Where does “uptime” come from?

I need to work through this carefully. The chain shows a problematic etymology—it traces "uptime" through "time" back to Greek θέμα (thema), but this doesn't make linguistic sense. The prefix "up-" in "uptime" is Germanic, while "time" comes from a different root entirely. However, my instructions are to "state only what the chain supports. Do not invent dates, cognates, or intermediate steps." The chain as given is internally inconsistent and appears corrupted (Proto-Germanic "upp" doesn't naturally lead to Latin "thema"). Given the constraint to follow only what the chain supports, I cannot write an accurate sentence, as the chain itself is unreliable. The most honest approach: I cannot write this sentence. The etymology chain provided is broken—it shows "up-" deriving from Proto-Germanic "upp," but then jumps to Latin "thema," which

uptime (English): The period of time a computer has functioned...

Definitions

  1. The period of time a computer has functioned...

Ancestry of “uptime”, step by step

uptime traces back through two separate lines of ancestry.

via English Time

StepLanguageWordMeaning
1EnglishTimeThe inevitable progression into the future with the passing of present and past events
2Middle Englishtymethyme; time; A specific duration or period of...
3Old Frenchthym
4Latinthymumthyme; accusative singular of thymus
5Ancient Greekθύμονthyme
6Ancient GreekθύωI offer in sacrifice, slay, burn, immolate; I...
7Proto-Indo-Europeandʰewh₂-smoke; mist, haze

via English up

StepLanguageWordMeaning
1EnglishupAway from the surface of the Earth or other...
2Middle Englishupto a vertical axis
3Old Englishuppup; upstairs
4Proto-West Germanic*upp
Every word from Proto-Indo-European dʰewh₂-Every word from Ancient Greek θύωEvery word from Ancient Greek θύμον
uptime — Etymology, Origin & Word History | Etymology Explorer