diff --git a/docs/docs/cli/llm-stamp-themes.md b/docs/docs/cli/llm-stamp-themes.md
index 1ebaf77..a8ca76c 100644
--- a/docs/docs/cli/llm-stamp-themes.md
+++ b/docs/docs/cli/llm-stamp-themes.md
@@ -21,7 +21,7 @@ Usage: stack llm stamp-themes [OPTIONS]
 │ --key               TEXT     Only this item key.                             │
 │ --top               INTEGER  Themes kept per chunk. [default: 2]             │
 │ --min-score         FLOAT    Cosine similarity a theme must reach.           │
-│                              [default: 0.55]                                 │
+│                              [default: 0.6]                                  │
 │ --force                      Re-stamp chunks already on the current          │
 │                              vocabulary version.                             │
 │ --help                       Show this message and exit.                     │
diff --git a/src/cli/llm.py b/src/cli/llm.py
index 6bb5f61..fccc8ea 100644
--- a/src/cli/llm.py
+++ b/src/cli/llm.py
@@ -489,7 +489,7 @@ def stamp_themes(
     key: str = typer.Option("", "--key", help="Only this item key."),
     top: int = typer.Option(2, "--top", help="Themes kept per chunk."),
     min_score: float = typer.Option(
-        0.55, "--min-score", help="Cosine similarity a theme must reach."
+        0.60, "--min-score", help="Cosine similarity a theme must reach."
     ),
     force: bool = typer.Option(
         False,
diff --git a/src/llm/search.py b/src/llm/search.py
index 6fab6d9..cd8cc6a 100644
--- a/src/llm/search.py
+++ b/src/llm/search.py
@@ -54,13 +54,16 @@ def _collections_for(collection: str) -> tuple[str, ...]:
     return (collection,)
 
 
-def _store_filter(filters: dict[str, str]) -> dict[str, str]:
+def _store_filter(filters: dict[str, str]) -> dict[str, Any]:
     """The langchain PGVector ``filter=`` metadata dict for *filters* —
     docket/item_key/kind and the manual coordinates (doctype, manual,
     chapter, iom_section) are pushed down to the store; ``year`` is
     applied in Python (:func:`_year_ok`) since it's a prefix of the
-    ``date`` field, not its own metadata key."""
-    return {
+    ``date`` field, not its own metadata key. A ``theme`` becomes an
+    ``$or`` of equalities over the ``theme_1..theme_3`` rank keys
+    ``llm.themes`` writes, so the overfetch is not spent on off-theme
+    chunks (the comma-joined ``themes`` is re-checked in Python)."""
+    out: dict[str, Any] = {
         key: filters[key]
         for key in (
             "docket",
@@ -73,6 +76,10 @@ def _store_filter(filters: dict[str, str]) -> dict[str, str]:
         )
         if filters.get(key)
     }
+    theme = str(filters.get("theme") or "")
+    if theme:
+        out["$or"] = [{f"theme_{i}": theme} for i in range(1, 4)]
+    return out
 
 
 def _year_ok(md: dict[str, Any], year: str) -> bool:
diff --git a/src/llm/themes.py b/src/llm/themes.py
index 881e466..adb461f 100644
--- a/src/llm/themes.py
+++ b/src/llm/themes.py
@@ -93,7 +93,7 @@ def stamp(
     doctype: str = "manual",
     item_key: str = "",
     top: int = 2,
-    min_score: float = 0.55,
+    min_score: float = 0.60,
     batch: int = 1000,
     force: bool = False,
 ) -> dict[str, int]:
@@ -136,6 +136,12 @@ def stamp(
                 "themes": ",".join(s for s, _ in chosen),
                 "theme_scores": ",".join(f"{s}:{sc}" for s, sc in chosen),
                 "themes_vocab": version,
+                # one scalar key per rank so the store can filter with an
+                # equality ($or over theme_1..theme_N) instead of a LIKE
+                **{
+                    f"theme_{i}": (chosen[i - 1][0] if i <= len(chosen) else "")
+                    for i in range(1, top + 1)
+                },
             }
             patches.append({"id": cid, "patch": json.dumps(patch)})
         if patches:
diff --git a/tests/llm/test_search.py b/tests/llm/test_search.py
index ab208c2..78a7a0b 100644
--- a/tests/llm/test_search.py
+++ b/tests/llm/test_search.py
@@ -391,3 +391,12 @@ class TestThemeFilter:
         assert not _theme_ok({"themes": "telehealth,supervision"}, "drugs")
         assert not _theme_ok({}, "drugs")
         assert _theme_ok({}, "")
+
+    def test_theme_is_pushed_down_as_an_or_of_rank_keys(self):
+        out = _store_filter({"theme": "telehealth", "doctype": "manual"})
+        assert out["doctype"] == "manual"
+        assert out["$or"] == [
+            {"theme_1": "telehealth"},
+            {"theme_2": "telehealth"},
+            {"theme_3": "telehealth"},
+        ]
diff --git a/tests/llm/test_themes.py b/tests/llm/test_themes.py
index 2503a75..c12538c 100644
--- a/tests/llm/test_themes.py
+++ b/tests/llm/test_themes.py
@@ -64,7 +64,14 @@ class TestStamp:
             by["a"]["themes"] == "telehealth,mixed" and by["a"]["themes_vocab"] == "2"
         )
         assert by["a"]["theme_scores"].startswith("telehealth:1.0,mixed:0.7071")
-        assert by["c"] == {"themes": "", "theme_scores": "", "themes_vocab": "2"}
+        assert by["a"]["theme_1"] == "telehealth" and by["a"]["theme_2"] == "mixed"
+        assert by["c"] == {
+            "themes": "",
+            "theme_scores": "",
+            "themes_vocab": "2",
+            "theme_1": "",
+            "theme_2": "",
+        }
         assert "b" not in by
 
     def test_force_restamps_everything_and_pages_by_id(self):