However the fact remains that if fermentation is complete and you crash cool, you will not magically get co2 from absolutely nowhere to dissolve into solution. That is physics and it's rather simple, with not much need for math, it's more of a concept.
This sums up the situation perfectly I believe. Crash cooled beer may absorb a tiny amount of co2 back into solution but the amount of co2 available to reabsorb is tiny and it is not going to pull it out of co2-thin air. The amount of headspace in my carboy while crash cooling is a few ounces. This, if absorbed would account for less than .01 of a volume in the beer.
Saying that because Palmer or BeerSmith say carb level is determined by temp at bottling it must be true is just wrong. They should be corrected so that they stop disseminating false info. There are also credible sources that claim that the warmest temp should be used for calculations.
Especially we here at HBT, who continually claim that we know better than the so-called experts.
I keg and before I crash cooled all of my beers I used the carbing calcs of BS and they worked for me. So before when I kegged my Ordinary bitters BS would tell me to set my regulator at 11 psi to achieve 1.5 vols of carb. My carb level would be perfect at about 7-10 days. I used the temp at kegging even though I would be refrigerating the keg.
When I started crash cooling I went to use BS and it told me to set the pressure at .02 psi(!) to achieve 1.5 vols of carb. Guess what would happen if I set the pressure to .02 on crash cooled beer. Absolutely flat beer.
For corn sugar calcs the numbers are even more stark. BS says to put in NEGATIVE .25 oz of sugar to achieve 1.5 vols of carb at 36 degrees. This is obviously wrong as there is no way that my beer is sitting there just naturally carbed at 1.6 volumes.
In short Beer Smith is wrong in how they calculate carb. If you crash cool and use that temp in determining co2 pressure, or priming amount you will have a different level of carbonation than they lead you to believe.
The implications here that beer will reabsorb dispelled co2 on a drop in temperature imples that in a crash cool situation with small headspace the beer will be subject to oxidation. Based on my own observations alone I disagree with this. My crash cooled beers show no more evidence of oxidation than my non-crashed beers. I have no scientific basis for this observation, just my tastebuds, which I trust.
One of the things I have learned most implicitly from basically living at this website is not to blindly believe as gospel everything said by Parker and Papazian and brewing software.
One last thing to consider. As liquids sit still dissolved gas will tend to come out of solution. Fresh water will lose its oxygen and become stale as it sits. Beer and wine will lose CO2. Wine makers count on this as they know that the longer a wine ages the less necessary it becomes to de-carb it before bottling.