feat(hex8): integrate paired HHT dynamic state and bounded verification

include/fesa/analysis/solid_hht_dynamic_procedure.h

@@ -0,0 +1,44 @@
+#ifndef FESA_ANALYSIS_SOLID_HHT_DYNAMIC_PROCEDURE_H_
+#define FESA_ANALYSIS_SOLID_HHT_DYNAMIC_PROCEDURE_H_
+
+#include "fesa/analysis/solid_dynamic_analysis_state.h"
+
+namespace fesa {
+class LinearSolver;
+class ParallelFor;
+class TangentSolver;
+
+/// @brief Owns the validated 3N dynamic result independently of serialization.
+struct SolidDynamicExecutionResult {
+  DofManager dofs;
+  SolidDynamicAnalysisState state;
+};
+
+/// @brief Integrates linear or TL Solid mechanics with constant consistent
+/// mass.
+class SolidHhtDynamicProcedureExecutor {
+ public:
+  /// @brief Retains caller-owned adapters which must outlive execution.
+  SolidHhtDynamicProcedureExecutor(const ParallelFor& parallel_for,
+                                   LinearSolver& mass_solver,
+                                   TangentSolver& tangent_solver);
+  /// @brief Returns complete accepted history without opening output files.
+  Result<SolidDynamicExecutionResult> Execute(const Domain& domain) const;
+  /// @brief Executes into an empty initialized state, preserving accepted
+  /// history on every failure. Domain must match the state inventory and
+  /// schedule.
+  Status ExecuteInto(const Domain& domain,
+                     SolidDynamicAnalysisState& state) const;
+  /// @brief Internal verification only; alpha0 verifies conservative dynamics.
+  /// @note This does not extend the approved INP parameter subset.
+  Status ExecuteIntoForVerification(const Domain& domain,
+                                    SolidDynamicAnalysisState& state,
+                                    double alpha) const;
+
+ private:
+  const ParallelFor& parallel_for_;
+  LinearSolver& mass_solver_;
+  TangentSolver& tangent_solver_;
+};
+}  // namespace fesa
+#endif  // FESA_ANALYSIS_SOLID_HHT_DYNAMIC_PROCEDURE_H_