feat(equipment): pure overlap/eligibility logic + Zod schemas

equipment-logic.ts: half-open intervalsOverlap, hasConflict (only
reserved rows block), reservationEligibility (status/active gate, future
window, no-overlap, required-cert with manager override). Dependency-free,
9 unit tests (suite 382 -> 391). validations.ts: equipment/reservation
schemas; reserve carries an optional manager-only memberId.

lib/validations.ts

@@ -829,6 +829,51 @@ export const listSessionSignupsSchema = z.object({
   sessionId: z.string().uuid('Invalid session ID'),
 })
 
+// ─── Equipment ───────────────────────────────────────────────────────────────
+
+const equipmentStatus = z.enum(['available', 'maintenance', 'retired'])
+
+export const createEquipmentSchema = z.object({
+  name: z.string().min(1, 'Name is required').max(200),
+  description: z.string().max(5000).optional().nullable(),
+  location: z.string().max(300).optional().nullable(),
+  status: equipmentStatus.optional().default('available'),
+  required_certification_id: z.string().uuid('Invalid certification ID').optional().nullable(),
+  asset_tag: z.string().max(120).optional().nullable(),
+})
+
+export const updateEquipmentSchema = z.object({
+  equipmentId: z.string().uuid('Invalid equipment ID'),
+  name: z.string().min(1).max(200).optional(),
+  description: z.string().max(5000).optional().nullable(),
+  location: z.string().max(300).optional().nullable(),
+  status: equipmentStatus.optional(),
+  required_certification_id: z.string().uuid('Invalid certification ID').optional().nullable(),
+  asset_tag: z.string().max(120).optional().nullable(),
+  is_active: z.boolean().optional(),
+})
+
+export const equipmentIdSchema = z.object({
+  equipmentId: z.string().uuid('Invalid equipment ID'),
+})
+
+export const reserveEquipmentSchema = z.object({
+  equipmentId: z.string().uuid('Invalid equipment ID'),
+  starts_at: z.string().min(1, 'A start time is required').max(40),
+  ends_at: z.string().min(1, 'An end time is required').max(40),
+  notes: z.string().max(2000).optional().nullable(),
+  // Manager-only: book on another member's behalf. Ignored for non-managers.
+  memberId: z.string().uuid('Invalid member ID').optional().nullable(),
+})
+
+export const cancelReservationSchema = z.object({
+  reservationId: z.string().uuid('Invalid reservation ID'),
+})
+
+export const listEquipmentReservationsSchema = z.object({
+  equipmentId: z.string().uuid('Invalid equipment ID'),
+})
+
 // ─── Generic ID schemas ──────────────────────────────────────────────────────
 
 export const uuidSchema = z.string().uuid('Invalid ID format')