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The freshness_check was a checksum like parameter that was calculated from the Internet Explorer cache of the current page and sent to Google along with the PR request.
My only guess is that it was designed to help Google spot pages that had changed contents since it was last indexed and send freshbot out to have a look. It could have also been used to find new pages.
There are some obvious problems with this type of system which stem from the fact that some software, such as filtering proxies, will alter the page contents before it reaches the IE cache.
Also, I have discovered how to calculate the ch= parameter in the PR request. Would anyone like to comment on the legalities of querying the toolbar PR from an external application? We all know there are tools out there that will query Google and find your position in the SERPs without using the Google API, even though this type of query goes against the TOS.