Tom Anderson wrote:

I think the strict answer is that the appropriate fare for a journey
from Liverpool Street to Harlow for the holder of a Z1-4 PAYG cap *is*
the price of a single from Liverpool Street to Harlow. A PAYG cap is not
a travelcard, and doesn't entitle you to tickets from a zone boundary.
Rather, it's a form of special offer from TfL - spend a certain amount
on travel on their network, get the rest free.

But capping is valid everywhere that PAYG is accepted, which includes
both TfL and non-TfL services - including a portion of the OP's route.
--
David of Broadway
temporarily in Paris
then back in New York