Nobel Prize vs Proof that the Death Penalty MUST kill innocents

No, it is not enough to ensure guilt. There would need to be a trial to determine sanity. Innocence by that reason is a possibility.

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I am asking the question if it is really true that we cannot create rules to determine in some cases that a person definitely commited a certain act.

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I think the term "definite" is the problem. When dealing with the actions of people, it is difficult to determine what is or is not "definite".To do this, would require thinking of all possible circumstances in advance in order to create rules that are "tight" enough to allow use of the term "definite". I don't believe, based merely on the evidence, we can be 100% sure of every detail.But if we could, determine with 100% accuracy, would that preclude a trial? Would we, based on the 100% accuracy of the evidence, proceed directly to execution?

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Yes, we have a trial and evidence is presented. Within the trial it may be determined if the evidence rises to a level of certainty which allows the DP to come into play. No the execution need not be immediate as there is always an appeals process. Yes, eventually that process may end and the person be killed.

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Then I'm missing your point. This doesn't sound much different than what we already have in the US. The prosecution determines if evidence is sufficient to seek the DP. If it is allowable, of course.