events: availability.sx — free/busy + conflict detection on Datalog + 16 tests

occurrence/booking EDB; rules busy/conflict (canonical pair, half-open
overlap)/busy_in. API ev-busy, ev-conflicts, ev-has-conflict?, ev-free?
(transient qwindow). Integrates with calendar expansion. 53/53 green.

Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>

plans/events-on-sx.md

@@ -18,7 +18,7 @@ capacity rules, transactional booking, and a flow-driven notification dispatcher
 
 ## Status (rolling)
 
-`bash lib/events/conformance.sh` → **37/37** (Phase 1: calendar recurrence)
+`bash lib/events/conformance.sh` → **53/53** (Phase 1: calendar + availability)
 
 ## Ground rules
 
@@ -56,7 +56,8 @@ lib/events/api.sx ── (events/schedule) (events/book) (events/agenda) ──
 ## Phase 1 — Calendar + recurrence
 - [x] `calendar.sx` — event facts, RRULE expansion in a window (DAILY/WEEKLY)
 - [x] `calendar.sx` — MONTHLY (bymonthday + nth-weekday byday)
-- [ ] `availability.sx` — free/busy rules
+- [x] `availability.sx` — free/busy rules (busy/conflict/busy_in on Datalog)
+- [ ] `availability.sx` — next-free slot search (same rules, different bindings)
 - [ ] `api.sx` + tests + scoreboard + conformance.sh
 
 ## Phase 2 — Ticketing + booking
@@ -77,6 +78,12 @@ lib/events/api.sx ── (events/schedule) (events/book) (events/agenda) ──
 
 ## Progress log
 
+- 2026-06-07 — `availability.sx`: free/busy + conflict detection as forward-
+  chained Datalog over `occurrence`/`booking` EDB. Rules `busy(A,S,E)`,
+  `conflict(A,O1,O2)` (canonical `O1<O2`, half-open overlap `S1<E2 ∧ S2<E1`),
+  `busy_in(A,QS,QE)` for window queries. API: `ev-busy`, `ev-conflicts`,
+  `ev-has-conflict?`, `ev-free?` (transient qwindow assert/retract). Integrates
+  with calendar expansion (book expanded occurrences). 16 tests, 53/53 green.
 - 2026-06-06 — MONTHLY recurrence. `ev-days-in-month`, `ev-add-months`,
   BYMONTHDAY (incl. negative = from month end), ordinal BYDAY (`{:ord N :wd W}`,
   ord<0 = nth-from-last), default day-of-month (skips months too short, e.g.