Robaharrison - Awesome job!! Thanks so much for attempting the challenge! Yes, this is 100% logical, without the use of temps or any assumptions.
However... my previous point still stands. Good attempt, but as a mathematician, "close" just doesn't quite cut it. In a week or so, when I have a bit more time to get back into creating puzzles, I'll give this challenge a go myself. But I'm not hopeful.
For those wondering, I posted the challenge here: https://www.hanjie-star.com/picross/lamp-25123.html.
Good attempt, though the numbers on the side aren't palindromic at all, and the top numbers aren't completly symmetrical. Now I'm really curious as to wether that is actually possible. I doubt it, but it would make for a great puzzle...