fix(places): phase links must stay in their own namespace

Every place page built its phase links as /schools/[slug]/[phase], the
shape that belongs to towns alone.

On an authority page that pointed into the town namespace. For 87 of the
151 authorities the target does not exist and the link 404s; for the
other 64 it resolves to the town of the same name — a different set of
schools, which is precisely the near-duplicate the two namespaces were
introduced to prevent. On an outcode page it 404s outright.

Two causes behind it, both a rule written twice and inherited by only
one of the places that needed it.

The authority phase route was in the spec and dropped by the plan, which
built the three bare routes and no fourth. The sitemap is generated from
the place registry, which was right about them all along, so 302
authority phase URLs have been submitted to Google and every one 404s.
Adding the route makes the sitemap true and serves a real query —
admissions are authority-run, so "primary schools in Kent" is how a
parent searches before they have settled on a town.

The outcode variants were the opposite: the registry computed phases for
outcodes although the spec gives them no route, and the sitemap knew to
skip them while the API did not. The registry now decides alone, and the
sitemap's duplicate of that rule is gone.

Also: an authority under the five-school threshold has no page, so the
API sends a null slug for it and the page names it without linking.
Two English authorities are in that position. It was unreachable in
today's data — verified across the EC and TR outcodes — but the thin
place redirect would have sent a reader to a 404 the year it isn't.

The e2e journey now walks every /schools link a page of each family
emits and requires a 200, which is the check that was missing.

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

nextjs-app/components/places/PlaceView.tsx

@@ -181,11 +181,18 @@ export function PlaceView({ detail, phase, englandAverage, neighbours }: Props)
                   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}>
+                <span key={a.name}>
                   {i > 0 && (i === authorities.length - 1 ? ' and ' : ', ')}
-                  <Link href={`/schools/authority/${a.slug}`} className={styles.inlineLink}>
-                    {a.name}
-                  </Link>
+                  {/* No slug means no page: City of London and the Isles of
+                      Scilly hold too few schools for one. Saying where the
+                      place is stays right; linking there would 404. */}
+                  {a.slug
+                    ? (
+                      <Link href={`/schools/authority/${a.slug}`} className={styles.inlineLink}>
+                        {a.name}
+                      </Link>
+                    )
+                    : a.name}
                 </span>
               ))}
             </>
@@ -196,7 +203,11 @@ export function PlaceView({ detail, phase, englandAverage, neighbours }: Props)
       {!phase && (place.phases ?? []).length > 0 && (
         <nav className={styles.phaseLinks} aria-label="By phase">
           {(place.phases ?? []).map((ph) => (
-            <Link key={ph} href={`/schools/${place.slug}/${ph}`} className={styles.phaseLink}>
+            /* placeUrl, not a template: the bare `/schools/[slug]/[phase]`
+               shape belongs to towns alone, and using it everywhere sent
+               every authority page into the town namespace. */
+            <Link key={ph} href={placeUrl(place.kind, place.slug, ph)}
+              className={styles.phaseLink}>
               {ph === 'secondary' ? 'Secondary schools' : 'Primary schools'} in {place.name}
             </Link>
           ))}