Is this a legitimate compression scheme?

A previous discussion in here has left me with this boiled-down question:

Suppose my computer contains in its memory the first 10 billion digits of
pi. Now suppose you generate a 10-digit random number and give it to me.
My computer program will compare your random number to its 10 billion digits
to see if at any point your 10-digit string exactly matches a 10-digit
stretch of pi. If the program finds a match, it returns the index into pi
(i.e. the Nth digit of pi) where your 10-digit string starts. If this index
has nine or fewer digits, would you agree that this is a legitimate
"compression" of your 10-digit number as the term "compression" is used in
algorithmic complexity or algorithmic information theory?


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