backend/data_loader.py

@@ -839,10 +839,44 @@ def _format_cohort_year(year) -> str | None:
     return text
 
 
-def _mask_for_disclosure(groups: dict) -> None:
-    """Add secondary suppression until no withheld figure can be recovered.
+_PUPIL_GROUPS = ("disadvantaged", "other", "all")
 
-    Not rendering a number is not the same as not publishing it. This endpoint
+
+def _lone_hidden_groups(groups: dict) -> list:
+    """Pupil groups hiding exactly one category — solvable by subtraction."""
+    return [
+        key for key, group in groups.items()
+        if sum(1 for c in group["categories"] if c["status"] == "suppressed") == 1
+    ]
+
+
+def _lone_hidden_categories(groups: dict) -> list:
+    """Categories hidden in exactly one of several pupil groups."""
+    lone = []
+    categories = {c["category"] for g in groups.values() for c in g["categories"]}
+    for category in categories:
+        found = [
+            c for g in groups.values() for c in g["categories"]
+            if c["category"] == category
+        ]
+        hidden = [c for c in found if c["status"] == "suppressed"]
+        if len(hidden) == 1 and len(found) > 1:
+            lone.append(category)
+    return lone
+
+
+def disclosure_invariant_holds(groups: dict) -> bool:
+    """Every row and every column hides none, or at least two.
+
+    Public so the tests can assert it directly rather than re-deriving it.
+    """
+    return not _lone_hidden_groups(groups) and not _lone_hidden_categories(groups)
+
+
+def _mask_for_disclosure(groups: dict) -> None:
+    """Withhold further cells until nothing suppressed can be solved for.
+
+    Not rendering a figure is not the same as not publishing it. This endpoint
     is public and unauthenticated, so anything left in the payload is
     published, whatever the UI chooses to draw — the same reasoning the
     admission_distance field carries in app.py.
@@ -855,17 +889,19 @@ def _mask_for_disclosure(groups: dict) -> None:
         category suppressed in exactly ONE of the three gives itself away.
 
     DfE's own answer is secondary suppression: withhold a second cell so the
-    residual spans two unknowns and identifies neither. This does the same,
-    iterating because each new suppression can break the other identity, and
-    terminating because cells are only ever added to the suppressed set.
+    residual spans two unknowns and identifies neither.
 
-    Mutates `groups` in place.
+    Where no companion can do that — a sparse cohort whose every other category
+    is `not_applicable`, which is common in special schools and alternative
+    provision — there is nothing left to withhold, so the pupil group is
+    DROPPED entirely. An earlier version simply gave up here and returned with
+    the violation intact and no signal, which is the one outcome this function
+    must never produce: a disclosure-control pass that fails silently is worse
+    than none, because everything downstream trusts it.
+
+    Mutates `groups` in place. Guaranteed to return with
+    disclosure_invariant_holds(groups) true.
     """
-    PAIRS = ("disadvantaged", "other", "all")
-
-    def cells(group_key):
-        group = groups.get(group_key)
-        return group["categories"] if group else []
 
     def suppress(cell):
         if cell["status"] == "published":
@@ -875,14 +911,13 @@ def _mask_for_disclosure(groups: dict) -> None:
             return True
         return False
 
-    def add_companion(candidates):
+    def add_companion(candidates) -> bool:
         """Withhold a second cell so the residual spans two unknowns.
 
         The companion must carry pupils. Suppressing a zero looks like
         secondary suppression and protects nothing: the residual still equals
-        the original withheld figure exactly. Where every remaining cell is
-        zero there is no companion that helps, so the whole set goes — losing
-        real data, but that beats publishing what DfE withheld.
+        the original withheld figure exactly. Returns False when no cell can
+        do the job, which escalates to dropping the group.
         """
         published = [c for c in candidates if c["status"] == "published"]
         useful = sorted(
@@ -891,31 +926,47 @@ def _mask_for_disclosure(groups: dict) -> None:
         )
         if useful:
             return suppress(useful[0])
-        return any([suppress(c) for c in published])
+        # Every remaining cell is zero or not applicable: withholding any of
+        # them leaves the residual equal to the original figure.
+        return False
 
-    changed = True
-    while changed:
+    # Fixpoint: each new suppression can break the other identity. Terminates
+    # because every pass either adds a suppression, drops a group, or stops.
+    while not disclosure_invariant_holds(groups):
         changed = False
 
-        # Column rule: a category must be suppressed in none of the three
-        # pupil groups, or in at least two of them.
-        categories = {c["category"] for key in PAIRS for c in cells(key)}
-        for category in categories:
-            found = [
-                c for key in PAIRS for c in cells(key) if c["category"] == category
+        for category in _lone_hidden_categories(groups):
+            siblings = [
+                c for g in groups.values() for c in g["categories"]
+                if c["category"] == category
             ]
-            hidden = [c for c in found if c["status"] == "suppressed"]
-            if len(hidden) == 1 and len(found) > 1:
-                if add_companion(found):
-                    changed = True
+            if add_companion(siblings):
+                changed = True
 
-        # Row rule: within a group, none suppressed or at least two.
-        for key in PAIRS:
-            group_cells = cells(key)
-            hidden = [c for c in group_cells if c["status"] == "suppressed"]
-            if len(hidden) == 1:
-                if add_companion(group_cells):
-                    changed = True
+        for key in _lone_hidden_groups(groups):
+            if add_companion(groups[key]["categories"]):
+                changed = True
+
+        if changed:
+            continue
+
+        # Nothing left to withhold. Drop the groups that are still solvable,
+        # and any category still solvable across the groups that remain.
+        for key in _lone_hidden_groups(groups):
+            del groups[key]
+            changed = True
+
+        for category in _lone_hidden_categories(groups):
+            for group in groups.values():
+                for cell in group["categories"]:
+                    if cell["category"] == category and suppress(cell):
+                        changed = True
+
+        if not changed:
+            # Unreachable given the two escalations above, but a masking pass
+            # must never spin or exit unsafely. Withhold everything.
+            groups.clear()
+            return
 
 
 def _destinations_block(rows: list) -> dict | None:
@@ -969,6 +1020,12 @@ def _destinations_block(rows: list) -> dict | None:
 
     _mask_for_disclosure(groups)
 
+    # Masking can empty the block entirely — a sparse cohort where no group
+    # could be made safe. Return None so the section is absent rather than
+    # rendering an empty shell.
+    if not groups:
+        return None
+
     return {"cohort_year": _format_cohort_year(latest_year), "groups": groups}
 
 

backend/tests/test_destinations_api.py

@@ -9,7 +9,9 @@ serialiser adds secondary suppression to prevent it.
 See docs/superpowers/specs/2026-08-28-destination-measures-design.md.
 """
 
-from backend.data_loader import _destinations_block, _format_cohort_year
+from backend.data_loader import (
+    _destinations_block, _format_cohort_year, disclosure_invariant_holds,
+)
 
 
 def _row(group, measure, pupils, status, cohort=180, percentage=None, year=202223):
@@ -148,13 +150,16 @@ def test_a_category_hidden_in_one_group_is_hidden_in_a_second():
         rows.append(_row("other", measure, o, "published", cohort=122))
 
     groups = _destinations_block(rows)["groups"]
-    for measure in ["school_sixth_form"]:
+    measures = {c["category"] for g in groups.values() for c in g["categories"]}
+    assert len(measures) == 6, "the fixture's six measures must all be checked"
+
+    for measure in sorted(measures):
         hidden = sum(
-            1 for key in ("all", "disadvantaged", "other")
-            for c in groups[key]["categories"]
+            1 for g in groups.values() for c in g["categories"]
             if c["category"] == measure and c["status"] == "suppressed"
         )
-        assert hidden >= 2, f"{measure} is solvable across the pupil groups"
+        # The invariant is "none, or at least two" — not "at least two".
+        assert hidden != 1, f"{measure} is solvable across the pupil groups"
 
 
 def test_a_suppressed_cell_never_keeps_its_percentage():
@@ -195,3 +200,70 @@ def test_a_fully_published_group_is_left_alone():
     group = _destinations_block(rows)["groups"]["all"]
     assert all(c["status"] == "published" for c in group["categories"])
     assert len(group["categories"]) == 7
+
+
+def test_the_invariant_is_asserted_directly_not_re_derived():
+    """A group with one suppressed category and nothing else to withhold."""
+    rows = [
+        _row("all", "school_sixth_form", None, "suppressed", cohort=9),
+        _row("all", "sixth_form_college", None, "not_applicable", cohort=9),
+        _row("all", "further_education", None, "not_applicable", cohort=9),
+    ]
+    block = _destinations_block(rows)
+    assert block is None or disclosure_invariant_holds(block["groups"])
+
+
+def test_a_sparse_cohort_with_no_companion_drops_the_group():
+    """Special schools and AP routinely have one suppressed category and every
+    other one not applicable. There is nothing left to withhold, so the group
+    goes — an earlier version returned here with the violation intact."""
+    rows = [
+        _row("all", "school_sixth_form", None, "suppressed", cohort=9),
+        _row("all", "sixth_form_college", None, "not_applicable", cohort=9),
+        _row("all", "further_education", None, "not_applicable", cohort=9),
+        _row("all", "apprenticeship", None, "not_applicable", cohort=9),
+        _row("all", "employment", None, "not_applicable", cohort=9),
+        _row("all", "not_sustained", None, "not_applicable", cohort=9),
+        _row("all", "not_captured", None, "not_applicable", cohort=9),
+    ]
+    block = _destinations_block(rows)
+    assert block is None or "all" not in block["groups"], (
+        "a group that cannot be made safe must not be served"
+    )
+
+
+def test_zeros_are_not_treated_as_a_usable_companion():
+    """Suppressing a zero protects nothing — the residual is unchanged. With
+    only zeros available the group must be dropped, not falsely 'fixed'."""
+    rows = [
+        _row("all", "school_sixth_form", None, "suppressed", cohort=5),
+        _row("all", "sixth_form_college", 0, "published", cohort=5),
+        _row("all", "further_education", 0, "published", cohort=5),
+    ]
+    block = _destinations_block(rows)
+    if block and "all" in block["groups"]:
+        group = block["groups"]["all"]
+        published = sum(c["pupils"] for c in group["categories"]
+                        if c["pupils"] is not None)
+        hidden = [c for c in group["categories"] if c["status"] == "suppressed"]
+        assert len(hidden) != 1, "a zero companion leaves the figure solvable"
+        assert group["cohort"] - published != 5
+
+
+def test_masking_always_terminates_in_a_safe_state():
+    """Exhaustive over every suppression pattern of a four-category group."""
+    from itertools import product
+    MEASURES = ["school_sixth_form", "sixth_form_college",
+                "further_education", "apprenticeship"]
+    for statuses in product(["published", "suppressed", "not_applicable"],
+                            repeat=len(MEASURES)):
+        rows = [
+            _row("all", m, 3 if st == "published" else None, st, cohort=12)
+            for m, st in zip(MEASURES, statuses)
+        ]
+        block = _destinations_block(rows)
+        if block is None:
+            continue
+        assert disclosure_invariant_holds(block["groups"]), (
+            f"invariant broken for {statuses}"
+        )

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

@@ -69,7 +69,17 @@ 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.
+withheld figure.
+
+Where no companion can do the job — a sparse cohort whose every other category
+is `not_applicable`, routine in special schools and alternative provision — the
+pupil group is **dropped from the payload entirely**. A first version simply
+returned at that point with the violation intact and no signal, which review
+caught: a disclosure-control pass that fails silently is worse than none,
+because everything downstream trusts it. The function now cannot terminate
+except in a state where `disclosure_invariant_holds()` is true, and an
+exhaustive test sweeps all 81 suppression patterns of a four-category group to
+prove it.
 
 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