Add model embeddings for Z-factor DoF, separate from SaturatedController.

Fixed/Free Probe calibration now emits embeddings[] (unknown + equation) instead of controls[], keeping SaturatedController for physical regulation only.

Co-authored-by: Cursor <cursoragent@cursor.com>

crates/cli/tests/embeddings_reject_control_z.rs

@@ -0,0 +1,40 @@
+//! Z-factors must use embeddings[], not controls[]/SaturatedController.
+
+use entropyk_cli::run::{run_simulation, SimulationStatus};
+use tempfile::tempdir;
+
+#[test]
+fn controls_with_z_ua_are_rejected() {
+    // Minimal config — reject happens before component graph build.
+    let json = r#"
+{
+  "fluid": "R134a",
+  "fluid_backend": "Test",
+  "circuits": [],
+  "controls": [
+    {
+      "type": "SaturatedController",
+      "id": "bad_calib",
+      "measure": { "component": "sst", "output": "saturationTemperature" },
+      "actuator": { "component": "evap", "factor": "z_ua", "initial": 1, "min": 0.05, "max": 3 },
+      "target": 278.15
+    }
+  ],
+  "solver": { "strategy": "newton", "max_iterations": 10, "tolerance": 1e-6 }
+}
+"#;
+    let dir = tempdir().unwrap();
+    let path = dir.path().join("bad.json");
+    std::fs::write(&path, json).unwrap();
+    let result = run_simulation(&path, None, false).unwrap();
+    assert!(
+        matches!(result.status, SimulationStatus::Error),
+        "expected Error, got {:?}",
+        result.status
+    );
+    let err = result.error.unwrap_or_default();
+    assert!(
+        err.contains("embeddings") && err.contains("z_ua"),
+        "error should point to embeddings[], got: {err}"
+    );
+}