feat(admissions): show the last distance offered where councils publish it

Adds the cut-off distance a parent actually asks about — "how close do we
need to live?" — end to end: a Singer tap, dbt staging and mart models, an
Airflow DAG, and a tile on both detail templates. 3,597 schools across 57
local authorities carry a figure; the rest are unchanged.

There is no national source for this. Each LA publishes its own cut-offs in
its own format, and the collected CSV is transcribed from PDFs, spreadsheets
and web pages — so most of the work here is deciding what is safe to show.

Data
  * tap-uk-school-distance loads the CSV verbatim into raw. Keyed on
    (urn, year, school_name), because school_name carries the admission
    route: (urn, year) alone collides on 118 keys and a reload would have
    silently dropped every band but one.
  * stg_school_distance applies a 25 m – 25 km plausibility band. The source
    contains 0.0-mile rows (published where a school filled on a higher
    criterion), 1-metre cut-offs, and one reading 533 miles — ~4% of rows,
    all of which would put a visibly wrong number on a live page.
  * fact_admission_distance collapses routes to one row per school per year
    using the furthest, and keeps route_count so the page can say the figure
    is the widest of several bands rather than the one for a given child.

Serving
  * Kept out of fact_admissions: that mart is EES-derived and near-complete
    for England, this one covers 57 LAs, and the two refresh independently.
  * Latest year only. Coverage is ragged — a school may have 2021 and 2026
    and nothing between — so a history array would invite a trend line drawn
    through gaps that are absences of publication, not of a cut-off.
  * The Admissions section now renders on either source. 3% of the schools
    that render have a cut-off and no EES admissions row, and gating on
    admissions alone would have hidden the figure on those pages.

Interface
  * The year travels with the figure everywhere it appears; a cut-off
    detached from its admissions round is not a fact about anything.
  * "Not a fixed catchment — it moves every year" sits under every instance,
    because that is the inference a parent will otherwise draw.
  * Replaces a hardcoded "Historical distance cut-off data is not available
    for this school" that appeared on every secondary page, including the
    ones whose council does publish it. The absence is now stated only when
    it is real, and names the authority that would hold it.

The tint costs the muted tokens their AA margin: measured on the composited
backdrop (not the computed one, which reports the untinted card), --text-muted
falls to 4.09:1 in dark theme. The tile uses --text-secondary instead — 6.50:1
dark, 6.60:1 light.

The DAG is manual, like the other annual ones: councils publish on allocation
day, each on its own timetable, so there is no date worth scheduling against.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01WDvkyqqHABm4bmth2kjAxE

nextjs-app/components/school/lastDistanceOffered.ts

@@ -0,0 +1,61 @@
+/**
+ * Shared logic and copy for the "last distance offered" figure.
+ *
+ * The primary and secondary admissions sections lay their metrics out
+ * differently (a seamless tile grid vs. metric cards), so the markup is not
+ * shared — but the words are. Every caveat below is doing a specific job, and
+ * a figure that appeared on one template without them would be misleading in a
+ * way the other template was not:
+ *
+ *   * The year, because a cut-off is the outcome of one particular admissions
+ *     round and means nothing detached from it.
+ *   * "not a fixed catchment", because that is the inference a parent will
+ *     otherwise draw, and it is wrong — the distance moves every year.
+ *   * The route count, because on a banded school the headline is the widest
+ *     of several cut-offs and does not apply to every child.
+ */
+
+import type { SchoolAdmissionDistance } from '@/lib/types';
+import { formatCutoffDistance, formatEntryYear } from '@/lib/utils';
+
+export interface CutoffDisplay {
+  /** Headline figure, e.g. "0.31 miles". */
+  primary: string;
+  /** Supporting conversion, e.g. "500 m". */
+  secondary: string;
+  /** Entry point the figure belongs to, e.g. "September 2025". */
+  entryYear: string;
+  /** Present only where several admission routes were collapsed into one figure. */
+  routeNote: string | null;
+}
+
+/** What the cut-off measures, and what it does not. Identical on both templates. */
+export const CUTOFF_NOTE =
+  'The furthest home offered a place, after higher priorities such as siblings, ' +
+  'faith and EHCP were applied. It is not a fixed catchment — it moves every year ' +
+  'with the number of applications.';
+
+/** Straight-line, because that is how councils measure it. */
+export const CUTOFF_MEASUREMENT_NOTE = 'Measured in a straight line from the school.';
+
+export function describeCutoff(
+  distance: SchoolAdmissionDistance | null | undefined
+): CutoffDisplay | null {
+  if (!distance) return null;
+
+  const figure = formatCutoffDistance(distance.distance_m);
+  if (!figure) return null;
+
+  const routes = distance.route_count ?? 1;
+
+  return {
+    primary: figure.primary,
+    secondary: figure.secondary,
+    entryYear: formatEntryYear(distance.year),
+    routeNote:
+      routes > 1
+        ? `Furthest of ${routes} admission routes at this school — the one that ` +
+          'applies to your child may have had a shorter cut-off.'
+        : null,
+  };
+}