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Real journalists are never going to take you seriously if you continually keep making these sorts of unprofessional moves:
Since then, The New York Times has published two piece... which make conclusively clear that the word "peripheral" [in what I wrote earlier] is inaccurate.
Not only did you admit an error, you LEAD with the admission of error, and you did so in unequivocal language "make conclusively clear."
If you absolutely must point out one of your own errors, it should take the following, less direct form:
"Earlier I claimed... but some critics have suggested that this may not have been entirely accurate."
That's just Journalism 101.