server+web: capacity / FULL gate (occupancy fold + transient refuse)

Occupancy is a fold over the signed ledger (entries minus exits per identity);
getOccupancy returns {count, capacity, free, full}. Capacity is a single-row
site_config table (admin-set; null = uncapped; migration 0001, additive).

FULL gate lives in the transient entry flow: when full, refuse (no ticket, no
vehicle_entry, no open) and sign an anomaly. Permit entry is NOT gated --
subscribers are admitted past transient-full (their own maxConcurrent still
applies), so occupancy can read over capacity by design (reserve-for-permits).

Routes: GET /api/occupancy + GET /api/site-config (any role), PUT
/api/site-config (admin; non-negative int or null). Web SiteSettings: live
occupancy + FULL badge (everyone), capacity editor (admin).

Verified: fill to cap -> 3rd transient refused; permit admitted past full; exit
frees a slot; RBAC (operator can't set, -5 -> 400); verifyChain ok. Physical
FULL-sign relay output deferred.

apps/server/src/occupancy.ts

@@ -0,0 +1,49 @@
+import { eq, ledgerEvents, siteConfig, type Db } from "@parking/db";
+
+// Occupancy = a FOLD over the signed ledger: the count of vehicle_entry events
+// with no matching vehicle_exit. Never a hand-maintained counter (which is
+// editable + drifts) — the chain is the truth. See wiki/concepts/capacity-occupancy.md.
+
+export interface Occupancy {
+  /** Cars currently inside (open sessions). */
+  readonly count: number;
+  /** Admin-set nominal capacity, or null = no limit. */
+  readonly capacity: number | null;
+  /** capacity − count, or null when uncapped. Can read 0 (or below) when full. */
+  readonly free: number | null;
+  /** True when count ≥ capacity (always false when uncapped). */
+  readonly full: boolean;
+}
+
+/** Count cars inside: entries minus exits, per identity, over the ledger. */
+export function occupancyCount(db: Db): number {
+  const rows = db
+    .select({ type: ledgerEvents.type, identity: ledgerEvents.identity })
+    .from(ledgerEvents)
+    .all();
+  const balance = new Map<string, number>();
+  for (const r of rows) {
+    if (r.type === "vehicle_entry") balance.set(r.identity ?? "", (balance.get(r.identity ?? "") ?? 0) + 1);
+    else if (r.type === "vehicle_exit") balance.set(r.identity ?? "", (balance.get(r.identity ?? "") ?? 0) - 1);
+  }
+  let open = 0;
+  for (const v of balance.values()) if (v > 0) open += 1;
+  return open;
+}
+
+/** Admin-set capacity (null = uncapped). */
+export function siteCapacity(db: Db): number | null {
+  const row = db.select().from(siteConfig).where(eq(siteConfig.id, 1)).get();
+  return row?.capacity ?? null;
+}
+
+export function getOccupancy(db: Db): Occupancy {
+  const count = occupancyCount(db);
+  const capacity = siteCapacity(db);
+  return {
+    count,
+    capacity,
+    free: capacity == null ? null : capacity - count,
+    full: capacity != null && count >= capacity,
+  };
+}