If the first ruling (upholding the testimony based on the opponent's admission) is accepted, does the witness's character affirmation ('ta'deel) apply to others besides the litigant who made the admission?

Primary text

If the first opinion is followed, the witness's character affirmation does not extend to others besides the litigant who made the admission. The judge ruled based on the litigant's confession regarding the fulfillment of the conditions necessary for judgment, and such a confession is valid only concerning the confessor and not against others, analogous to when a person admits a debt owed by himself and another, where the admission only binds the confessor.