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

backend/places.py

@@ -30,6 +30,12 @@ class Place:
     name: str
     urns: tuple[int, ...]
     parent_authority: str | None    # authority NAME, for the 301 target
+    # Every authority the place meaningfully sits in, largest first. A quarter
+    # of outcodes and a third of towns straddle a boundary — SW19 is mostly
+    # Merton but partly Wandsworth — so naming only one asserts something
+    # false. parent_authority stays single because a redirect needs one
+    # target; this is what the page shows.
+    authorities: tuple[tuple[str, int], ...] = ()
     # URNs per phase, so the per-phase threshold can be applied without
     # re-querying. A place with 30 primaries and 2 secondaries publishes a
     # primary variant and no secondary one.
@@ -71,6 +77,42 @@ def _phase_urns(group, publishable: set[int]) -> dict[str, tuple[int, ...]]:
     return out
 
 
+# A place is described by an authority when it holds at least a tenth of the
+# schools, and at least two. GIAS carries occasional 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.
+_AUTHORITY_MIN_SHARE = 0.10
+_AUTHORITY_MIN_SCHOOLS = 2
+_AUTHORITY_MAX_SHOWN = 3
+
+
+def _authorities(group) -> tuple[tuple[str, int], ...]:
+    """Authorities this place meaningfully sits in, largest first."""
+    from backend.app import EXCLUDED_FILTER_VALUES
+
+    if "local_authority" not in group.columns:
+        return ()
+    counts = group["local_authority"].dropna().value_counts()
+    total = int(counts.sum())
+    if not total:
+        return ()
+
+    kept = [
+        (str(name), int(n)) for name, n in counts.items()
+        if str(name) not in EXCLUDED_FILTER_VALUES
+        and n >= _AUTHORITY_MIN_SCHOOLS
+        and n / total >= _AUTHORITY_MIN_SHARE
+    ]
+    # A place too small or too fragmented for the share rule still names its
+    # largest authority, or the page would say nothing about where it is.
+    if not kept:
+        for name, n in counts.items():
+            if str(name) not in EXCLUDED_FILTER_VALUES:
+                return ((str(name), int(n)),)
+        return ()
+    return tuple(kept[:_AUTHORITY_MAX_SHOWN])
+
+
 def _parent_authority(group) -> str | None:
     """The most common authority in a group — the useful 301 target.
 
@@ -104,6 +146,7 @@ def _group(df, column: str, kind: str, publishable: set[int]) -> dict[str, Place
         place = Place(
             kind=kind, slug=slug, name=name, urns=urns,
             parent_authority=_parent_authority(group) if kind == "town" else None,
+            authorities=() if kind == "authority" else _authorities(group),
             phase_urns=_phase_urns(group, publishable),
         )
         out[place.key] = place
@@ -138,6 +181,7 @@ def _outcode_places(df, publishable: set[int]) -> dict[str, Place]:
             continue
         place = Place(kind="outcode", slug=str(oc).lower(), name=str(oc),
                       urns=urns, parent_authority=_parent_authority(group),
+                      authorities=_authorities(group),
                       phase_urns=_phase_urns(group, publishable))
         out[place.key] = place
     return out
@@ -181,6 +225,7 @@ def _locality_places(df, publishable: set[int],
             continue
         place = Place(kind="locality", slug=slug, name=name, urns=urns,
                       parent_authority=_parent_authority(group),
+                      authorities=_authorities(group),
                       phase_urns=_phase_urns(group, publishable))
         out[place.key] = place
     return out