Evidence, broadly construed, is anything presented in support of an assertion.
As Keith pointed out, that isn't the issue. You had stipulated absolute conditions. Which is why I said (emphasis added):
There can be something that others mistake for evidence of something you did (but actually did not do), but if you did not, in fact, do something, then there cannot be any evidence that you did, in fact, do something.
You’re confusing perceptual mistakes with objective evidence.
You do it again here:
You have bank video surveillance supporting the assertion I robbed a bank
But if we already know that you did not rob the bank--i.e., it is stipulated in the hypothetical, as you did previously--then we know that the evidence could not support such an assertion.
NOW, however, you are removing absolute certainty and proposing an entirely different hypothetical:
You have evidence that I did rob a bank, and I have evidence that I did not rob a bank.
False. I have evidence that I
think depicts you robbing a bank, not evidence that you
did rob a bank. It could not be you in the video, however, because you were in lock up at the time and that's corroborated, so that necessarily means I am mistaken in my perception that it is you in the bank video.
Your evidence supports the assertion irregardless of whether the assertion is true.
Now you are diluting the term "supports." Supports and "prove" are generally considered to be the same thing in a colloquial sense, with "supports" being a less concrete term. Regardless, all you have done in saying something like, "I have evidence in support of my assertion" is turn the focus on the type of evidence and how definitively (or not) it "supports" your assertion.
Iow, and once again, you are shifting the focus onto your ability to properly discern whether or not the evidence you do have is in fact evidence that
proves you assertion. You've kicked it up a notch and turned focus on the evidence.
That’s what it means to be evidence, not that it guarantees the truth of the assertion but rather if it supports it.
Wrong again. Evidence is supposed to guarantee (aka, "prove") the truth of an assertion. So the question is always, how good is the evidence? Does it prove an assertion; to move beyond assertion and into "truth" or "fact"?
An assertion is essentially a strongly held belief. The strength of the evidence is what shifts that from a belief to a fact. Or not.