feat(places): name every authority a place sits in

SW19 is mostly Merton but partly Wandsworth, and the page said only Merton.
The cause was one field doing two jobs: _parent_authority takes the modal
authority, which is right for a 301 target and wrong as a statement about
where a place is.

This is not a corner case. A quarter of viable outcodes (425 of 1,760) and a
third of viable towns (263 of 783) cross an authority boundary — Bedford the
town spans Bedford and Central Bedfordshire.

Place now carries `authorities`, every authority holding at least a tenth of
the schools and at least two of them, largest first. parent_authority stays
single and unchanged, because a redirect still needs one target.

The share threshold exists because GIAS carries postcode errors: EN6 lists two
Shropshire schools among fourteen in Hertfordshire, and a bare "any authority
present" rule would print those as though they were real. A place too small or
too fragmented to clear the threshold still names its largest, so the page
never goes silent about where it is.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_015mWQnpye9F299NVRCCSRvj

nextjs-app/components/places/PlaceView.tsx

@@ -106,6 +106,13 @@ function SchoolTable({ schools, phase }: { schools: School[]; phase: PhaseKey })
 
 export function PlaceView({ detail, phase, englandAverage, neighbours }: Props) {
   const { place, schools, averages } = detail;
+  // Fall back to the single parent when the API predates the authorities
+  // field, so a stale cache never blanks the line entirely.
+  const authorities = place.authorities?.length
+    ? place.authorities
+    : place.parent_authority
+      ? [{ name: place.parent_authority, slug: authoritySlug(place.parent_authority), count: 0 }]
+      : [];
   const local = averages[METRICS[phase ?? 'primary'].key];
   const phaseWord = phase === 'secondary' ? 'Secondary schools'
     : phase === 'primary' ? 'Primary schools' : 'Schools';
@@ -163,13 +170,20 @@ export function PlaceView({ detail, phase, englandAverage, neighbours }: Props)
         <h1>{phaseWord} in {place.name}</h1>
         <p className={styles.summary}>
           {place.count} schools
-          {place.parent_authority && (
+          {authorities.length > 0 && (
             <>
               {' · '}
-              <Link href={`/schools/authority/${authoritySlug(place.parent_authority)}`}
-                className={styles.inlineLink}>
-                {place.parent_authority}
-              </Link>
+              {/* Every authority, not just the largest. A quarter of outcodes
+                  and a third of towns cross a boundary: SW19 is mostly Merton
+                  but partly Wandsworth, and naming one asserts otherwise. */}
+              {authorities.map((a, i) => (
+                <span key={a.slug}>
+                  {i > 0 && (i === authorities.length - 1 ? ' and ' : ', ')}
+                  <Link href={`/schools/authority/${a.slug}`} className={styles.inlineLink}>
+                    {a.name}
+                  </Link>
+                </span>
+              ))}
             </>
           )}
         </p>