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/benches/lu_solve.rs

@@ -0,0 +1,30 @@
+//! Phase-0 benchmark: dense LU solve on an assembled Jacobian.
+//!
+//! The Jacobian is taken from the deterministic mock refrigeration cycle so the
+//! benchmark is independent of the heavy CoolProp backend and measures only the
+//! linear algebra path used by the Newton solver (Ruiz equilibration + LU).
+
+use criterion::{black_box, criterion_group, criterion_main, Criterion};
+
+mod common;
+
+fn bench_lu_solve(c: &mut Criterion) {
+    let (system, state) = common::build_mock_system();
+    let jacobian = common::assemble_jacobian(&system, &state);
+
+    // Residual vector at the analytical solution is non-zero for the mock
+    // components because they read from fixed ports, not from the state slice.
+    // We therefore benchmark the LU solve with a representative RHS.
+    let residuals: Vec<f64> = (0..jacobian.nrows())
+        .map(|i| state[i].sin() * 1e-3)
+        .collect();
+
+    c.bench_function("lu_solve_mock_9x9", |b| {
+        b.iter(|| {
+            black_box(jacobian.solve(&residuals));
+        });
+    });
+}
+
+criterion_group!(benches, bench_lu_solve);
+criterion_main!(benches);