Fix per-juror assignment caps: read correct field + inline edit UI

- Fix bug: AI assignment router read non-existent `(m as any).maxAssignments`
  instead of the actual schema field `m.maxAssignmentsOverride`
- Wire `jurorLimits` record into AI assignment constraints so per-juror
  caps are respected during both AI scoring and algorithmic assignment
- Add inline editable cap in jury members table (click to edit, blur/enter
  to save, empty = no cap / use group default)
- Add inline editable cap badges on round page member list so admins can
  set caps right from the assignment workflow

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

src/app/(admin)/admin/rounds/[roundId]/page.tsx

@@ -84,6 +84,7 @@ import {
   MoreHorizontal,
   ShieldAlert,
   Eye,
+  Pencil,
 } from 'lucide-react'
 import {
   Command,
@@ -370,6 +371,14 @@ export default function RoundDetailPage() {
     onError: (err) => toast.error(err.message),
   })
 
+  const updateJuryMemberMutation = trpc.juryGroup.updateMember.useMutation({
+    onSuccess: () => {
+      if (juryGroupId) utils.juryGroup.getById.invalidate({ id: juryGroupId })
+      toast.success('Cap updated')
+    },
+    onError: (err) => toast.error(err.message),
+  })
+
   const advanceMutation = trpc.round.advanceProjects.useMutation({
     onSuccess: (data) => {
       utils.round.getById.invalidate({ id: roundId })
@@ -1533,6 +1542,15 @@ export default function RoundDetailPage() {
                           </p>
                           <p className="text-xs text-muted-foreground truncate">{member.user.email}</p>
                         </div>
+                        <div className="flex items-center gap-2 shrink-0">
+                          <InlineMemberCap
+                            memberId={member.id}
+                            currentValue={member.maxAssignmentsOverride as number | null}
+                            onSave={(val) => updateJuryMemberMutation.mutate({
+                              id: member.id,
+                              maxAssignmentsOverride: val,
+                            })}
+                          />
                         <AlertDialog>
                           <AlertDialogTrigger asChild>
                             <Button
@@ -1561,6 +1579,7 @@ export default function RoundDetailPage() {
                             </AlertDialogFooter>
                           </AlertDialogContent>
                         </AlertDialog>
+                        </div>
                       </div>
                     ))}
                   </div>
@@ -2057,6 +2076,73 @@ export default function RoundDetailPage() {
 // Sub-components
 // ═══════════════════════════════════════════════════════════════════════════
 
+// ── Inline cap editor for jury members on round page ─────────────────────
+
+function InlineMemberCap({
+  memberId,
+  currentValue,
+  onSave,
+}: {
+  memberId: string
+  currentValue: number | null
+  onSave: (val: number | null) => void
+}) {
+  const [editing, setEditing] = useState(false)
+  const [value, setValue] = useState(currentValue?.toString() ?? '')
+  const inputRef = useRef<HTMLInputElement>(null)
+
+  useEffect(() => {
+    if (editing) inputRef.current?.focus()
+  }, [editing])
+
+  const save = () => {
+    const trimmed = value.trim()
+    const newVal = trimmed === '' ? null : parseInt(trimmed, 10)
+    if (newVal !== null && (isNaN(newVal) || newVal < 1)) {
+      toast.error('Enter a positive number or leave empty for no cap')
+      return
+    }
+    if (newVal === currentValue) {
+      setEditing(false)
+      return
+    }
+    onSave(newVal)
+    setEditing(false)
+  }
+
+  if (editing) {
+    return (
+      <Input
+        ref={inputRef}
+        type="number"
+        min={1}
+        className="h-6 w-16 text-xs"
+        value={value}
+        placeholder="\u221E"
+        onChange={(e) => setValue(e.target.value)}
+        onBlur={save}
+        onKeyDown={(e) => {
+          if (e.key === 'Enter') save()
+          if (e.key === 'Escape') { setValue(currentValue?.toString() ?? ''); setEditing(false) }
+        }}
+      />
+    )
+  }
+
+  return (
+    <button
+      type="button"
+      className="inline-flex items-center gap-1 rounded px-1.5 py-0.5 text-xs hover:bg-muted transition-colors group"
+      title="Click to set max assignment cap"
+      onClick={() => { setValue(currentValue?.toString() ?? ''); setEditing(true) }}
+    >
+      <span className="text-muted-foreground">max:</span>
+      <span className="font-medium">{currentValue ?? '\u221E'}</span>
+      <Pencil className="h-2.5 w-2.5 text-muted-foreground opacity-0 group-hover:opacity-100 transition-opacity" />
+    </button>
+  )
+}
+
 // ── Unassigned projects queue ────────────────────────────────────────────
 
 function RoundUnassignedQueue({ roundId, requiredReviews = 3 }: { roundId: string; requiredReviews?: number }) {