Squognart is defined as "the perfect ten dollars you owe me."
Consider, furthermore, the definition of perfection as "lacking any flaw," and the axiom "inexistence is a flaw."
Now, presume that squognart does not exist.
If squognart does not exist, then it bears a flaw. However, since squognart is perfect, it cannot bear a flaw.
Therefore, squognart must exist, and, thus, you owe me ten dollars.
Please note furthermore that "being paid less than immediately", "being paid in any manner other than hard U.S. currency", or "Ted having to pay for shipping" are also imperfections, and therefore cannot exist.