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There is no distinction in law between a “Citizen of the United States at Birth” and a “Natural-born Citizen.” One is an 18th century term, the other is a 19th century term, but they are synonymous.

Okay, here you are again, repeating the same demonstrably wrong theory. If you persist in repeating it, I'm going to persist in asking you how Bellei LOST HIS CITIZENSHIP. Obviously there *IS* a distinction.

Your aversion to discussing Bellei moves you out of the category of "objective but misinformed" and into the category of "advocacy for a specific preferred outcome." You are fully aware that Bellei blows your theory to h3ll, and that's why you don't want to discuss it.

So once again, if I don't report for Induction, will I lose my citizenship?

Bellei lost his citizenship due to a State Department interpretation of the Immigration and Naturalization Act that was upheld by the Supreme Court and later rendered moot by subsequent legislation.
That subsequent legislation was passed before Senator Cruz was born.

“Any person who is a national and citizen of the United States at birth under paragraph (7) of subsection (a) of this section, shall lose his nationality and citizenship unless he shall come to the United States prior to attaining the age of twenty-three years and shall immediately following any such coming be continuously physically present in the United States for at least five years. . ..”

Bellei visited the United States under his American passport in 1948, 1952, 1955, and 1962. His last trip was made in 1965 on his Italian passport.”

Senator Cruz, on the other hand, has been permanently domiciled in the USA.