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/components/src/compressor.rs

@@ -1083,6 +1083,23 @@ impl Compressor<Connected> {
     pub fn set_operational_state(&mut self, state: OperationalState) {
         self.operational_state = state;
     }
+
+    /// Live energy-retention factor \(f_w\): fraction of shaft work kept in the
+    /// refrigerant (`1` = adiabatic, `0` = all work lost to ambient).
+    ///
+    /// Reads `state[calib_indices.f_w]` when free; otherwise stored calib.
+    /// Clamped to [0, 1].
+    fn live_f_w(&self, state: Option<&StateSlice>) -> f64 {
+        let raw = if let Some(st) = state {
+            self.calib_indices
+                .f_w
+                .map(|idx| st.get(idx).copied().unwrap_or(self.calib.f_w))
+                .unwrap_or(self.calib.f_w)
+        } else {
+            self.calib.f_w
+        };
+        raw.clamp(0.0, 1.0)
+    }
 }
 
 impl Component for Compressor<Connected> {
@@ -1194,9 +1211,13 @@ impl Component for Compressor<Connected> {
         // ṁ_calc - ṁ_state = 0
         residuals[0] = mass_flow_calc - mass_flow_state;
 
-        // Residual 1: Energy balance
-        // Power_calc - ṁ × (h_discharge - h_suction) / η_mech = 0
+        // Residual 1: Energy balance with retention factor f_w
+        // (fraction of shaft work kept in the refrigerant):
+        //   ṁ·Δh = Ẇ·f_w / η_mech  ⇒  Ẇ·f_w − ṁ·Δh/η_mech = 0
+        // so h_dis ≈ h_suc + f_w·Ẇ/(ṁ·η_mech).
+        // f_w = 1 → adiabatic (default); f_w = 0 → all work lost to ambient.
         let enthalpy_change = h_discharge - h_suction;
+        let f_w = self.live_f_w(Some(state));
 
         // Prevent division by zero
         if self.mechanical_efficiency.abs() < 1e-10 {
@@ -1205,7 +1226,8 @@ impl Component for Compressor<Connected> {
             ));
         }
 
-        residuals[1] = power_calc - mass_flow_state * enthalpy_change / self.mechanical_efficiency;
+        residuals[1] =
+            power_calc * f_w - mass_flow_state * enthalpy_change / self.mechanical_efficiency;
 
         // r2: ṁ_discharge − ṁ_suction = 0  (mass conservation, CM1.3)
         // CM1.4: skip when same_branch_m — ṁ_dis == ṁ_suc (same state index),
@@ -1265,7 +1287,8 @@ impl Component for Compressor<Connected> {
         )?;
         jacobian.add_entry(0, suc_h_idx, dr0_dh_suction);
 
-        // Row 1: Energy residual  r1 = power_calc − ṁ × Δh / η_mech
+        // Row 1: Energy residual  r1 = power·f_w − ṁ·Δh/η_mech
+        let f_w = self.live_f_w(Some(state));
         // ∂r1/∂ṁ_suction = −(h_discharge − h_suction) / η_mech
         let dr1_dm = -(h_discharge - h_suction) / self.mechanical_efficiency;
         jacobian.add_entry(1, suc_m_idx, dr1_dm);
@@ -1280,7 +1303,7 @@ impl Component for Compressor<Connected> {
                     Temperature::from_kelvin(t),
                     Temperature::from_kelvin(t_discharge),
                     None,
-                ))
+                ) * f_w)
             },
             h_suction,
             1.0,
@@ -1296,7 +1319,7 @@ impl Component for Compressor<Connected> {
                     Temperature::from_kelvin(t_suction),
                     Temperature::from_kelvin(t),
                     None,
-                ))
+                ) * f_w)
             },
             h_discharge,
             1.0,
@@ -1326,7 +1349,18 @@ impl Component for Compressor<Connected> {
                 Temperature::from_kelvin(t_discharge_k),
                 None,
             );
-            jacobian.add_entry(1, z_power_idx, p_nominal);
+            // r1 = (z_power·Ẇ_nom)·f_w − …  ⇒  ∂r1/∂z_power = Ẇ_nom·f_w
+            jacobian.add_entry(1, z_power_idx, p_nominal * f_w);
+        }
+
+        if let Some(f_w_idx) = self.calib_indices.f_w {
+            let p_live = self.power_consumption_cooling(
+                Temperature::from_kelvin(t_suction_k),
+                Temperature::from_kelvin(t_discharge_k),
+                Some(state),
+            );
+            // r1 = Ẇ·f_w − …  ⇒  ∂r1/∂f_w = +Ẇ
+            jacobian.add_entry(1, f_w_idx, p_live);
         }
 
         // ∂r0/∂f_etav (AHRI 540 only): ṁ_calc = f_m · f_etav · base with