—“The world’s first murderer stands before a common law court. No applicable statute or precedent. How is law made?”—

By Natural Law: reciprocity.

The violation of reciprocity by aggression against life, body, mate, kin, property, interest.
In history, common law developed to prevent reciprocity (retaliation), because of retaliation cycles. (Feuds)

States imposed uniform laws once people came into conflict between groups. And if one ‘group’s punishments were too different from the others retaliation cycles would ensue (Feuds).

—“Can you define reciprocity?”—

Reciprocity is just the promise of doing unto others only as one would have done unto you; and not doing unto others that which you would not have done unto you.

But once this is broken how do we restore a condition of reciprocity? We do so by restitution.

–“Does restitution necessitate capital punishment?”–

Technically it is impossible to perform restitution for murder except with capital punishment.

However, in most cases it is possible to pay a high price for murder. And people generally have been forced to pay a high price depending upon the status of the killer and killed.

But, in the end, the real reason we use capital punishment is because if someone will break the last rule, the one-rule, of not murdering, then they must be eliminated from the group.

—“Standardization means that a superior authority is set?”—

Not sure what you mean. Not authority, but decidability.

Natural law is decidable. It’s perfectly decidable in all cases, everywhere, at all times, between all people. We can define restitution regardless of opinion or preference of members – in order to maintain ‘the peace’ (the rewards of cooperation).

Natural law means people can’t prey upon each other. That is different from a standard. As far as I know that’s a truth. It’s just science. We don’t get to choose.

Two people or parties can settle their differences however they want as long as the settlement of differences does not export harm or risk to others. but if we are asked or forced to resolve a conflict, we can do so by natural law regardless of our individual opinions.

–“If natural law means we can’t prey on each other, is it not a priori? Or is it empirically discovered as a function of the rewards of not preying?”—

Well you know asking that question is fallacious. The apriori is simply a trivial case of the empirical, and the empirical merely a trivial case of the scientific.

It’s observable, it’s logical, it’s possible, it’s demonstrable, and it’s thoroughly demonstrated – and moreover it’s actually impossible to contradict rationally. (You can’t even try to contradict it without confirming it.)

I mean, we are part of the physical universe, despite our ability to outwit it on a regular basis through the use of sense, perception, memory, prediction, reason. If an organism tolerates parasitism and predation why does it do so? If an organism can cooperate, and cooperation produces extraordinary returns, and parasitism disincentivizes cooperation, and deprives an organism of returns, then what adaptation must an organism evolve in order to preserve cooperation?

Just what we see: altruistic punishment (costly retaliation). Because even though retaliation is costly, the cumulative parasitism is much more costly, and possibly deadly.

Any organism that can cooperate and becomes dependent upon cooperation cannot survive significant non-cooperation.

However, some minimum of non-cooperation is necessary in order to preserve the incentive to preserve the instinct to punish parasites.

And some minimum non-cooperation is necessary to provide evolutionary routes to superiority that may be integrated into the whole.