feat(door): P3-B pure slot allocator (lowest-free, range-generic) + tests

pickLowestFreeSlot fills gaps before extending (deterministic, compact,
predictable for admins reading the controller). Range is a parameter
(HeatSync passes 0-200) so it stays adapter-generic. Ignores duplicate/
out-of-range/non-integer used slots; reports slot_exhausted when full.
slotCapacity for 'controller full N/N' messaging. 8 unit tests.

lib/door-slots-logic.ts

@@ -0,0 +1,43 @@
+// Pure, dependency-free slot allocation for the Door epic. No Supabase/React.
+// Some controllers key cards by an integer "slot" (the verified HeatSync/23b
+// firmware: 0-200). The slot space is per door connection. This decides which
+// slot a newly granted card should take; the action layer holds the actual
+// allocation state (door_card_slots) and the DB unique constraint arbitrates
+// concurrent grants. Kept adapter-generic: the range is a parameter, not a
+// HeatSync constant, even though HeatSync is the first caller.
+
+// Default range matches the HeatSync firmware (slots 0-200 inclusive, 201
+// usable). The user chose the full range with no reserved slots.
+export const HEATSYNC_SLOT_MIN = 0
+export const HEATSYNC_SLOT_MAX = 200
+
+export type SlotPick =
+  | { ok: true; slot: number }
+  | { ok: false; reason: 'slot_exhausted' }
+
+// Lowest free slot first: deterministic (testable), compact, and predictable
+// for an admin reading the controller's user list. `used` may contain
+// duplicates or out-of-range values; both are ignored.
+export function pickLowestFreeSlot(
+  used: number[],
+  min: number = HEATSYNC_SLOT_MIN,
+  max: number = HEATSYNC_SLOT_MAX,
+): SlotPick {
+  const taken = new Set<number>()
+  for (const n of used) {
+    if (Number.isInteger(n)) taken.add(n)
+  }
+  for (let slot = min; slot <= max; slot++) {
+    if (!taken.has(slot)) return { ok: true, slot }
+  }
+  return { ok: false, reason: 'slot_exhausted' }
+}
+
+// Total addressable slots for a range, for capacity messaging
+// ("controller is full, 201/201 slots used").
+export function slotCapacity(
+  min: number = HEATSYNC_SLOT_MIN,
+  max: number = HEATSYNC_SLOT_MAX,
+): number {
+  return max < min ? 0 : max - min + 1
+}