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It was a rough week for President Trump.

Michael D. Cohen, his former lawyer and longtime fixer, admitted that he’d paid $130,000 in hush money to the pornographic film star Stormy Daniels — real name Stephanie Clifford — “at the direction” of Mr. Trump “for the principal purpose of influencing the election.”

It’s a saga that has been unfolding erratically since January, with admissions, denials and conflicting accounts.

But a central theme to this case has not wavered amid the blithering: It is about how the most powerful person on the planet treats women. And it is about how Ms. Clifford, a woman who would be easy to cast aside as not credible, has remained persistent and vocal — despite repeated attempts from the Trump camp to diminish and silence her.