diff --git a/layouts/partials/openapi/render-object-table.html b/layouts/partials/openapi/render-object-table.html
index 6caca3756..e78dd901c 100644
--- a/layouts/partials/openapi/render-object-table.html
+++ b/layouts/partials/openapi/render-object-table.html
@@ -94,24 +94,21 @@
 
     {{ end }}
 
-   {{/* NB: the OpenAPI spec says "Consistent with JSON Schema, additionalProperties
-         defaults to true." Our schemas tend to omit additionalProperties; I think we
-         effectively assume it defaults to false. Therefore: we only output regarding
-         additionalProperties if it is explicitly set (i.e. is non-nil). */}}
+ {{/* Additional properties should either be an OpenAPI schema object, or a
+       boolean. If it's the former, look for a `description` and render it as a note.
+       If it's `true`, do nothing. If it's `false`, raise a build-time error:
+       "Everything is extensible in Matrix unless otherwise noted". */}}
    {{ if (ne $additionalProperties nil )}}
   <tr class="row-additional-properties">
    <td colspan="3">
         {{ if (and (reflect.IsMap $additionalProperties)) -}}
             {{ if (index $additionalProperties "description") -}}
-May have additional properties: {{ $additionalProperties.description }}
+Notes on additional properties: {{ $additionalProperties.description }}
             {{ end }}
-        {{/* TODO: should we handle the case where additional properties are permitted,
-                    but must follow an explicit schema? */}}
-        {{ else if $additionalProperties -}}
-May have additional properties.
+            {{/* TODO: should we handle the case where additional properties are
+                       permitted, but must follow an explicit schema? */}}
         {{ else if (not $additionalProperties) -}}
-        {{/* At present we don't have any schema with additionalProperties: false.
-        But if we ever do, let's support it. */}}
+             {{ errorf "Unexpected additionalProperties=false for %s" $caption }}
 May **not** have additional properties.
         {{ end }}
    </td>