Absence of evidence

I make an important distinction here.

The statement:

“The theory is supported because there is no evidence against it”

is not logically justified merely from the absence of contradictory evidence.

Why?

Because no contradictory evidence could mean several things:

the theory is true;

nobody has looked carefully;

relevant evidence was destroyed;

relevant records never existed;

the evidence exists but has not been discovered.

So absence of contrary evidence does not itself establish truth.

My second statement

“The theory is unsupported because there is no evidence for it.”

That is also different from saying it is false.

It means:

We currently lack evidence sufficient to support it.

So your formulation is correct:

The proposition remains unresolved pending adequate evidence.

Why ask what evidence should reasonably exist?

Suppose someone claims:

“Lincoln secretly intended X.”

If that were true, we might reasonably expect some evidence in:

correspondence,

private notes,

cabinet discussions,

speeches,

political communications.

If absolutely nothing exists after extensive searching, that absence may become relevant.

But it still doesn't automatically prove the claim false, because records can be destroyed or never created.