Air carrier Captain reported encountering GPS jamming that was first noticed at the departure gate in LTFM; and they later regained functionality with one GPS but not the other. GPS abnormality continued throughout flight.

Narrative

During preflight we were having issues with our GPS position. Ground and Dispatch confirmed it was a common problem in Turkish airspace. We elected to push pack and update the GPS as we were told that's usually when it would come back. When it did not we discussed and decided to continue as long as the FMC position updated on takeoff; which it did. In the air we tried to acquire the GPS updating again. We advised dispatch we still had no GPS signal from either receiver. About an hour or 2 in flight the L GPS appeared to be working again. We advised Dispatch and let them know the R GPS was still out. After passing our coast out point ATC advised us they were not receiving ADSB reports. I told them we had encountered GPS spoofing in Turkish airspace and were single GPS. They asked if we were still RNP4 capable (2 GPS per the manual limitations) which I replied unable and told them we were filed RNP10. Or so I thought since we had looked up the CNS requirements at the gate and referenced the oceanic supplemental procedures which labeled A1 as flight plan Item 18 RNP10. Which confusingly we discovered on the flight plan later also had L1 (RNP4). ATC pointed out we were filed for RNP4 and we should have advised them of degraded performance. They climbed us to FL330 and we continued with voice reports. Cause: I had been more focused and occupied on verifying that our position was continuously accurate throughout the flight and that we were never drifting off course. Our ANP/RNP was 4.00/0.06 during most of the flight. I kept dispatch informed but didnt think to inform oceanic ATC. Suggestions: In hindsight I should have asked dispatch to verify our equipment requirements instead of simply giving them status updates. Also having a more centralized pilot friendly equipment failure/CNS requirement reference for just such an occasion would be beneficial. Much like the Cat II/III equipment chart.