Laws are codified in statutes, so don't worry about the label "common law jurisdiction." Nevertheless, we're not dealing with common law. Your answer is in the 5th Amendment.There's no "concrete case" (we call this caselaw) because the scenario you propose is not possible. Once a defendant is acquitted in state court, the state("prosecuting agency")cannot try him/her again,for the same charges, regardless of what evidence comes out after. The prosecuting agency is barred from appealing the verdict. With no right to appeal, cases like the one you're looking for don't exist.If there is evidence of a different crime, or separate criminal transaction,then the double jeopardy clause doesn't apply because they're not the same offense. Also, beyond a reasonable doubt is always the burden of proof in criminal trials. And the hypothetical facts in your question would require probable cause not clear and convincing.
Examples Everywhere If you look at it differently, then there are thousands of concrete cases; anyone who has ever been acquitted. There are caveats to double jeopardy, such as whether the federal government can also prosecute or whether the new evidence is related enough to the originally charged offense(s), to constitute the "same offense." But that's beyond the scope of your question.
Rationale For The Double Jeopardy: Double jeopardy means that no person can be tried twice for the same offense. It's an absolute right, and is incorporated to the states through the due process clause in the 14th Amendment. No state can change it. The purpose of the right is to create finality in criminal proceedings. Without it, the government would have unlimited chances to prosecute the accused.
Fact Pattern related to your question Suppose A gets into a fight with B on January 1, 2021. A is charged with assault and related charges. At this stage the double jeopardy clause is not applicable. It is triggered when a jury is sworn in or when the prosecutor begins it's case in chief for a bench trial (judge is fact finder not jury). A is acquitted on all charges. A few days after the acquittal a video comes out showing A hitting B with a gun during the fight. The gun has A's DNA and fingerprints all over it. Plus A confesses to the whole thing. What then? Nothing. It doesn't matter because A was acquitted. And yes, this scenario falls within the same offense because it arises out of the same criminal transaction. Whatever A was charged with is secondary to the criminal conduct A was arrested for. Thus, the prosecutor is barred entirely from trying A for any conduct on January 1, 2021, regarding the fight.