fix(admissions): state distance in miles throughout, never mixed

The postcode check read "69 m away — inside the September 2026 cut-off of
0.17 miles". Both numbers are right and the sentence is still useless: the
reader has to convert one of them to check a comparison we had already made
for them.

The cause was a readability rule of mine in formatCutoffDistance, which swapped
to metres below 100m on the grounds that "0.04 miles" carries less than "69 m".
Taken one figure at a time that holds. Taken in a sentence containing two
figures it guarantees a mismatch whenever they fall either side of the
threshold — and a 270m cut-off with a nearby home does exactly that.

Miles now lead everywhere. It is the unit UK school admissions runs on:
councils publish cut-offs in miles (90% of the collected source rows), and it
is what a parent has already been quoted in their booklet and offer letter.
The metric figure survives only as support beside the miles figure on the
Admissions tile, where it converts the same value rather than presenting a
second one to compare.

Below 0.01 miles the decimal places run out rather than the unit being wrong,
so a very short distance is described — "under 0.01 miles" — instead of
rounding to a flat "0.00 miles", which would read as no distance at all.

Both figures in the verdict now go through one formatter with no fallback that
could reach for another unit. The old `?? "N m"` fallbacks on that line were a
second route to the same defect and are gone.

Covered by a sweep over sixty home/cut-off combinations spanning the old
switch point, asserting no verdict contains a metric reading and that exactly
two miles figures appear; plus the reported case pinned verbatim, and an e2e
guard on the rendered verdict.

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

nextjs-app/__tests__/lib/lastDistanceOffered.test.ts

@@ -7,7 +7,7 @@
  * place — so both are pinned here rather than left to the component.
  */
 
-import { formatCutoffDistance, formatEntryYear } from '@/lib/utils';
+import { formatCutoffDistance, formatMiles, formatEntryYear } from '@/lib/utils';
 import {
   describeCutoff, describeCutoffAbsence, compareToCutoff, CUTOFF_UNCERTAINTY_M,
 } from '@/components/school/lastDistanceOffered';
@@ -32,8 +32,19 @@ describe('formatCutoffDistance', () => {
     expect(formatCutoffDistance(3472.96)!.secondary).toBe('3.5 km');
   });
 
-  it('leads with metres below 100 m, where a miles figure carries nothing', () => {
-    expect(formatCutoffDistance(27)).toEqual({ primary: '27 m', secondary: '0.02 miles' });
+  it('stays in miles at short range, where it used to swap to metres', () => {
+    // The swap made a single number easier to read and a comparison harder:
+    // "69 m away — inside the cut-off of 0.17 miles" asked the reader to
+    // convert between units to check a claim we had already made for them.
+    expect(formatCutoffDistance(27)).toEqual({ primary: '0.02 miles', secondary: '30 m' });
+    expect(formatCutoffDistance(69)!.primary).toMatch(/miles$/);
+  });
+
+  it('describes a distance too short for two decimal places', () => {
+    // Rather than a flat "0.00 miles", which reads as no distance at all.
+    expect(formatMiles(5)).toBe('under 0.01 miles');
+    expect(formatMiles(0)).toBe('under 0.01 miles');
+    expect(formatMiles(20)).toBe('0.01 miles');
   });
 
   it('returns null rather than a zero cut-off', () => {
@@ -84,6 +95,36 @@ describe('describeCutoff', () => {
 // ── "Would we have got in?" ────────────────────────────────────────────
 
 describe('compareToCutoff', () => {
+  it('never states the two figures in different units', () => {
+    /*
+     * The reported defect: "69 m away — inside the September 2026 cut-off of
+     * 0.17 miles". Both numbers are correct and the sentence is still useless,
+     * because checking it means converting one of them.
+     *
+     * Swept across the range where the old formatter switched units, so a
+     * future readability tweak to one figure cannot reintroduce the mismatch
+     * in the other.
+     */
+    const mixed: string[] = [];
+    for (const homeM of [0, 5, 27, 69, 99, 100, 260, 800, 1609, 5000]) {
+      for (const cutoffM of [30, 69, 100, 270, 1000, 3500]) {
+        const { headline } = compareToCutoff(homeM, cutoffM, 2026);
+        const hasMetres = /\d\s?m\b/.test(headline);
+        const milesCount = (headline.match(/miles/g) ?? []).length;
+        // Two figures, both in miles, and no metric reading anywhere near them.
+        if (hasMetres || milesCount !== 2) {
+          mixed.push(`home=${homeM}m cutoff=${cutoffM}m -> ${headline}`);
+        }
+      }
+    }
+    expect(mixed).toEqual([]);
+  });
+
+  it('reads back the reported case in one unit', () => {
+    expect(compareToCutoff(69, 270, 2026).headline)
+      .toBe('0.04 miles away — inside the September 2026 cut-off of 0.17 miles.');
+  });
+
   it('calls a clearly nearer home inside, and names the year', () => {
     const r = compareToCutoff(300, 800, 2026);
     expect(r.verdict).toBe('inside');