Snapshot WIP: solver HP epic progress, BPHX/HX physics, BMAD skill refresh.

Capture uncommitted solver robustness work (regularization, domain errors, linear solver lifecycle, tube DP/MSH), web workbench updates, and synced BMAD skills across IDE agent folders before starting BPHX pressure-drop.

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

crates/solver/tests/timeout_budgeted_solving.rs

@@ -27,9 +27,12 @@ struct LinearSystem2x2 {
 
 impl LinearSystem2x2 {
     fn well_conditioned() -> Self {
+        // CM1.3: the solver clamps pressure (state[1]) to >= 10_000 Pa.  Choose
+        // the linear system so that the analytical solution lands at the bound
+        // (P = h = 10_000), keeping Newton convergence exact in one iteration.
         Self {
             a: [[2.0, 1.0], [1.0, 2.0]],
-            b: [3.0, 3.0],
+            b: [30_000.0, 30_000.0],
         }
     }
 }
@@ -301,10 +304,11 @@ fn test_picard_timeout_returns_error_when_configured() {
             return_best_state_on_timeout: false,
             zoh_fallback: false,
         },
-        // CM1.2: Picard's positional update is misaligned by the ṁ-front /
-        // closure-back layout for this synthetic 2×2, so seed it at the analytical
-        // solution (ṁ=seed, P=1, h=1). CM1.3 restores alignment with real residuals.
-        initial_state: Some(vec![DEFAULT_MASS_FLOW_SEED_KG_S, 1.0, 1.0]),
+        // CM1.3: keep the Picard seed at the analytical solution so the test
+        // focuses on timeout/pre-allocation wiring, not Picard convergence.
+        // Pressure must respect the 10_000 Pa lower bound, so the solution is
+        // (ṁ=seed, P=10_000, h=10_000).
+        initial_state: Some(vec![DEFAULT_MASS_FLOW_SEED_KG_S, 10_000.0, 10_000.0]),
         ..Default::default()
     };
 
@@ -416,9 +420,9 @@ fn test_picard_config_best_state_preallocated() {
     let mut solver = PicardConfig {
         timeout: Some(Duration::from_millis(100)),
         max_iterations: 10,
-        // CM1.2: seed Picard at the analytical solution (ṁ=seed, P=1, h=1) — the
-        // synthetic ṁ-closure misaligns Picard's positional update until CM1.3.
-        initial_state: Some(vec![DEFAULT_MASS_FLOW_SEED_KG_S, 1.0, 1.0]),
+        // CM1.3: seed Picard at the analytical solution (ṁ=seed, P=10_000, h=10_000)
+        // so the test targets pre-allocation wiring and not Picard convergence.
+        initial_state: Some(vec![DEFAULT_MASS_FLOW_SEED_KG_S, 10_000.0, 10_000.0]),
         ..Default::default()
     };