Using the present tense or past tense for a fact

I know that we should use the present tense when talking about facts. However, in some instances I cannot decide which tense to use.

For example,

"The analysis assumes that a and b are independent of y."
"The analysis assumed that a and b are (were?) independent of y."

It is a fact that the analysis makes that assumption, yet the analysis was done in an earlier chapter.

Another example:
"He built the house in 1800." Passive: The house was built in 1800.
"He builds the house in 1800." Passive: The house is built in 1800.

Even right now in 2020, the fact remains that the house was built in 1800, so which tense is correct?

Can anyone help?