The product of a national constitutional convention is not an amendment to the Constitution. The outcome of such a convention is an officially proposed amendment to the Constitution. The proposed amendment is then either ratified by 3/4 of the states or ignored.
Article V:The Congress, whenever two thirds of both Houses shall deem it necessary, shall propose Amendments to this Constitution, or, on the Application of the Legislatures of two thirds of the several States, shall call a Convention for proposing Amendments, which, in either Case, shall be valid to all Intents and Purposes, as Part of this Constitution, when ratified by the Legislatures of three fourths of the several States, or by Conventions in three fourths thereof (emphasis added), as the one or the other Mode of Ratification may be proposed by the Congress; Provided that no Amendment which may be made prior to the Year One thousand eight hundred and eight shall in any Manner affect the first and fourth Clauses in the Ninth Section of the first Article; and that no State, without its Consent, shall be deprived of its equal Suffrage in the Senate.
Note that the federal government has no constitutional authority to ratify a proposed amendment. Ratification is entirely up to the states.
when ratified by the Legislatures of three fourths of the several States
OR < ————————
“by Conventions in three fourths thereof “
if a convention is called.. and 3/4 of the representatives of the states agree... they can do ANYTHING, no later ratification is necessary.
Ratification is only necessary when a constitutional amendment is put forward by congress. Since the states are the ones that are calling for convention, and since those very states will send representatives to said convention, agreement among 3/4 of said representatives is implicitly implied.