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Had a look at what you've spotted, and here it goes, its an internal Yahoo ID based on your IP, irrelavent of your search terms, or any cookies.
Hence its tracking, but not by URL, but IP, though the real question become's is it time based tracking within their servers or a perminent watch of fixed IP's searching across their system, and possibly all their systems, i.e. AV, Overture, ATW, etc. Because if it is then they are probably trying to amase one heck of a demographic, technological, and search pattern insight into the vast majority of users of the WWW. However - no pun intended, corporations/companies and power users use fixed IP's, where as most surfers use dynamic IP's - so how they're getting around a consistent identification of them - is beyond me!
What i would suggest is watching the numbers every time you on yahoo, and whether it stays the same accross hours/days/time, etc. Further more are you on a fixed IP or dynamic, and are the numbers the same, i will check tomorrow.
Certainly at first i thought it was a number assigned to a keyword combination but, after a couple of tests, i don't see it that way no. Might be worth writing the number down, and other particulars and we will have to watch this.