POST /v1/availability-resolve
Give it a search window, a meeting length, and for each participant a list of busy blocks — start and end, nothing else — and it returns the windows in which the meeting fits. Each participant carries their own IANA timezone and working hours, so nine-to-five means nine-to-five where they are, across daylight saving changes, and a meeting is only offered when it lies entirely inside one working-hours block for everyone counted as present. Windows are returned with the participants who can attend, those who cannot, and a rank that puts full attendance first and the earliest slot next; setting min_attendees or marking participants as optional produces partial windows too, each labelled with exactly who is missing. Alongside the windows every participant gets a load figure — busy minutes, free minutes inside working hours, and a percentage — and all of them are measured over the identical search window, because a percentage from a two-week sample set beside one from three weeks compares nothing. The input is deliberately impoverished: it takes no calendar credentials, no event titles, no attendee names, no location, and an identifier may be a single letter. Nothing is stored beyond the response. What it does not do is decide: it will not rank by anyone seniority, guess which meeting may be moved, or read a busy block as tentative — a block is busy, and a slot that fits is offered without any claim that it is a good time.