feat: adopt lumped mass and reduced-coordinate shell HHT

Integrate Hex8 mass verification and fixed-null-basis shell dynamics with numerical and physics handoff evidence. Preserve interrupted reference and full-validation status; full integration validation is deferred until after performance optimization.

include/fesa/analysis/dynamic_analysis_state.h

@@ -14,8 +14,16 @@
 
 namespace fesa {
 
+/// @brief Identifies the update and the meaning of a frame's full auxiliary A.
+enum class DynamicTimeIntegrationFormulation {
+  kFullCoordinateHht,
+  kReducedCoordinateHht
+};
+
 /// @brief Stores one accepted endpoint of an HHT dynamic step.
 struct DynamicAcceptedFrameState {
+  DynamicTimeIntegrationFormulation time_integration_formulation =
+      DynamicTimeIntegrationFormulation::kFullCoordinateHht;
   std::uint32_t frame_index = 0U;
   std::uint32_t increment_index = 0U;
   std::uint32_t iteration_count = 0U;
@@ -26,6 +34,8 @@ struct DynamicAcceptedFrameState {
   Vector generalized_coordinates{0U};
   Vector velocity{0U};
   Vector acceleration{0U};
+  /// Full-coordinate history stores the predictor driver. Reduced-coordinate
+  /// history stores (1+alpha)*a_n-alpha*a_previous; frame zero stores a0.
   Vector algorithmic_acceleration{0U};
   std::vector<std::array<std::array<double, 3>, 3>> nodal_triad;
   std::vector<std::array<double, 3>> nodal_director;