Snapshot WIP: Probe calibration path, faer LU backend, and BPHX phase-change duty.

Checkpoint incomplete calibration work (cond SDT green, evap SST failing) plus related solver/UI changes so the next pass can fix and extend safely.

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

crates/solver/src/system.rs

@@ -224,6 +224,11 @@ pub struct System {
     /// Registry of component names for constraint validation.
     /// Maps human-readable names (e.g., "evaporator") to NodeIndex.
     component_names: HashMap<String, NodeIndex>,
+    /// Per-component calibration indices snapshot, captured at `finalize()` time.
+    /// Lets external readers (e.g. result extraction) learn which Z-factors
+    /// (z_ua, z_dp, z_flow, …) were promoted to free unknowns and where they
+    /// live in the state vector, so the solved values can be surfaced to the user.
+    calib_indices_by_name: HashMap<String, entropyk_core::CalibIndices>,
     finalized: bool,
     total_state_len: usize,
     /// When `true` (default), `finalize` rejects **over-constrained** systems.
@@ -246,6 +251,7 @@ impl System {
             saturated_controllers: Vec::new(),
             free_actuators: Vec::new(),
             component_names: HashMap::new(),
+            calib_indices_by_name: HashMap::new(),
             finalized: false,
             total_state_len: 0,
             enforce_dof_gate: true,
@@ -682,6 +688,10 @@ impl System {
             }
         }
 
+        // Persist the per-component calib map so external readers (result
+        // extraction) can surface solved Z-factor values (z_ua, z_dp, …).
+        self.calib_indices_by_name = comp_calib_indices;
+
         // Wire physical thermal couplings (Story 3.4 completion): each coupling
         // owns one state unknown Q [W] at `coupling_state_index(i)`. The
         // cold-side receiver component (e.g. `ThermalLoad`) reads Q in its
@@ -1145,6 +1155,15 @@ impl System {
         self.component_names.keys().map(|s| s.as_str())
     }
 
+    /// Per-component `CalibIndices` snapshot captured at `finalize()`.
+    /// Each `Some(idx)` slot (z_ua, z_dp, z_flow, z_flow_eco, z_power, z_etav,
+    /// actuator) means that factor was promoted to a free solver unknown and
+    /// its solved value lives at `state[idx]`. Used by result extraction to
+    /// surface solved calibration/control values to the user.
+    pub fn calib_indices_by_name(&self) -> &HashMap<String, entropyk_core::CalibIndices> {
+        &self.calib_indices_by_name
+    }
+
     /// Returns a reference to the component stored at the given node index.
     ///
     /// # Panics
@@ -2514,11 +2533,11 @@ impl System {
         self.total_state_len + self.inverse_control.mapping_count() + i
     }
 
-    fn saturated_base_index(&self) -> usize {
+    pub fn saturated_base_index(&self) -> usize {
         self.total_state_len + self.inverse_control.mapping_count() + self.coupling_residual_count()
     }
 
-    fn saturated_u_index(&self, i: usize) -> usize {
+    pub fn saturated_u_index(&self, i: usize) -> usize {
         self.saturated_base_index() + 2 * i
     }