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/entropyk/src/result.rs

@@ -526,19 +526,18 @@ pub fn extract_solved_variables(system: &System, state: &[f64]) -> Vec<SolvedVar
         }
     }
 
-    // Calibration factors (z_ua, z_dp, z_flow, z_flow_eco, z_power, z_etav)
-    // promoted to free unknowns via control loops. Each `Some(idx)` slot means
-    // the solver computed a value for that factor at `state[idx]`. The generic
-    // `actuator` slot (physical opening / fan speed) is already covered by the
-    // bounded-variable path above, so we only surface the six named Z-factors.
+    // Calibration factors promoted to free unknowns via control loops.
+    // Each `Some(idx)` slot means the solver computed a value at `state[idx]`.
+    // The generic `actuator` slot is already covered by the bounded-variable path.
     for (name, indices) in system.calib_indices_by_name() {
-        for (factor, slot) in [
-            ("z_flow", indices.z_flow),
-            ("z_flow_eco", indices.z_flow_eco),
-            ("z_dp", indices.z_dp),
-            ("z_ua", indices.z_ua),
-            ("z_power", indices.z_power),
-            ("z_etav", indices.z_etav),
+        for (factor, slot, min, max) in [
+            ("z_flow", indices.z_flow, 0.5, 2.0),
+            ("z_flow_eco", indices.z_flow_eco, 0.5, 2.0),
+            ("z_dp", indices.z_dp, 0.5, 2.0),
+            ("z_ua", indices.z_ua, 0.5, 2.0),
+            ("z_power", indices.z_power, 0.5, 2.0),
+            ("z_etav", indices.z_etav, 0.5, 2.0),
+            ("f_w", indices.f_w, 0.0, 1.0),
         ] {
             if let Some(idx) = slot {
                 if idx < state.len() {
@@ -552,10 +551,8 @@ pub fn extract_solved_variables(system: &System, state: &[f64]) -> Vec<SolvedVar
                         component: Some(name.clone()),
                         variable: factor.to_string(),
                         value: state[idx],
-                        // Calibration factors are bounded to [0.5, 2.0]
-                        // (see entropyk_core::CalibValidationError).
-                        min: 0.5,
-                        max: 2.0,
+                        min,
+                        max,
                     });
                 }
             }