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.

src/fesa/io/hdf5/dynamic_hdf5_results_writer.cpp

@@ -241,8 +241,24 @@ void DeleteAttribute(const hid_t object, const char* name) {
   }
 }
 
+/// @brief Maps a validated frame's integration semantics to its schema.
+std::uint64_t SchemaVersion(const DynamicAcceptedFrameState& frame) {
+  return frame.time_integration_formulation ==
+                 DynamicTimeIntegrationFormulation::kReducedCoordinateHht
+             ? 2U
+             : 1U;
+}
+
+/// @brief Returns the explicit integration discriminator without aliases.
+const char* IntegrationFormulation(const DynamicAcceptedFrameState& frame) {
+  return SchemaVersion(frame) == 2U
+             ? "reduced-coordinate-HHT-with-physical-rate-reconstruction"
+             : "full-coordinate-HHT";
+}
+
 /// @brief Writes the dynamic procedure identity and fixed time schedule.
-void WriteMetadata(const hid_t file, const Domain& domain) {
+void WriteMetadata(const hid_t file, const Domain& domain,
+                   const DynamicAcceptedFrameState& frame) {
   Hdf5Handle metadata{
       hdf5_internal::RequireHdf5Id(H5Gopen2(file, "/metadata", H5P_DEFAULT),
                                    "The model metadata group is missing."),
@@ -252,7 +268,7 @@ void WriteMetadata(const hid_t file, const Domain& domain) {
         "mass_formulation", "internal_formulation", "initial_state",
         "acceleration_convention", "step_name", "source_step_name",
         "unit_system_label", "coordinate_convention", "integration_rule",
-        "frame_index"}) {
+        "frame_index", "time_integration_formulation"}) {
     DeleteAttribute(metadata.Get(), name);
   }
   const DynamicStepDefinition* const step = domain.Dynamic();
@@ -260,9 +276,13 @@ void WriteMetadata(const hid_t file, const Domain& domain) {
                                       "hht-implicit-dynamics");
   hdf5_internal::WriteStringAttribute(metadata.Get(), "analysis_procedure",
                                       "hht-implicit-dynamics");
-  hdf5_internal::WriteUint64Attribute(metadata.Get(), "schema_version", 1U);
+  hdf5_internal::WriteUint64Attribute(metadata.Get(), "schema_version",
+                                      SchemaVersion(frame));
+  hdf5_internal::WriteStringAttribute(metadata.Get(),
+                                      "time_integration_formulation",
+                                      IntegrationFormulation(frame));
   hdf5_internal::WriteStringAttribute(metadata.Get(), "mass_formulation",
-                                      "consistent-kinetic");
+                                      "nodal-lumped-kinetic");
   hdf5_internal::WriteStringAttribute(metadata.Get(), "internal_formulation",
                                       "FESA-MITC4-total-lagrangian");
   hdf5_internal::WriteStringAttribute(metadata.Get(), "initial_state",
@@ -292,7 +312,8 @@ void WriteMetadata(const hid_t file, const Domain& domain) {
 /// @brief Records exact accepted endpoint identity on a result dataset.
 void WriteFrameAttributes(const hid_t dataset,
                           const DynamicAcceptedFrameState& frame) {
-  hdf5_internal::WriteUint64Attribute(dataset, "schema_version", 1U);
+  hdf5_internal::WriteUint64Attribute(dataset, "schema_version",
+                                      SchemaVersion(frame));
   hdf5_internal::WriteStringAttribute(dataset, "step_name", "Step-1");
   hdf5_internal::WriteUint64Attribute(dataset, "frame_index",
                                       frame.frame_index);
@@ -329,7 +350,7 @@ void ProcessDataset(const hid_t file, const std::string& path,
   string_attribute("source_step_name", source_step);
   if (readback) {
     CheckAttribute(dataset.Get(), "schema_version", H5T_STD_U64LE,
-                   H5T_NATIVE_UINT64, std::uint64_t{1U});
+                   H5T_NATIVE_UINT64, SchemaVersion(frame));
     CheckString(dataset.Get(), "step_name", "Step-1");
     CheckAttribute(dataset.Get(), "frame_index", H5T_STD_U64LE,
                    H5T_NATIVE_UINT64, std::uint64_t{frame.frame_index});
@@ -354,7 +375,9 @@ void ProcessDataset(const hid_t file, const std::string& path,
         leaf == "displacement" ? "global-translation-and-total-rotation-vector"
         : leaf == "velocity"   ? "global-translation-rate-and-chart-rate"
         : leaf == "acceleration" ? "physical-endpoint-chart-acceleration"
-                                 : "auxiliary-HHT-chart-acceleration");
+        : SchemaVersion(frame) == 2U
+            ? "full-chart-HHT-filter-combination-not-predictor-driver"
+            : "auxiliary-HHT-chart-acceleration");
   }
   if (leaf == "triad") string_attribute("axis_names", "A,B,D");
   if (path.find("/element/shell/") != std::string::npos) {
@@ -886,7 +909,7 @@ Status SelfCheck(const std::filesystem::path& path, const Domain& domain,
     const auto& step = *domain.Dynamic();
     CheckString(metadata.Get(), "feature_id", "hht-implicit-dynamics");
     CheckString(metadata.Get(), "analysis_procedure", "hht-implicit-dynamics");
-    CheckString(metadata.Get(), "mass_formulation", "consistent-kinetic");
+    CheckString(metadata.Get(), "mass_formulation", "nodal-lumped-kinetic");
     CheckString(metadata.Get(), "internal_formulation",
                 "FESA-MITC4-total-lagrangian");
     CheckString(metadata.Get(), "initial_state", "zero-q-v-step-load-0+");
@@ -899,7 +922,10 @@ Status SelfCheck(const std::filesystem::path& path, const Domain& domain,
     CheckString(metadata.Get(), "source_input_identity",
                 hdf5_internal::SourceInputIdentity(domain));
     CheckAttribute(metadata.Get(), "schema_version", H5T_STD_U64LE,
-                   H5T_NATIVE_UINT64, std::uint64_t{1U});
+                   H5T_NATIVE_UINT64,
+                   SchemaVersion(state.AcceptedFrames().front()));
+    CheckString(metadata.Get(), "time_integration_formulation",
+                IntegrationFormulation(state.AcceptedFrames().front()));
     CheckAttribute(metadata.Get(), "increment_count", H5T_STD_U64LE,
                    H5T_NATIVE_UINT64, std::uint64_t{step.increment_count});
     CheckAttribute(metadata.Get(), "maximum_increments", H5T_STD_U64LE,
@@ -988,7 +1014,7 @@ Status DynamicHdf5ResultsWriter::Write(
                     H5Fclose};
     (void)hdf5_internal::CreateGroup(file.Get(), "/model/shell");
     hdf5_internal::WriteModel(file.Get(), domain, model);
-    WriteMetadata(file.Get(), domain);
+    WriteMetadata(file.Get(), domain, state.AcceptedFrames().front());
     WriteDensity(file.Get(), domain);
     (void)hdf5_internal::CreateGroup(file.Get(), "/steps");
     (void)hdf5_internal::CreateGroup(file.Get(), "/steps/Step-1");

src/fesa/io/hdf5/solid_hdf5_results_writer.cpp

@@ -349,7 +349,7 @@ Result<SolidPlan> BuildSolidPlan(const Domain& domain, SolidStateView view,
                                            : "linear-static"},
         {"element_formulation", "FESA-Hex8"},
         {"integration_rule", "gauss-2x2x2"},
-        {"mass_formulation", "consistent-reference"},
+        {"mass_formulation", "lumped-reference"},
         {"source_input_identity", SourceInputIdentity(domain)},
         {"source_step_name", domain.Steps()[0].Name()},
         {"unit_system_label", "user-consistent-unspecified"},