feat(admissions): add admissions guide page and homepage countdown strip

- New /admissions route with AdmissionsView client component
- Live countdowns (days until) to Primary/Secondary deadlines and Offer Days
- Step-by-step timelines for both tracks with highlighted milestone rows
- Tips section covering equal preference rule, late applications, waiting lists
- Homepage countdown strip (4 cards) between discovery chips and how-it-works
- Admissions nav link and footer link added

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

nextjs-app/components/HomeView.tsx

@@ -24,6 +24,39 @@ interface HomeViewProps {
   totalSchools?: number | null;
 }
 
+function daysUntil(month: number, day: number): number {
+  const today = new Date();
+  today.setHours(0, 0, 0, 0);
+  const y = today.getFullYear();
+  let target = new Date(y, month - 1, day);
+  if (target <= today) target = new Date(y + 1, month - 1, day);
+  return Math.round((target.getTime() - today.getTime()) / 86_400_000);
+}
+
+function formatCountdownDate(month: number, day: number): string {
+  const today = new Date();
+  today.setHours(0, 0, 0, 0);
+  const y = today.getFullYear();
+  let target = new Date(y, month - 1, day);
+  if (target <= today) target = new Date(y + 1, month - 1, day);
+  return target.toLocaleDateString('en-GB', { weekday: 'short', day: 'numeric', month: 'long', year: 'numeric' });
+}
+
+interface CountdownChipData {
+  type: 'deadline' | 'offer';
+  track: string;
+  milestone: string;
+  month: number;
+  day: number;
+}
+
+const ADMISSIONS_CHIPS: CountdownChipData[] = [
+  { type: 'offer',    track: 'Primary · Offer Day',        milestone: 'Primary National Offer Day',     month: 4,  day: 16 },
+  { type: 'deadline', track: 'Secondary · Deadline',       milestone: 'Secondary applications close',   month: 10, day: 31 },
+  { type: 'deadline', track: 'Primary · Deadline',         milestone: 'Primary applications close',     month: 1,  day: 15 },
+  { type: 'offer',    track: 'Secondary · Offer Day',      milestone: 'Secondary National Offer Day',   month: 3,  day: 1  },
+];
+
 export function HomeView({ initialSchools, filters, totalSchools }: HomeViewProps) {
   const searchParams = useSearchParams();
   const router = useRouter();
@@ -43,6 +76,7 @@ export function HomeView({ initialSchools, filters, totalSchools }: HomeViewProp
   const prevSearchParamsRef = useRef(searchParams.toString());
   const [geoState, setGeoState] = useState<'idle' | 'requesting' | 'error'>('idle');
   const [geoError, setGeoError] = useState<string | null>(null);
+  const [chipDays, setChipDays] = useState<(number | null)[]>(ADMISSIONS_CHIPS.map(() => null));
 
   const hasSearch = searchParams.get('search') || searchParams.get('postcode');
   const isLocationSearch = !!searchParams.get('postcode');
@@ -100,6 +134,11 @@ export function HomeView({ initialSchools, filters, totalSchools }: HomeViewProp
       .catch(() => {});
   }, []);
 
+  // Compute admissions countdown days client-side to avoid SSR mismatch
+  useEffect(() => {
+    setChipDays(ADMISSIONS_CHIPS.map(c => daysUntil(c.month, c.day)));
+  }, []);
+
   const handleLoadMore = async () => {
     if (isLoadingMore || !hasMore) return;
     setIsLoadingMore(true);
@@ -240,6 +279,47 @@ export function HomeView({ initialSchools, filters, totalSchools }: HomeViewProp
         </div>
       )}
 
+      {/* Admissions countdown strip — only on landing page */}
+      {!isSearchActive && (
+        <section className={styles.admissionsStrip}>
+          <div className={styles.stripHeader}>
+            <span className={styles.stripLabel}>Key admissions deadlines</span>
+            <a href="/admissions" className={styles.stripCta}>Full admissions guide →</a>
+          </div>
+          <div className={styles.countdownRail}>
+            {ADMISSIONS_CHIPS.map((chip, i) => {
+              const days = chipDays[i];
+              const isUrgent = days !== null && days <= 14;
+              const chipClass = [
+                styles.countdownChip,
+                chip.type === 'deadline' ? styles.countdownChipDeadline : styles.countdownChipOffer,
+                isUrgent ? styles.countdownChipUrgent : '',
+              ].filter(Boolean).join(' ');
+              const trackClass = [
+                styles.chipTrack,
+                chip.type === 'deadline' ? styles.chipTrackDeadline : styles.chipTrackOffer,
+              ].join(' ');
+              return (
+                <div key={chip.milestone} className={chipClass}>
+                  <span className={trackClass}>
+                    <span className={styles.chipTrackDot} aria-hidden="true" />
+                    {chip.track}
+                  </span>
+                  <div>
+                    <span className={styles.chipDays}>{days ?? '—'}</span>
+                    {days !== null && <span className={styles.chipDaysUnit}>days</span>}
+                  </div>
+                  <div className={styles.chipMilestone}>{chip.milestone}</div>
+                  <div className={styles.chipDate}>
+                    {days !== null ? formatCountdownDate(chip.month, chip.day) : ''}
+                  </div>
+                </div>
+              );
+            })}
+          </div>
+        </section>
+      )}
+
       {/* How it works — only on landing page */}
       {!isSearchActive && (
         <section className={styles.howItWorks}>