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PCR test amplifies whatever was swabbed, usually from the nose (an air filter). A positive result does not prove there is an infection.

Our state-run testing facility always did PCR tests using a throat swab, and since I was the one who drew the short straw and took each of our kids there for mandatory tests, I've observed this being done a couple of dozen times over the last three years.

> People who recovered from C19 many weeks ago and are no longer contagious can still test positive on a PCR test

Which is why the EU issued the "recovery certificate" and put it on the same basis as a negative test, and why our schools didn't test recovered children (to clarify: were mandated not to test recovered children) after they returned to school after having Covid.

Testing positive months after does happen, but is extremely rare, and yes, missing few days of school/work is not that big of a deal considering risks involved.