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  Is it possible to modify the delay for publishing a punishment on a case-by-case basis?

Yes. At the start of the year, you configure the delay for the default publication of each punishment. But this configuration can be modified on a case-by-case basis, to suit the situation of each student. Publication can even be postponed to a date of your choice.

In Discipline > Punishments > Enter the punishments, select the student, then the punishment. In the rubric Notify the guardians, double-click on the date indicated, then modify the publication date.