events: next-free slot search + 6 tests

ev-next-free finds the earliest free slot >= after for a duration within a
horizon, probing 'after' + busy-interval ends via the busy_in rule (ev-free?).
Finds gaps, skips too-short gaps, half-open at edges. 59/59 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` → **53/53** (Phase 1: calendar + availability)
+`bash lib/events/conformance.sh` → **59/59** (Phase 1: calendar + availability)
 
 ## Ground rules
 
@@ -57,8 +57,9 @@ lib/events/api.sx ── (events/schedule) (events/book) (events/agenda) ──
 - [x] `calendar.sx` — event facts, RRULE expansion in a window (DAILY/WEEKLY)
 - [x] `calendar.sx` — MONTHLY (bymonthday + nth-weekday byday)
 - [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
+- [x] `availability.sx` — next-free slot search (same rules, different bindings)
+- [ ] `api.sx` — public entry points (schedule/agenda/free-check)
+- [ ] tests + scoreboard + conformance.sh [done incrementally; api.sx pending]
 
 ## Phase 2 — Ticketing + booking
 - [ ] capacity rules; transactional booking → `persist` (no overbooking)
@@ -78,6 +79,11 @@ lib/events/api.sx ── (events/schedule) (events/book) (events/agenda) ──
 
 ## Progress log
 
+- 2026-06-07 — `next-free` slot search: earliest start ≥ after where
+  [s,s+duration) is free and ends ≤ horizon, else nil. Candidates are `after`
+  plus each busy-interval end (interval-packing); each probe reuses the
+  `busy_in` Datalog rule via `ev-free?`. Finds gaps between bookings, skips
+  too-short gaps, half-open at edges. +6 tests, 59/59.
 - 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`),