diff --git a/core/src/castle_core/relations.py b/core/src/castle_core/relations.py
index e557515..91a0941 100644
--- a/core/src/castle_core/relations.py
+++ b/core/src/castle_core/relations.py
@@ -15,6 +15,7 @@ dependencies — env is generated *from* requirements, not the reverse.
 from __future__ import annotations
 
 import shutil
+import subprocess
 from collections import Counter
 from dataclasses import dataclass, field
 from pathlib import Path
@@ -134,10 +135,25 @@ def requirements_of(config: CastleConfig, dep_name: str) -> list[Requirement]:
     return out
 
 
+def _dpkg_installed(pkg: str) -> bool:
+    """Whether a dpkg package is installed (the authoritative 'installed' check on
+    Debian/Ubuntu). Returns False where dpkg isn't available."""
+    dpkg = shutil.which("dpkg")
+    if not dpkg:
+        return False
+    r = subprocess.run([dpkg, "-s", pkg], capture_output=True, text=True)
+    return r.returncode == 0 and "install ok installed" in r.stdout
+
+
 def _check(config: CastleConfig, req: Requirement) -> bool:
     """Is a single requirement satisfied? (The check is fixed by its kind.)"""
     if req.kind == "system":
-        return shutil.which(req.ref) is not None
+        # `system_dependencies` holds PACKAGE names, not executables. A PATH lookup
+        # only coincides with 'installed' when the package name equals its command
+        # (pandoc, rsync) — for names like poppler-utils / texlive-latex-base /
+        # docker-compose-plugin it never matches. Fast-path `which`, then ask the
+        # package manager (the real meaning of 'installed').
+        return shutil.which(req.ref) is not None or _dpkg_installed(req.ref)
     if req.kind == "deployment":
         return req.ref in config.deployments
     return True
diff --git a/core/tests/test_relations.py b/core/tests/test_relations.py
index 45f1a11..b709a93 100644
--- a/core/tests/test_relations.py
+++ b/core/tests/test_relations.py
@@ -91,13 +91,27 @@ def test_functional_predicate_reports_unmet(monkeypatch: pytest.MonkeyPatch) ->
         {"web": prog, "api": ProgramSpec(id="api")},
         {"web": _dep("web"), "api": _dep("api")},
     )
-    monkeypatch.setattr(R.shutil, "which", lambda _: None)  # nothing installed
+    monkeypatch.setattr(R.shutil, "which", lambda _: None)  # not on PATH
+    monkeypatch.setattr(R, "_dpkg_installed", lambda _: False)  # nor as a package
     m = R.build_model(cfg, check=True)
     web = next(n for n in m.nodes if n.name == "web")
     assert web.unmet == ["system:pandoc"]  # deployment:api exists → satisfied
     assert web.functional is False
 
 
+def test_system_requirement_satisfied_by_package_not_on_path(
+    monkeypatch: pytest.MonkeyPatch,
+) -> None:
+    """A package name that isn't a command (poppler-utils) is satisfied when the
+    package is installed — a PATH lookup alone would wrongly report it unmet."""
+    prog = ProgramSpec(id="t", system_dependencies=["poppler-utils"])
+    cfg = _cfg({"t": prog}, {"t": _dep("t")})
+    monkeypatch.setattr(R.shutil, "which", lambda _: None)  # no `poppler-utils` binary
+    monkeypatch.setattr(R, "_dpkg_installed", lambda pkg: pkg == "poppler-utils")
+    t = next(n for n in R.build_model(cfg, check=True).nodes if n.name == "t")
+    assert t.functional is True and t.unmet == []
+
+
 def test_missing_deployment_requirement_is_unmet() -> None:
     prog = ProgramSpec(id="web", requires=[Requirement(kind="deployment", ref="ghost")])
     cfg = _cfg({"web": prog}, {"web": _dep("web")})