fix(destinations): withhold at the API, not just in the chart

Code review found the disclosure the whole design was meant to prevent.
R1 was written as a rendering rule and implemented as one: canRenderBar
stopped the bar being drawn, but GET /api/schools/{urn} still carried the
cohort and every published category. cohort - sum(published) returned
Whitley Bay's withheld further-education figure exactly — 18 pupils — to
any caller, and the RSC payload put it in the browser too.

app.py already stated the principle for admission_distance: this endpoint
is public and unauthenticated, so a field left in the payload is a
published field. The same reasoning applies here and did not get applied.

_mask_for_disclosure now closes both identities before serialisation —
categories sum to the cohort, and disadvantaged + other = all — by adding
secondary suppression until every row and column hides none or at least
two. My first attempt picked the smallest published cell as the companion
and a new test caught it choosing a zero, which protects nothing: the
residual still resolved to 18. The companion must carry pupils.

DfE's own aggregates are no longer served. Nothing rendered them, and one
spanning a single suppressed component names it.

Cost, measured over 262 mainstream secondaries: the all-pupils bar
survives on 94% rather than 100%. Zero lone-suppressed groups remain.

The e2e helper now tells a missing feature apart from missing data: it
fails if the API serves no destinations key at all, and skips if the key
is served but the annual DAG has not populated the marts. Failing on the
second would redden the staging gate for unrelated commits.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01BvdDKvFFSZuMVDH5fEyTob

docs/superpowers/specs/2026-08-28-destination-measures-design.md

@@ -42,17 +42,47 @@ Those are the precise numbers the `c` exists to hide, and in a random 400-school
 sample **22% of mainstream secondaries** have exactly one suppressed category in
 their disadvantaged group. This is the normal case, not an edge case.
 
-Two rules follow, and everything else in this document is downstream of them.
+Three rules follow, and everything else in this document is downstream of them.
 
-**R1 — Never render a derived remainder.** Not as a number, and not as a bar
-segment: a segment sized by the residual can be read straight off the axis. Where
-any category in a pupil group is suppressed, the page shows the published
-categories, says the rest are withheld, and stops.
+**R1 — Never *publish* enough to derive a remainder.**
 
-**R2 — Never aggregate across a suppression boundary.** A group total is
-publishable only when DfE published that total itself, or when the aggregate
-spans **two or more** suppressed cells. Summing published components to fill a
-gap is R1 with extra steps.
+An earlier draft of this rule said "never *render* a derived remainder", and
+that was the defect code review caught in PR #137. Not drawing a number does
+nothing to stop it being computed: `GET /api/schools/{urn}` is public and
+unauthenticated, so anything in the payload is published whatever the UI
+chooses to draw. The rendering guards shipped; the payload still carried the
+cohort and every published category, and `cohort - sum(published)` returned
+Whitley Bay's withheld figure exactly.
+
+The rule is therefore about the serialiser, and the UI guards are a second line
+of defence behind it. Two identities have to be closed:
+
+- within a pupil group the categories sum to the cohort, so a group with
+  exactly **one** suppressed category gives it away;
+- across groups, disadvantaged + other = all for every category, so a category
+  suppressed in exactly **one** of the three gives itself away.
+
+`_mask_for_disclosure` applies DfE's own answer — secondary suppression —
+withholding a companion cell until every row and every column hides either none
+or at least two. It iterates, because each new suppression can break the other
+identity, and terminates because cells are only ever added.
+
+The companion must carry pupils. Suppressing a zero looks like secondary
+suppression and protects nothing: the residual still equals the original
+withheld figure. Where no non-zero companion exists, the whole set is withheld.
+
+Measured cost on the 400-school sample: the all-pupils bar survives on **94%**
+of mainstream secondaries rather than 100%. That is the price of not
+republishing what DfE withheld.
+
+**R2 — Never aggregate across a suppression boundary.** Summing published
+components to fill a gap is R1 with extra steps.
+
+DfE's own aggregates (`Sustained education destination`, `Sustained education,
+employment & apprenticeships`) are ingested but **not served**. An aggregate
+spanning exactly one suppressed component names it, and nothing renders them
+today — an unused field that leaks is not a trade-off worth carrying. They can
+be re-added with their own guard if the fallback ladder is ever built.
 
 **R3 — The three pupil groups are one disclosure surface, not three.**
 Disadvantaged and Not-known-to-be-disadvantaged partition All pupils, so
@@ -116,12 +146,17 @@ the counts — the published percentages do not sum to 100.
 
 Random 400-school sample, 2022/23, mainstream secondaries (n=262):
 
-| View | Published | Consequence |
-|---|---|---|
-| All pupils, all categories | **100%** | Full bar works everywhere |
-| Disadvantaged, headline rate | 95% | Gap panel works |
-| Disadvantaged, three grouped cards | 68% | Degrades card by card |
-| Disadvantaged, all six categories | **20%** | Bar unusable for this group |
+| View | As published by DfE | After R1–R3 masking | Consequence |
+|---|---|---|---|
+| All pupils, all categories | 100% | **94%** | Bar works nearly everywhere |
+| Disadvantaged, headline rate | 95% | 95% | Gap panel works |
+| Disadvantaged, three grouped cards | 68% | 68% | Degrades card by card |
+| Disadvantaged, all six categories | 20% | **20%** | Bar unusable for this group |
+
+The middle column is what the site actually serves. Masking costs the
+all-pupils bar on 6% of mainstream secondaries — those are schools where a
+category was suppressed in exactly one pupil group and no non-zero companion
+existed below the all-pupils row.
 
 Special schools and alternative provision are far worse: 13% and 41% respectively
 have the whole cohort suppressed even for all pupils. The empty state is
@@ -325,10 +360,12 @@ and the staging E2E gate runs post-merge.
 
 ## Risks
 
-**A later change reintroduces the disclosure.** The likeliest route is someone
-applying `safe_numeric` to a destination column for consistency, or adding a
-`coalesce` in a mart. Mitigation is the dbt test plus the unit tests on
-`canAggregate()` — the rule has to be executable, not documentary.
+**A later change reintroduces the disclosure.** The likeliest routes are
+applying `safe_numeric` to a destination column for consistency, adding a
+`coalesce` in a mart, or — as happened in review — enforcing a disclosure rule
+at the rendering layer instead of the publishing layer. Mitigation is the dbt
+tests plus `backend/tests/test_destinations_api.py`, which reconstructs the
+residual the way an attacker would and asserts it no longer resolves.
 
 **The two-year lag reads as staleness.** Mitigated by dating the cohort in the
 section header rather than only in a tooltip.