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It is BEYOND THE AUTHORITY of US Law to define a constitutional term

I have to disagree with that. Congress was constitutionally given power over naturalization AND the power to make any laws necessary to implement that power.

So, to define who needs to be naturalized one MUST define who does not need to be naturalized, ie., those who are already natural.

-- So, to define who needs to be naturalized one MUST define who does not need to be naturalized, ie., those who are already natural. --

As a matter of logic, I don't think that holds without adding some limiting assumptions.

There are billions of people outside of the set of "citizen by operation of statute," and by far most of them are not natural born citizens of the US.

To protect Cruz, your position MUST be that "citizen at birth by operation of statute" is the same as natural born citizen. IOW, Cruz is in the set of people made citizen by a naturalization act that includes citizenship by dint of criteria in place at birth.

Birth to U.S. Citizen Parents ("Acquisition")
In many circumstances, even though a child is born outside the United States, if at least one parent was a U.S. citizen at the time of the child's birth, the child automatically "acquires" citizenship. When this child marries and has children, those children may also acquire U.S. citizenship at birth.
The laws governing whether or not a child born outside of the United States acquires U.S. citizenship from parents have changed several times. You'll need to look at the law that was in effect on the date of the child's birth (and the parents' birth, if grandparents were U.S. citizens) for guidance. These laws differ for the following time periods:

prior to May 24, 1934
May 25, 1934 to January 12, 1941
January 13, 1941 to December 23, 1952
December 24, 1952 to November 13, 1986, and
November 14, 1986 to present.

U.S. Citizenship by Birth or Through Parents | Nolo.com

I have to disagree with that. Congress was constitutionally given power over naturalization AND the power to make any laws necessary to implement that power.

You are still tripping over the obvious.

So, to define who needs to be naturalized one MUST define who does not need to be naturalized, ie., those who are already natural.

The one thing is not a subset of the other. As I have pointed out before, NO children of Naturalized immigrants have a naturalization ceremony. Does this make them non-naturalized?

The absence of a ceremony or a certificate does not make them a "natural" citizen.