Is the mathematics, science and engineering really available for analysis?
Yes the mathematics, science and engineering are really available for analysis.
You can easily search with Google and find that all “green” power technologies use as much or more carbon than fossil fuels, or are so variable and unreliable as to require additional reliable power plants as backup.
All of the arguments against nuclear power basically boil down to : it’s icky. There are power plant designs that cannot melt down, designs that burn today’s nuclear waste down to 1% residue, and designs that use thorium instead of uranium.
Nuclear power is by far the safest, most economical, most environmentally responsible technology available. It’s reputation has been ruined by stupid and unsafe designs that were intended solely to produce material for weaponry, and a moron President named Carter who signed an Executive Order preventing using nuke waste as fuel.