the melt-pool to be very small, it will be unstable, and it will expand to between 3/4" and 1" diameter… and then stop growing.
Apparently there is a range of sizes of hole-diameter where once a surrounding “lip” has formed, the melt-pool will neither grow nor shrink in diameter. On the other hand, if your huge candle ends up boring a 2" diameter hole through the center… that’s normal. The flame doesn’t put out enough energy to make the melt pool bigger than that.
I had trouble producing a smaller candle-hole simply by lighting a candle and then blowing it out prematurely. When re-lit, the melt pool grew right past the older diameter with no problem. Only if the melt-pool had dug a hole for itself a little deeper than about 3/16" deep, only then would the pool be unable to eat its way through the surrounding “cliff” and continue to expand to 2" diameter.
One possible conclusion: people light candles and then REPEATEDLY blow them out prematurely. This would let the flame consume lots of wax and eat its way down into the candle during each burn-period, rather than creating a 2" melt pool during a much longer burn.
Another possibility: cheap candles. I encountered candles made from rammed-powder wax rather than cast solid wax. They’re full of air, and the flame eats rapidly downwards into the wax much faster than it does with a solid cast block of paraffin. Perhaps if these kinds of candles were blown out prematurely, they would become trapped in the “small melt-pool” mode. And perhaps the lower limit would be less than 3/4" diameter (but I didn’t test these things.)
Another possibility: cold environment. At 70degF the melt-pool would grow to 2", but it grew very slowly as it approached its final size. If the room temperature was far lower, the melt pool and the resulting hole would no doubt be significantly smaller, yet this would have nothing to do with “candle memory.”
Another interesting bit: convection of liquid wax in the melt-pool delivers hot wax all the way to the border of the melt-pool. The hot wax even crawls up a steep incline as a thin film before settling deeper to the solid wax surface and returning inwards to the center. I put lots of bits of soot as tracer particles in the melt pools, and could watch the high-speed outward motion of the surface layer of the liquid wax (and the low-speed opposite motion of wax throughout the rest of the volume of the melt pool.)