Dear Doc,
Salamun Alaikum and welcome to the forum.
With regards to 'salata' (prayer), verse 4:103 makes use of the Arabic 'kitaban mawquta' which refers to 'prescribed' times. Although 'waqt' from which 'mawqutun' is formed means a state, fixed time or a period of time, the word 'kitaban' means prescribed / enjoined / appointed / inscribed what is written or ordained.
It has a similar construct as used in the phrase "Kataba ala nafsihirahma" where God says he has inscribed / ordained / prescribed for Himself (the rule of) Mercy as in 6:12 and 6:54
Therefore there is clear mention in the Quran for 'salat' (prayer) to be enjoined / prescribed on believers and at specific times / periods of the day.
You are correct, there are no direct punishments that are mentioned for missing prayer (as in what the retribution for missing a certain prayer would be). However, God has asked believers not to abandon / neglect prayer (19:59-60) and in light of verse 4:103 above, those who are not mindful of their prayers (for one reason or another) are rebuked (107:4-5). In contrast, the references to 'establish prayer' are numerous in the Quran.
I hope that helps.
Joseph