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

src/fesa/elements/hex8_linear_tangent_cache.h

@@ -0,0 +1,21 @@
+#ifndef FESA_SRC_FESA_ELEMENTS_HEX8_LINEAR_TANGENT_CACHE_H_
+#define FESA_SRC_FESA_ELEMENTS_HEX8_LINEAR_TANGENT_CACHE_H_
+
+#include <mutex>
+
+#include "fesa/math/matrix.h"
+
+namespace fesa::hex8_internal {
+/// @brief Shares one immutable paired Hessian among identical element copies.
+/// @note Only call_once preparation writes. Linear readers synchronize through
+/// the flag; nonlinear trials do not access this optional state. At most two
+/// 24-by-24 matrices (9216 value bytes) are retained after successful preparation.
+struct LinearTangentCache {
+  std::once_flag preparation;
+  bool ready{false};
+  Matrix high{0U, 0U};
+  Matrix low{0U, 0U};
+};
+}  // namespace fesa::hex8_internal
+
+#endif  // FESA_SRC_FESA_ELEMENTS_HEX8_LINEAR_TANGENT_CACHE_H_