perf(hex8): defer optional paired tangent until a valid linear trial

include/fesa/elements/hex8_element.h

@@ -2,6 +2,7 @@
 #define FESA_ELEMENTS_HEX8_ELEMENT_H_
 
 #include <array>
+#include <memory>
 #include <optional>
 
 #include "fesa/elements/element.h"
@@ -9,6 +10,9 @@
 #include "fesa/results/solid_result_records.h"
 
 namespace fesa {
+namespace hex8_internal {
+struct LinearTangentCache;
+}
 
 /// @brief Owns all local quantities from one validated linear or TL trial.
 struct Hex8Response {
@@ -90,7 +94,8 @@ class Hex8Element final : public Element {
                                 bool nonlinear) const;
   /// @brief Uses one paired gradient for energy, force and analytic Hessian.
   Result<Hex8HighLowResponse> EvaluateHighLow(
-      const Vector& high, const Vector& low, bool nonlinear) const;
+      const Vector& high, const Vector& low, bool nonlinear,
+      bool prepare_linear_cache = true) const;
   /// @brief Attaches stable source context to a model failure.
   Status Failure(const char* message) const;
 
@@ -103,11 +108,9 @@ class Hex8Element final : public Element {
   SourceLocation location_;
   std::array<ReferencePoint, 8> points_{};
   Matrix stiffness_{24U, 24U};
-  // Optional immutable Hessian from the same paired quadrature graph. Failure
-  // to build it does not reject models supported by the original F64 paths.
-  bool paired_linear_tangent_ready_{false};
-  Matrix paired_linear_tangent_high_{24U, 24U};
-  Matrix paired_linear_tangent_low_{24U, 24U};
+  // Optional immutable paired Hessian, prepared once on the first valid paired
+  // linear trial. Copies share only their identical owned reference definition.
+  std::shared_ptr<hex8_internal::LinearTangentCache> paired_linear_tangent_;
 };
 
 }  // namespace fesa