The section I pointed out in my link was to show how a president's actions predated the Senates by 6 months. Now that I see you can read look at page 113 and 114 ---
G. INTERIM BETWEEN SIGNING AND ENTRY INTO FORCE;
PROVISIONAL APPLICATION ---
It ‘‘must normally rest on the President’s own con-
stitutional authority.’’68According to the Department of State, the
President may also make a unilateral policy decision, without
reaching agreement with the other parties to apply the treaty pro-
visionally, ‘‘so long as the obligations undertaken are all within the
competence of the President under U.S. law.’’69The primary factor
for determining the appropriateness of provisional application, in
the State Department view, ‘‘relates to the immediate need to set-
tle quickly matters in the interest of the United States which are
within the President’s domestic law competence.’’70
An example of a treaty pending in the Senate that has been pro-
visionally applied by executive agreement is the maritime bouhttp://www.youtube.com/embed/KPW_E16fmwc?autoplay=1nd-
ary agreement between the United States and Cuba, signed Decem-
ber 16, 1977. ......
Now you want to debate the US Constitution?
Article. VI. - Debts, Supremacy, Oaths --- Paragraph 2 ---
This Constitution, and the Laws of the United States which shall be made in Pursuance
thereof; and all Treaties made, or which shall be made, under the Authority of the United
States, shall be the supreme Law of the Land; and the Judges in every State shall be
bound thereby, any Thing in the Constitution or Laws of any State to the Contrary
notwithstanding.
Bold inserts of emphasis by me.