Pin halfvec index-identity test to the production e.embedding alias

The dense search path qualifies the column as e.embedding; the test
was asserting against a bare embedding identity that production never
emits. Also document that the dense channel uses cosineDistanceExpr
(plain vector or halfvec) rather than a hard-coded embedding <=> $vector.

Author: TheGreatAxios

IMPLEMENTATION.md

@@ -299,7 +299,10 @@ search); otherwise it throws `KnowledgeSearchInputError` (400).
 3. **Dense channel** — `fetchDenseCandidates`: embeds the query
    (`embedTexts`), resolves the tenant's single active embedding table
    (`resolveActiveEmbedTable` — **not** generation-scoped, see limitation
-   below), runs a raw-SQL cosine-distance ANN query (`embedding <=> $vector`)
+   below), runs a raw-SQL cosine-distance ANN query via `cosineDistanceExpr`
+   (`e.embedding <=> $vector` up to 2000 dims, or the matching
+   `(e.embedding::halfvec(N)) <=> $vector::halfvec(N)` expression above that
+   so the halfvec HNSW index is used)
    against that table joined back to
    `knowledge_chunk`/`knowledge_version`/`knowledge_document` with the
    **exact same visibility predicate**, hand-mirrored as

src/core/embed-model-registry.test.ts

@@ -189,10 +189,15 @@ describe("activateEmbedModel", () => {
     expect(indexQuery?.sql).not.toContain("ivfflat");
 
     // The planner only uses an expression index when the query reproduces
-    // the indexed expression verbatim — pin the two to the same string.
-    const indexedExpr = `(embedding::halfvec(${dims}))`;
-    expect(indexQuery?.sql).toContain(`(${indexedExpr} halfvec_cosine_ops)`);
-    expect(cosineDistanceExpr("embedding", "$1", dims).startsWith(indexedExpr)).toBe(true);
+    // the indexed expression. DDL indexes bare `embedding`; production dense
+    // search (search.ts) passes the table-qualified alias `e.embedding` —
+    // pin the query identity the live path actually emits.
+    expect(indexQuery?.sql).toContain(
+      `((embedding::halfvec(${dims})) halfvec_cosine_ops)`,
+    );
+    expect(cosineDistanceExpr("e.embedding", "$1", dims)).toBe(
+      `(e.embedding::halfvec(${dims})) <=> $1::halfvec(${dims})`,
+    );
   });
 
   it("does not fall back to ivfflat when halfvec index creation fails", async () => {