Can I demonstrate a proposition without a rigorous proof? Writing a paper, I want to declare a certain proposition, but is only supported by other research's empirical result. In this sort of case, what can I name to my argument in my paper? CONJECTURE is so much informal and seems to be so lazy. Otherwise, is it possible just to write down PROPOSITION in my paper without rigorous proof, but with some procedures attaining to that proposition including previous empirical results?
Thank in advance!

Technically, it is a conditional proof.
In practice, it suffices to convert your result into a conditional statement. Two examples

Under the Riemann hypothesis, the following inequality holds...
If P = NP, then the polynomial hierarchy collapses.

If your result relies on a someone else's result, you may write.

S. Else proposed in [1] the following conjecture
Conjecture [S. Else, 2014] ...
Proposition If Else's conjecture is true, then my result is correct.

