This sounds like a center math problem.
But let’s use 3000’ and pretend they are right for direction.
Aircraft A has a ground speed of 420knots leaving Denver headed to JFK flying at FL330. Aircraft B has an airspeed of 360knots and has left JFK flying to Denver at an altitude of FL300. As aircraft A passes over aircraft B, you grant aircraft B’s request to climb to FL340.
At what climb rate would it set off the snitch, and they have less than 5 miles assuming an instantaneous climb at the very moment they passed each other.
13 mile a minute closure rate, means that they would be 5 miles apart (and thus separated) in ~23.07seconds. To lose separation would require the climbing aircraft to reach FL321 in 23 seconds per se.
So if they suddenly managed a 5500 foot per minute climb rate, you’d totally have a deal… maybe.
Now imagine if we add 3 seconds for us to transmit it to them, and 3 for them to read it back, executing it immediately upon completion of the read back. ~2100 feet in 17 seconds. Isn’t that a greater than 7500fpm climb?
i like maths!