Each requested dimension is a key of the model's $this->facets whitelist (the filterable facets become the counted facets). One LET sub-query per dimension counts values over the same conjunctive filter as the list, so the buckets reflect the currently filtered set:

LET category = (FOR doc IN @@coll FILTER <same filters> COLLECT value = doc.category WITH COUNT INTO count SORT count DESC, value ASC RETURN { value, count })
LET status   = (FOR doc IN @@coll FILTER <same filters> COLLECT value = doc.status   WITH COUNT INTO count SORT count DESC, value ASC RETURN { value, count })
RETURN { category, status }

Supported types: the scalar Facet::FIELD, the array-membership Facet::IN family (Facet::LIST, Facet::LIST_FIELD, Facet::LIST_FIELD_SORTED) and the two linked facets Facet::EDGE and Facet::JOIN; other facet types are skipped. A Facet::PROPERTY carrying the [*] array-expansion marker (e.g. offers[*].priceCurrency) unwinds the object array and counts the sub-field per element — see FacetCountsQueryTrait::buildFacetCountSubquery().

A linked dimension counts the documents reached through the relation it already filters on — an INBOUND edge traversal or a key-join — bucketing on a field of the related document named by Facet::VALUE (default _key):

LET location = (FOR doc IN @@coll FILTER <same filters> FOR doc_location IN INBOUND doc places_edges COLLECT value = doc_location.name WITH COUNT INTO count SORT count DESC, value ASC RETURN { value, count })

The unwinding facet types (the [*] expansion, the Facet::IN family and the linked facets) count rows by default, so a document reaching the same value several times — a repeated array element, two parallel edges to the same vertex, several joined documents — is counted several times, diverging from the equivalent ?filter= existence test, which counts documents. Declaring Facet::DISTINCT => true on such a facet switches its bucket count to COUNT_DISTINCT( doc._key ), so the count reflects distinct root documents and matches the filter. The flag is opt-in (default unchanged) and a no-op on the scalar Facet::FIELD type, which already counts one row per document.

Top-N buckets. Every dimension returns all its values by default, which a sidebar showing ten entries does not need. Facet::LIMIT => n closes the shared tail with a LIMIT n placed after the sort, so what survives is the n biggest buckets. It is read once for every type — the scalar field, the unwound array, the [*] sub-field and the linked relations — because they all end on the same tail. Arango::FACET_COUNTS_LIMIT overrides it per request, so the declaration is a default rather than a ceiling.

A total order. Buckets are sorted count DESC, value ASC. The second criterion is what makes a top-N mean something: ordering by the count alone leaves equal-count buckets in whatever order the server produced, and AQL guarantees no stable sort — so a LIMIT n falling inside a run of equal counts could keep a different subset from one request to the next. The bucket value is unique per bucket (it is the COLLECT key), so the order is total.

Permission. The dimension gate runs before the type is dispatched, so it covers the linked types unchanged — but the two guards do not weigh the same for them: the projection inheritance (isAttributeAuthorized) looks the dimension up in the main model's fields, which cannot say anything about a field of another collection. A linked facet is therefore gated by the Field::REQUIRES declared on the facet itself, exactly as on the filtering side.