A field guide
A field guide for the apology you actually mean.
Take your hundred percent of your half. In private. With no audience. The only apology that lands for someone else is one written by a person who has already made peace with their own conduct.
Name the hurt. Don't bury it. Don't soften it. "I am sorry" with no "but" attached.
Say you were wrong. No deflection. No explanations dressed up as ownership. The hardest for most people. Do it anyway.
Bring receipts. Action you have already taken. Don't ask what they want you to do. Show what you've already done.
Name what's open. Don't demand a date. Don't set terms. Leave the door open on their timeline, not yours.
Most apologies that don't work are demands disguised as apologies. Asking makes it about you again. Give the gift. Ask for nothing back.
Walk the building one more time. Ask yourself: is there one more thing I can consider for the other person before I call this complete? When the answer is no, you can rest.
Now get to work.