I'm extremely leery about this, especially given what may constitute of 'evidence' may in fact be nothing of value.
Yes, the innocent have a right to live peacefully after trial. We have the presumption of innocent until proven guilty for a reason. I fear that if we allowed this, innocent people would spend their lives in fear of retrial because "evidence" arose leading to another costly trial and defense.
"Absolute" is also difficult to define. Even absolutely evidence can sometimes be explained away.
Absolute is difficult to define, I agree, and yes, it should be reasonable for people to live peacefully after trial. However, how can we impose absolute limits on the ability to try someone again, provided evidence comes to light? Should there be stringent restrictions? Yes. Should we be constitutionally unable to have retrials? I'm not so sure.
It's so difficult to define these things though. We implement the doubt jeopardy rule because otherwise, upset victims of crimes would hail the suspect into court continuously until they just gave up.
Sure, some cases slip through the cracks and someone is wrongfully convicted or wrongfully acquitted, but no system in perfect. Writing something like this into the constitution could potentially create a nightmare for people who are accused of such crimes that they did not commit and literally put them in jail regardless of whether they are guilty or not because of constant fear of being called back into court for another "round" of evidence.
In a case where someone was acquitted and then video evidence surfaces of the crime, then maybe this would work, but how often does that happen? What about statute of limitations laws?
I have no power over amendments like this, but this is my two cents. The justice system isn't perfect, but more often than not, it works as intended.