feat: MITC4 drilling 두 방식과 직접 스프링 기본값 구현

include/fesa/elements/mitc4_drilling_mode.h

@@ -0,0 +1,26 @@
+#ifndef FESA_ELEMENTS_MITC4_DRILLING_MODE_H_
+#define FESA_ELEMENTS_MITC4_DRILLING_MODE_H_
+
+namespace fesa {
+
+/// @brief Identifies the immutable numerical MITC4 drilling formulation.
+enum class Mitc4DrillingMode { kDirectSpring, kLegacyCorotatedTwist };
+
+/// @brief Returns the stable storage name of a supported drilling formulation.
+constexpr const char* Mitc4DrillingModeName(Mitc4DrillingMode mode) noexcept {
+  switch (mode) {
+    case Mitc4DrillingMode::kDirectSpring:
+      return "direct-initial-director-spring";
+    case Mitc4DrillingMode::kLegacyCorotatedTwist:
+      return "legacy-corotated-twist";
+  }
+  return "";
+}
+
+namespace mitc4_drilling_internal {
+struct TestAccess;
+}  // namespace mitc4_drilling_internal
+
+}  // namespace fesa
+
+#endif  // FESA_ELEMENTS_MITC4_DRILLING_MODE_H_

include/fesa/elements/mitc4_shell.h

@@ -8,6 +8,7 @@
 #include "fesa/core/status.h"
 #include "fesa/elements/element.h"
 #include "fesa/elements/mitc4_shell_definition.h"
+#include "fesa/elements/mitc4_drilling_mode.h"
 #include "fesa/materials/isotropic_linear_elastic_material.h"
 #include "fesa/math/matrix.h"
 #include "fesa/math/vector.h"
@@ -92,6 +93,11 @@ class Mitc4Shell final : public Element {
       std::array<std::array<double, 3>, 4> initial_directors,
       const ShellSection& section, const LinearElasticMaterial& material);
 
+  /// @brief Returns this immutable kernel's production drilling formulation.
+  [[nodiscard]] Mitc4DrillingMode DrillingMode() const noexcept {
+    return drilling_mode_;
+  }
+
   /// @brief Returns the factory-bound MITC4 DOF order.
   const ElementDofLayout& DofLayout() const noexcept override;
 
@@ -163,6 +169,7 @@ class Mitc4Shell final : public Element {
 
  private:
   friend class ElementFactory;
+  friend struct mitc4_drilling_internal::TestAccess;
 
   /// @brief Binds Domain identity after the numerical candidate is valid.
   void BindRuntime(ElementDofLayout layout, EntityIndex element_index,
@@ -203,6 +210,7 @@ class Mitc4Shell final : public Element {
   double thickness_;
   double youngs_modulus_;
   double poisson_ratio_;
+  Mitc4DrillingMode drilling_mode_;
   SourceLocation source_location_;
   std::string identity_;
   ElementDofLayout dof_layout_;

include/fesa/elements/nonlinear_mitc4_shell.h

@@ -54,6 +54,8 @@ struct NonlinearMitc4InternalEquilibrium {
   Matrix drilling_metric{0U, 0U};
   double drilling_energy = 0.0;
   Vector force_directional_second{0U};
+  /// @brief Stores D2(f_drill)[v,v] separately; direct springs give exact zero.
+  Vector drilling_force_directional_second{0U};
   Vector drilling_constraint{0U};
   Matrix drilling_constraint_gradient{0U, 0U};
   std::array<Matrix, 4> drilling_constraint_hessian{
@@ -104,6 +106,11 @@ class NonlinearMitc4Shell {
       std::array<ShellNodeInitialFrame, 4> initial_frames,
       const ShellSection& section, const LinearElasticMaterial& material);
 
+  /// @brief Returns this immutable kernel's numerical drilling formulation.
+  [[nodiscard]] Mitc4DrillingMode DrillingMode() const noexcept {
+    return drilling_mode_;
+  }
+
   /// @brief Evaluates trial physical kinematics and fixed recovery rows.
   /// @param trial Global nodal translation and fixed-global rotation vectors.
   /// @return Physical recovery or a fail-closed trial diagnostic.
@@ -134,6 +141,7 @@ class NonlinearMitc4Shell {
 
  private:
   friend struct nonlinear_mitc4_internal::ConfigurationSnapshot;
+  friend struct mitc4_drilling_internal::TestAccess;
 
   /// @brief Retains validated fixed-reference data without analysis ownership.
   NonlinearMitc4Shell(std::array<Vector3, 4> coordinates,
@@ -155,6 +163,7 @@ class NonlinearMitc4Shell {
   double youngs_modulus_;
   double poisson_ratio_;
   double drilling_stiffness_;
+  Mitc4DrillingMode drilling_mode_;
   SourceLocation source_location_;
   std::string identity_;
 };

src/fesa/elements/mitc4_drilling_internal.h

@@ -0,0 +1,28 @@
+#ifndef FESA_SRC_FESA_ELEMENTS_MITC4_DRILLING_INTERNAL_H_
+#define FESA_SRC_FESA_ELEMENTS_MITC4_DRILLING_INTERNAL_H_
+
+#include "fesa/elements/nonlinear_mitc4_shell.h"
+
+namespace fesa::mitc4_drilling_internal {
+
+// The sole production selection. Change this constant and rebuild all targets.
+inline constexpr Mitc4DrillingMode kProductionDrillingMode =
+    Mitc4DrillingMode::kDirectSpring;
+
+/// @brief Provides explicit alternate formulations only for internal tests.
+/// @note Production factories use the single compile-time selection above.
+struct TestAccess {
+  static Mitc4Shell WithMode(Mitc4Shell shell, Mitc4DrillingMode mode) {
+    shell.drilling_mode_ = mode;
+    return shell;
+  }
+  static NonlinearMitc4Shell WithMode(NonlinearMitc4Shell shell,
+                                      Mitc4DrillingMode mode) {
+    shell.drilling_mode_ = mode;
+    return shell;
+  }
+};
+
+}  // namespace fesa::mitc4_drilling_internal
+
+#endif  // FESA_SRC_FESA_ELEMENTS_MITC4_DRILLING_INTERNAL_H_

src/fesa/elements/mitc4_shell.cpp

@@ -12,6 +12,7 @@
 #include "math/finite_values.h"
 #include "math/vector3_operations.h"
 #include "elements/shell_kernel_values.h"
+#include "elements/mitc4_drilling_internal.h"
 
 namespace fesa {
 
@@ -1002,6 +1003,7 @@ Mitc4Shell::Mitc4Shell(std::array<Vector3, 4> coordinates,
       thickness_{thickness},
       youngs_modulus_{youngs_modulus},
       poisson_ratio_{poisson_ratio},
+      drilling_mode_{mitc4_drilling_internal::kProductionDrillingMode},
       source_location_{std::move(source_location)},
       identity_{std::move(identity)} {}
 

src/fesa/elements/nonlinear_mitc4_configuration_internal.h

@@ -12,6 +12,7 @@ namespace fesa::nonlinear_mitc4_internal {
 /// key.
 struct ConfigurationSnapshot {
   std::array<double, 64> values{};
+  Mitc4DrillingMode drilling_mode = Mitc4DrillingMode::kDirectSpring;
   SourceLocation source{};
   std::string identity;
 

src/fesa/elements/nonlinear_mitc4_shell.cpp

@@ -12,6 +12,7 @@
 
 #include "fesa/elements/finite_rotation.h"
 #include "elements/nonlinear_mitc4_configuration_internal.h"
+#include "elements/mitc4_drilling_internal.h"
 #include "math/dense_blas_internal.h"
 #include "math/jet_arithmetic.h"
 #include "math/jet_linear_solve.h"
@@ -39,6 +40,7 @@ nonlinear_mitc4_internal::ConfigurationSnapshot::Read(
   result.values[index++] = element.youngs_modulus_;
   result.values[index++] = element.poisson_ratio_;
   result.values[index] = element.drilling_stiffness_;
+  result.drilling_mode = element.drilling_mode_;
   result.source = element.source_location_;
   result.identity = element.identity_;
   return result;
@@ -1227,8 +1229,91 @@ Jet DrillSpinRate(const JetVector3& phi, const Vector3& director) {
   return Reciprocal(Sqrt(Dot(preimage, preimage)));
 }
 
+/// @brief Uses precisely the current inertia kernel's cubic rotation maps.
+/// @note This is deliberately distinct from the legacy analytic null. Keep the
+/// cubic Exp/Jacobian order synchronized with EvaluateDynamicRotation; it is
+/// not an approximation to be silently replaced by the exact exponential
+/// inverse.
+JetVector3 InertiaDrillNull(const JetVector3& phi, const Vector3& director) {
+  const JetMatrix3 skew = Skew(phi);
+  JetMatrix3 rotation = Identity();
+  JetMatrix3 jacobian = Identity();
+  JetMatrix3 term = Identity();
+  double rotation_factorial = 1.0;
+  double jacobian_factorial = 1.0;
+  for (std::size_t order = 1U; order <= 3U; ++order) {
+    term = Multiply(term, skew);
+    rotation_factorial *= static_cast<double>(order);
+    jacobian_factorial *= static_cast<double>(order + 1U);
+    rotation = Add(rotation, Scale(1.0 / rotation_factorial, term));
+    jacobian = Add(jacobian, Scale(1.0 / jacobian_factorial, term));
+  }
+  const JetVector3 rhs = Multiply(rotation, ConstantVector(director));
+  Matrix primal{3U, 3U};
+  for (std::size_t row = 0U; row < 3U; ++row)
+    for (std::size_t column = 0U; column < 3U; ++column)
+      primal(row, column) = jacobian[row][column].value;
+  const auto factor = dense_blas_internal::DenseFactor::Lu(primal);
+  const std::array<std::size_t, 4> channels{1U, kGlobalDofCount + 1U,
+                                            kHessianSize + 1U + kGlobalDofCount,
+                                            kGlobalDofCount};
+  JetVector3 preimage{};
+  if (!factor.HasValue() ||
+      !math_internal::SolveJetAction(jacobian, rhs, factor.Value(), channels,
+                                     Constant, ReadChannel, WriteChannel,
+                                     preimage)) {
+    preimage.fill(Constant(std::numeric_limits<double>::quiet_NaN()));
+    return preimage;
+  }
+  return Scale(Reciprocal(Sqrt(Dot(preimage, preimage))), preimage);
+}
+
+/// @brief Evaluates the fixed initial-director spring without corotation.
+Jet DirectDrillingEnergy(
+    const std::array<Vector3, kNodeCount>& initial_directors,
+    const JetTrial& trial, double drilling_stiffness, Matrix* metric,
+    std::array<Jet, 4>* constraints) {
+  Jet energy{};
+  double* tangent = energy.second.Data();
+  for (std::size_t node = 0U; node < kNodeCount; ++node) {
+    const auto d0 = ConstantVector(initial_directors[node]);
+    const Jet gamma = Dot(d0, trial.rotation[node]);
+    // Retain the validated spring scale through subnormal intermediates.
+    // Fill its linear derivatives explicitly, without differentiating a
+    // floating half-energy that can round kd before doubling it again.
+    energy.value += 0.5 * gamma.value * (drilling_stiffness * gamma.value);
+    energy.directional_first +=
+        drilling_stiffness * gamma.value * gamma.directional_first;
+    energy.directional_second +=
+        drilling_stiffness * gamma.directional_first * gamma.directional_first;
+    for (std::size_t i = 0U; i < 3U; ++i) {
+      const auto row = 6U * node + 3U + i;
+      energy.first[row] =
+          drilling_stiffness * gamma.value * initial_directors[node][i];
+      energy.mixed_first[row] = drilling_stiffness * gamma.directional_first *
+                                initial_directors[node][i];
+    }
+    // D2 f_drill[v,v] is identically zero; mixed_second retains exact zeros.
+    if (constraints != nullptr) {
+      const auto null =
+          InertiaDrillNull(trial.rotation[node], initial_directors[node]);
+      (*constraints)[node] = drilling_stiffness * gamma * Dot(null, d0);
+    }
+    for (std::size_t i = 0U; i < 3U; ++i)
+      for (std::size_t j = 0U; j < 3U; ++j) {
+        const auto row = 6U * node + 3U + i;
+        const auto column = 6U * node + 3U + j;
+        const double value = drilling_stiffness * initial_directors[node][i] *
+                             initial_directors[node][j];
+        tangent[row * kGlobalDofCount + column] = value;
+        (*metric)(row, column) = value;
+      }
+  }
+  return energy;
+}
+
 /// @brief Evaluates the objective numerical drilling potential and variations.
-Jet DrillingEnergy(const std::array<Vector3, kNodeCount>& coordinates,
+Jet LegacyDrillingEnergy(const std::array<Vector3, kNodeCount>& coordinates,
                    const std::array<Vector3, kNodeCount>& initial_directors,
                    const JetTrial& trial, const double thickness,
                    const double drilling_stiffness, bool& valid, Matrix* metric,
@@ -1323,6 +1408,7 @@ NonlinearMitc4Shell::NonlinearMitc4Shell(
       youngs_modulus_{youngs_modulus},
       poisson_ratio_{poisson_ratio},
       drilling_stiffness_{drilling_stiffness},
+      drilling_mode_{mitc4_drilling_internal::kProductionDrillingMode},
       source_location_{std::move(source_location)},
       identity_{std::move(identity)} {}
 
@@ -1640,7 +1726,10 @@ NonlinearMitc4Shell::EvaluateExternalDrillingConstraint(
     jet_phi[component] = Variable(phi[component], component,
                                   phi_dot[component]);
   }
-  const JetVector3 null_direction = DrillNull(jet_phi, initial_directors_[node]);
+  const JetVector3 null_direction =
+      drilling_mode_ == Mitc4DrillingMode::kDirectSpring
+          ? InertiaDrillNull(jet_phi, initial_directors_[node])
+          : DrillNull(jet_phi, initial_directors_[node]);
   const Jet scalar = -1.0 * Dot(null_direction, ConstantVector(force));
   const Jet scalar_time =
       -1.0 * Dot(null_direction, ConstantVector(force_rate));
@@ -1741,10 +1830,17 @@ Result<NonlinearMitc4InternalEquilibrium> EvaluateInternalResidualAndTangent(
                      element.poisson_ratio_, valid);
   Matrix drilling_metric{kGlobalDofCount, kGlobalDofCount};
   std::array<Jet, 4> constraints{};
-  const Jet drilling = DrillingEnergy(
+  const Jet drilling =
-      element.coordinates_, element.initial_directors_, jet_trial,
+      element.drilling_mode_ == Mitc4DrillingMode::kDirectSpring
-      element.thickness_, element.drilling_stiffness_, valid, &drilling_metric,
+          ? DirectDrillingEnergy(
-      coordinate_direction != nullptr ? &constraints : nullptr);
+                element.initial_directors_, jet_trial,
+                element.drilling_stiffness_, &drilling_metric,
+                coordinate_direction != nullptr ? &constraints : nullptr)
+          : LegacyDrillingEnergy(
+                element.coordinates_, element.initial_directors_, jet_trial,
+                element.thickness_, element.drilling_stiffness_, valid,
+                &drilling_metric,
+                coordinate_direction != nullptr ? &constraints : nullptr);
   const Jet internal_energy = physical + drilling;
   if (!valid || !IsFinite(internal_energy)) {
     return Failure<NonlinearMitc4InternalEquilibrium>(
@@ -1815,10 +1911,13 @@ Result<NonlinearMitc4InternalEquilibrium> EvaluateInternalResidualAndTangent(
   equilibrium.drilling_metric = std::move(drilling_metric);
   equilibrium.drilling_energy = drilling.value;
   equilibrium.force_directional_second = Vector{kGlobalDofCount};
+  equilibrium.drilling_force_directional_second = Vector{kGlobalDofCount};
   for (std::size_t index = 0U; index < kGlobalDofCount; ++index) {
     equilibrium.internal_force[index] = equilibrium.internal_residual[index];
     equilibrium.physical_force[index] = physical.first[index];
     equilibrium.drilling_force[index] = drilling.first[index];
+    equilibrium.drilling_force_directional_second[index] =
+        drilling.mixed_second[index];
     equilibrium.force_directional_second[index] =
         internal_energy.mixed_second[index];
     for (std::size_t column = 0U; column < kGlobalDofCount; ++column) {

tests/unit/elements/element_capabilities_test.cpp

@@ -133,6 +133,7 @@ TEST(ElementCapabilities, ShellTrialPreservesCompleteDirectionalResponseAndFailu
   Same(a.drilling_metric, b.drilling_metric);
   Same(a.drilling_energy, b.drilling_energy);
   Same(a.force_directional_second, b.force_directional_second);
+  Same(a.drilling_force_directional_second, b.drilling_force_directional_second);
   Same(a.drilling_constraint, b.drilling_constraint);
   Same(a.drilling_constraint_gradient, b.drilling_constraint_gradient);
   for (std::size_t n = 0; n < 4; ++n) {

tests/unit/elements/nonlinear_mitc4_shell_tangent_test.cpp

@@ -6,6 +6,7 @@
 #include <cstddef>
 #include <cstdint>
 #include <limits>
+#include <cstring>
 #include <stdexcept>
 #include <string>
 
@@ -13,6 +14,8 @@
 #include "fesa/elements/nonlinear_mitc4_inertia.h"
 #include "fesa/elements/nonlinear_mitc4_shell.h"
 #include "fesa/model/model_types.h"
+#include "elements/mitc4_drilling_internal.h"
+#include "elements/nonlinear_mitc4_configuration_internal.h"
 
 namespace {
 
@@ -44,7 +47,7 @@ std::array<fesa::ShellNodeInitialFrame, 4> Frames() {
            {3U, {0.0, 0.0, 1.0}, {1.0, 0.0, 0.0}, {0.0, 1.0, 0.0}}}};
 }
 
-fesa::NonlinearMitc4Shell Shell(const std::array<fesa::Node, 4>& nodes) {
+fesa::NonlinearMitc4Shell ProductionShell(const std::array<fesa::Node, 4>& nodes) {
   const fesa::ShellSection section{
       "Section", 0.2, 0U, {"nonlinear-mitc4-tangent.inp", 20U}};
   const fesa::LinearElasticMaterial material{
@@ -57,6 +60,11 @@ fesa::NonlinearMitc4Shell Shell(const std::array<fesa::Node, 4>& nodes) {
   return shell.Value();
 }
 
+fesa::NonlinearMitc4Shell LegacyShell(const std::array<fesa::Node, 4>& nodes) {
+  return fesa::mitc4_drilling_internal::TestAccess::WithMode(
+      ProductionShell(nodes), fesa::Mitc4DrillingMode::kLegacyCorotatedTwist);
+}
+
 fesa::NonlinearMitc4TrialDofs Trial() {
   fesa::NonlinearMitc4TrialDofs trial{};
   trial.displacement[0U] = {-0.02, 0.01, 0.03};
@@ -200,7 +208,7 @@ void ExpectRelative(const double actual, const double expected) {
 // NSNR-ELEM-TAN-001
 TEST(NonlinearMitc4Residual, EvaluatesResidualTangentAndRecoveryAtOneTrial) {
   const auto nodes = Nodes();
-  const auto shell = Shell(nodes);
+  const auto shell = LegacyShell(nodes);
   const auto trial = Trial();
   const auto recovery = shell.RecoverState(trial);
   const auto result = fesa::EvaluateInternalResidualAndTangent(shell, trial);
@@ -230,7 +238,7 @@ TEST(NonlinearMitc4Residual, EvaluatesResidualTangentAndRecoveryAtOneTrial) {
 // NSNR-ELEM-TAN-002 and NSNR-ELEM-TAN-003
 TEST(NonlinearMitc4Tangent, MatchesTheApprovedDirectionalSchedule) {
   const auto nodes = Nodes();
-  const auto shell = Shell(nodes);
+  const auto shell = LegacyShell(nodes);
   const auto trial = Trial();
   const auto direction = WorkConjugateDirection(nodes);
   const double length = ReferenceLength(nodes);
@@ -295,7 +303,7 @@ TEST(NonlinearMitc4Tangent, MatchesTheApprovedDirectionalSchedule) {
 TEST(NonlinearMitc4Tangent, PreservesRigidTranslationNullspaceAndSymmetry) {
   const auto nodes = Nodes();
   const auto equilibrium =
-      fesa::EvaluateInternalResidualAndTangent(Shell(nodes), {});
+      fesa::EvaluateInternalResidualAndTangent(LegacyShell(nodes), {});
   ASSERT_TRUE(equilibrium.HasValue());
   const double length = ReferenceLength(nodes);
 
@@ -326,9 +334,9 @@ TEST(NonlinearMitc4Tangent, PreservesRigidTranslationNullspaceAndSymmetry) {
 TEST(NonlinearMitc4Residual, DoesNotAcceptExternalLoadShares) {
   const auto nodes = Nodes();
   const auto first =
-      fesa::EvaluateInternalResidualAndTangent(Shell(nodes), Trial());
+      fesa::EvaluateInternalResidualAndTangent(LegacyShell(nodes), Trial());
   const auto second =
-      fesa::EvaluateInternalResidualAndTangent(Shell(nodes), Trial());
+      fesa::EvaluateInternalResidualAndTangent(LegacyShell(nodes), Trial());
   ASSERT_TRUE(first.HasValue());
   ASSERT_TRUE(second.HasValue());
   for (std::size_t index = 0U; index < 24U; ++index) {
@@ -357,7 +365,7 @@ TEST(NonlinearMitc4Objectivity, FiniteRigidMotionHasZeroInternalForce) {
     trial.rotation_vector[node] = rotation;
   }
   const auto result =
-      fesa::EvaluateInternalResidualAndTangent(Shell(nodes), trial);
+      fesa::EvaluateInternalResidualAndTangent(LegacyShell(nodes), trial);
   ASSERT_TRUE(result.HasValue());
   EXPECT_LE(result.Value().internal_residual.Norm(), kNumericalTolerance);
   EXPECT_LE(result.Value().physical_strain_energy, kNumericalTolerance);
@@ -366,7 +374,7 @@ TEST(NonlinearMitc4Objectivity, FiniteRigidMotionHasZeroInternalForce) {
 // NSNR-ELEM-TAN-008
 TEST(NonlinearMitc4Patch, RetainsPhysicalRecoveryIdentities) {
   const auto nodes = Nodes();
-  const auto shell = Shell(nodes);
+  const auto shell = LegacyShell(nodes);
   constexpr double kMembraneStrain = 1.0e-2;
   const double green_strain =
       kMembraneStrain + 0.5 * kMembraneStrain * kMembraneStrain;
@@ -409,7 +417,7 @@ TEST(NonlinearMitc4Residual, RejectsNonfiniteTrialData) {
   trial.rotation_vector[2U] = {std::numeric_limits<double>::quiet_NaN(), 0.0,
                                0.0};
   const auto result =
-      fesa::EvaluateInternalResidualAndTangent(Shell(nodes), trial);
+      fesa::EvaluateInternalResidualAndTangent(LegacyShell(nodes), trial);
   ASSERT_FALSE(result.HasValue());
   EXPECT_EQ(result.GetStatus().Diagnostics()[0U].code,
             "invalid-nonlinear-shell-trial");
@@ -417,13 +425,13 @@ TEST(NonlinearMitc4Residual, RejectsNonfiniteTrialData) {
   auto overflow = Trial();
   overflow.displacement[1U] = {1.0e300, 0.0, 0.0};
   const auto overflow_result =
-      fesa::EvaluateInternalResidualAndTangent(Shell(nodes), overflow);
+      fesa::EvaluateInternalResidualAndTangent(LegacyShell(nodes), overflow);
   EXPECT_FALSE(overflow_result.HasValue());
 }
 
 void CheckThirdSweep(const fesa::NonlinearMitc4TrialDofs& trial) {
   const auto nodes = Nodes();
-  const auto shell = Shell(nodes);
+  const auto shell = LegacyShell(nodes);
   auto direction = Direction();
   double norm = 0.0;
   const auto unscaled = ToVector(direction);
@@ -488,7 +496,7 @@ TEST(NonlinearMitc4Residual,
   nodes[1].coordinates = {4.23076923, 2.30769231, 0.0};
   nodes[2].coordinates = {4.23076923, 2.69230769, 0.0};
   nodes[3].coordinates = {3.84615385, 2.69230769, 0.0};
-  const auto shell = Shell(nodes);
+  const auto shell = LegacyShell(nodes);
   const auto evaluated = fesa::EvaluateInternalResidualAndTangent(shell, {});
   ASSERT_TRUE(evaluated.HasValue());
   for (std::size_t i = 0; i < 24U; ++i)
@@ -566,7 +574,7 @@ TEST(NonlinearMitc4Residual,
   for (bool warped : {false, true}) {
     auto nodes = Nodes();
     if (warped) nodes[2U].coordinates[2U] = 0.1;
-    const auto shell = Shell(nodes);
+    const auto shell = LegacyShell(nodes);
     auto trial = Trial();
     trial.rotation_vector[0U] = {.6, -.2, .1};
     const auto direction = Direction();
@@ -636,7 +644,7 @@ TEST(NonlinearMitc4Residual,
 TEST(NonlinearMitc4Residual,
      ExposesExactDrillingConstraintThirdDirectionalGradient) {
   const auto nodes = Nodes();
-  const auto shell = Shell(nodes);
+  const auto shell = LegacyShell(nodes);
   const auto trial = Trial();
   const auto direction = Direction();
   const auto velocity = ToVector(direction);
@@ -679,7 +687,7 @@ TEST(NonlinearMitc4Residual,
 TEST(NonlinearMitc4Residual,
      ExternalDrillingConstraintIncludesForceTimeAndCurvatureTerms) {
   const auto nodes = Nodes();
-  const auto shell = Shell(nodes);
+  const auto shell = LegacyShell(nodes);
   const fesa::Vector3 phi{.6, -.2, .1};
   const fesa::Vector3 phi_dot{.2, -.1, .3};
   const fesa::Vector3 force{1.7, -.8, .4};
@@ -742,7 +750,7 @@ TEST(NonlinearMitc4Residual,
 
 TEST(NonlinearMitc4Residual,
      ExternalDrillingConstraintRejectsInvalidRotationAndHasZeroForceValue) {
-  const auto shell = Shell(Nodes());
+  const auto shell = LegacyShell(Nodes());
   const auto zero = shell.EvaluateExternalDrillingConstraint(
       0U, {.2, -.1, .3}, {.1, .2, -.3}, {}, {}, {});
   ASSERT_TRUE(zero.HasValue());
@@ -838,4 +846,470 @@ TEST(NonlinearMitc4Residual, TinyRotationPreservesPhysicalForceAndRecoveryEnergy
   }
 }
 
+// Independent fixed-initial-director spring oracle: a total-chart rigid spin
+// carries numerical energy even though the physical shell is undeformed.
+TEST(Mitc4DrillingSelection, ProductionUsesDirectInitialDirectorSpring) {
+  const auto nodes = Nodes();
+  const auto shell = ProductionShell(nodes);
+  const fesa::ShellSection section{"Section", 0.2, 0U, {"spring.inp", 1U}};
+  const fesa::LinearElasticMaterial material{
+      "Material", 120.0, 0.25, {"spring.inp", 2U}};
+  const auto linear = fesa::Mitc4Shell::Create(
+      NodePointers(nodes),
+      {{{0., 0., 1.}, {0., 0., 1.}, {0., 0., 1.}, {0., 0., 1.}}}, section,
+      material);
+  ASSERT_TRUE(linear.HasValue());
+  const auto stiffness = linear.Value().Stiffness();
+  ASSERT_TRUE(stiffness.HasValue());
+  double rotary_trace = 0.0;
+  for (std::size_t node = 0; node < 4; ++node)
+    for (std::size_t c = 3; c < 5; ++c)
+      rotary_trace +=
+          stiffness.Value().physical_local20(5 * node + c, 5 * node + c);
+  const double kd = 1e-3 * rotary_trace / 8.;
+  fesa::NonlinearMitc4TrialDofs trial{};
+  const fesa::Vector3 phi{0., 0., 0.4};
+  const auto rotation = fesa::ExpSkew(phi);
+  for (std::size_t node = 0; node < 4; ++node) {
+    const fesa::Vector3 x{nodes[node].coordinates};
+    trial.rotation_vector[node] = phi;
+    fesa::Vector3 rotated{
+        rotation(0, 0) * x[0] + rotation(0, 1) * x[1] + rotation(0, 2) * x[2],
+        rotation(1, 0) * x[0] + rotation(1, 1) * x[1] + rotation(1, 2) * x[2],
+        rotation(2, 0) * x[0] + rotation(2, 1) * x[1] + rotation(2, 2) * x[2]};
+    trial.displacement[node] = rotated - x;
+  }
+  const auto actual = fesa::EvaluateInternalResidualAndTangent(shell, trial);
+  ASSERT_TRUE(actual.HasValue());
+  EXPECT_NEAR(actual.Value().physical_strain_energy, 0., 1e-25);
+  EXPECT_NEAR(actual.Value().drilling_energy, .5 * kd * 4 * .4 * .4, 1e-14);
+  for (std::size_t row = 0; row < 24; ++row) {
+    const double force = row % 6 == 5 ? kd * .4 : 0.;
+    EXPECT_NEAR(actual.Value().drilling_force[row], force, 1e-14);
+    for (std::size_t col = 0; col < 24; ++col) {
+      const double tangent = row == col && row % 6 == 5 ? kd : 0.;
+      EXPECT_NEAR(actual.Value().drilling_tangent(row, col), tangent, 1e-14);
+    }
+  }
+}
+
+TEST(Mitc4DrillingSelection,
+     DirectSpringUsesEachInitialDirectorAndConstantBlocks) {
+  for (const bool warped : {false, true}) {
+    auto nodes = Nodes();
+    if (warped) nodes[2].coordinates[2] = .1;
+    auto frames = Frames();
+    const auto transform = [](const fesa::Matrix& r, const Coordinates& x) {
+      Coordinates y{};
+      for (std::size_t i = 0; i < 3; ++i)
+        for (std::size_t j = 0; j < 3; ++j) y[i] += r(i, j) * x[j];
+      return y;
+    };
+    const auto global = fesa::ExpSkew({.4, -.3, .2});
+    std::array<Coordinates, 4> directors{};
+    for (std::size_t n = 0; n < 4; ++n) {
+      const auto r =
+          fesa::ExpSkew({0., warped ? .03 * static_cast<double>(n) : 0., 0.});
+      frames[n].director = transform(global, transform(r, frames[n].director));
+      frames[n].tangent_a =
+          transform(global, transform(r, frames[n].tangent_a));
+      frames[n].tangent_b =
+          transform(global, transform(r, frames[n].tangent_b));
+      nodes[n].coordinates = transform(global, nodes[n].coordinates);
+      directors[n] = frames[n].director;
+    }
+    const fesa::ShellSection section{"Section", .2, 0, {"spring.inp", 1}};
+    const fesa::LinearElasticMaterial material{
+        "Material", 120., .25, {"spring.inp", 2}};
+    const auto shell = fesa::NonlinearMitc4Shell::Create(
+        NodePointers(nodes), frames, section, material);
+    const auto linear = fesa::Mitc4Shell::Create(NodePointers(nodes), directors,
+                                                 section, material);
+    ASSERT_TRUE(shell.HasValue());
+    ASSERT_TRUE(linear.HasValue());
+    const auto k = linear.Value().Stiffness();
+    ASSERT_TRUE(k.HasValue());
+    double trace = 0.;
+    for (std::size_t n = 0; n < 4; ++n)
+      for (std::size_t c = 3; c < 5; ++c)
+        trace += k.Value().physical_local20(5 * n + c, 5 * n + c);
+    const double kd = 1e-3 * trace / 8.;
+    auto trial = Trial();
+    trial.rotation_vector[0] = {.65, -.4, .3};
+    const auto direction = ToVector(Direction());
+    const auto response = fesa::EvaluateInternalResidualAndTangent(
+        shell.Value(), trial, &direction);
+    const auto shifted = fesa::EvaluateInternalResidualAndTangent(
+        shell.Value(), AddScaled(trial, Direction(), .2), &direction);
+    ASSERT_TRUE(response.HasValue());
+    ASSERT_TRUE(shifted.HasValue());
+    double energy = 0.;
+    for (std::size_t n = 0; n < 4; ++n) {
+      const double gamma =
+          fesa::Vector3{directors[n]}.Dot(trial.rotation_vector[n]);
+      energy += .5 * kd * gamma * gamma;
+      const fesa::Vector3 d{directors[n]};
+      const auto rotation = fesa::EvaluateDynamicRotation(
+          trial.rotation_vector[n], d, Direction().rotation_vector[n], {});
+      ASSERT_TRUE(rotation.HasValue());
+      EXPECT_NEAR(response.Value().drilling_constraint[n],
+                  kd * gamma * rotation.Value().drill_null.Dot(d), 1e-14);
+      for (std::size_t c = 0; c < 3; ++c) {
+        double ds = 0.;
+        for (std::size_t j = 0; j < 3; ++j)
+          ds += d[j] * rotation.Value().null_gradient(j, c);
+        EXPECT_NEAR(
+            response.Value().drilling_constraint_gradient(n, 6 * n + 3 + c),
+            kd * (d[c] * rotation.Value().drill_null.Dot(d) + gamma * ds),
+            1e-14);
+      }
+      for (std::size_t c = 0; c < 3; ++c)
+        EXPECT_NEAR(response.Value().drilling_force[6 * n + 3 + c],
+                    kd * gamma * directors[n][c], 1e-14);
+    }
+    EXPECT_NEAR(response.Value().drilling_energy, energy, 1e-14);
+    for (std::size_t i = 0; i < 24; ++i) {
+      EXPECT_DOUBLE_EQ(response.Value().drilling_force_directional_second[i],
+                       0.);
+      if (i % 6 < 3) EXPECT_DOUBLE_EQ(response.Value().drilling_force[i], 0.);
+      for (std::size_t j = 0; j < 24; ++j) {
+        const double expected =
+            i / 6 == j / 6 && i % 6 >= 3 && j % 6 >= 3
+                ? kd * directors[i / 6][i % 6 - 3] * directors[i / 6][j % 6 - 3]
+                : 0.;
+        EXPECT_NEAR(response.Value().drilling_tangent(i, j), expected, 1e-14);
+        EXPECT_NEAR(response.Value().drilling_metric(i, j), expected, 1e-14);
+        EXPECT_DOUBLE_EQ(response.Value().drilling_tangent(i, j),
+                         shifted.Value().drilling_tangent(i, j));
+        if (expected == 0.)
+          EXPECT_DOUBLE_EQ(response.Value().drilling_tangent(i, j), 0.);
+      }
+    }
+  }
+}
+
+TEST(Mitc4DrillingSelection,
+     DirectConstraintUsesPhysicalNullAndItsHighDerivatives) {
+  const auto nodes = Nodes();
+  const auto shell = ProductionShell(nodes);
+  auto trial = Trial();
+  trial.rotation_vector[0] = {.65, -.4, .3};
+  const auto direction = Direction();
+  const auto velocity = ToVector(direction);
+  const auto response =
+      fesa::EvaluateInternalResidualAndTangent(shell, trial, &velocity);
+  ASSERT_TRUE(response.HasValue());
+  const auto zero =
+      fesa::EvaluateInternalResidualAndTangent(shell, {}, &velocity);
+  ASSERT_TRUE(zero.HasValue());
+  const double kd = zero.Value().drilling_tangent(5, 5);
+  // Independent inertia API provides n, Dn and D2n, never a twist angle.
+  const fesa::Vector3 d{0., 0., 1.};
+  const auto scalar_gradient = [&](const fesa::Vector3& phi, std::size_t c) {
+    const auto r = fesa::EvaluateDynamicRotation(phi, d, {}, {});
+    EXPECT_TRUE(r.HasValue());
+    double projection_derivative = 0.;
+    for (std::size_t k = 0; k < 3; ++k)
+      projection_derivative += r.Value().null_gradient(k, c) * d[k];
+    return kd * (d[c] * r.Value().drill_null.Dot(d) +
+                 d.Dot(phi) * projection_derivative);
+  };
+  constexpr double h = .002;
+  for (std::size_t n = 0; n < 4; ++n) {
+    const auto phi = trial.rotation_vector[n];
+    const auto v = direction.rotation_vector[n];
+    const auto r = fesa::EvaluateDynamicRotation(phi, d, v, {});
+    ASSERT_TRUE(r.HasValue());
+    const double gamma = d.Dot(phi);
+    const double gamma_dot = d.Dot(v);
+    double projection_dot = 0.;
+    for (std::size_t i = 0; i < 3; ++i)
+      for (std::size_t j = 0; j < 3; ++j)
+        projection_dot += d[i] * r.Value().null_gradient(i, j) * v[j];
+    const double expected_second =
+        kd * (2. * gamma_dot * projection_dot +
+              gamma * r.Value().null_directional_second.Dot(d));
+    double actual_second = 0.;
+    EXPECT_NEAR(response.Value().drilling_constraint[n],
+                kd * gamma * r.Value().drill_null.Dot(d), 1e-14);
+    for (std::size_t i = 0; i < 24; ++i) {
+      const double gradient =
+          i / 6 == n && i % 6 >= 3 ? scalar_gradient(phi, i % 6 - 3) : 0.;
+      EXPECT_NEAR(response.Value().drilling_constraint_gradient(n, i), gradient,
+                  1e-14);
+      for (std::size_t j = 0; j < 24; ++j)
+        actual_second += velocity[i] *
+                         response.Value().drilling_constraint_hessian[n](i, j) *
+                         velocity[j];
+      if (i / 6 == n && i % 6 >= 3) {
+        const auto c = i % 6 - 3;
+        const double fd =
+            (scalar_gradient(phi + h * v, c) - 2. * scalar_gradient(phi, c) +
+             scalar_gradient(phi - h * v, c)) /
+            (h * h);
+        const double actual =
+            response.Value()
+                .drilling_constraint_third_directional_gradient[n][i];
+        EXPECT_NEAR(actual, fd,
+                    2e-5 * (std::abs(actual) + std::abs(fd) + kd * 1e-4));
+      } else {
+        EXPECT_DOUBLE_EQ(
+            response.Value()
+                .drilling_constraint_third_directional_gradient[n][i],
+            0.);
+      }
+    }
+    EXPECT_NEAR(actual_second, expected_second, 1e-14);
+  }
+}
+
+TEST(Mitc4DrillingSelection, DirectExternalConstraintUsesActualInertiaNull) {
+  const auto nodes = Nodes();
+  const auto shell = ProductionShell(nodes);
+  const fesa::Vector3 phi{.65, -.4, .3}, velocity{.2, .1, -.15};
+  const fesa::Vector3 force{.7, -.3, .2}, rate{-.1, .2, .4},
+      acceleration{.5, -.2, .1};
+  const auto actual = shell.EvaluateExternalDrillingConstraint(
+      0, phi, velocity, force, rate, acceleration);
+  const auto rotation =
+      fesa::EvaluateDynamicRotation(phi, {0., 0., 1.}, velocity, {});
+  ASSERT_TRUE(actual.HasValue());
+  ASSERT_TRUE(rotation.HasValue());
+  const double h = .002;
+  const auto plus = shell.EvaluateExternalDrillingConstraint(
+      0, phi + h * velocity, velocity,
+      force + h * rate + .5 * h * h * acceleration, rate + h * acceleration,
+      acceleration);
+  const auto minus = shell.EvaluateExternalDrillingConstraint(
+      0, phi - h * velocity, velocity,
+      force - h * rate + .5 * h * h * acceleration, rate - h * acceleration,
+      acceleration);
+  ASSERT_TRUE(plus.HasValue());
+  ASSERT_TRUE(minus.HasValue());
+  for (std::size_t c = 0; c < 3; ++c) {
+    EXPECT_NEAR(
+        actual.Value().gradient_directional_first[c],
+        (plus.Value().gradient[c] - minus.Value().gradient[c]) / (2. * h),
+        1e-7);
+    EXPECT_NEAR(actual.Value().gradient_directional_second[c],
+                (plus.Value().gradient[c] - 2. * actual.Value().gradient[c] +
+                 minus.Value().gradient[c]) /
+                    (h * h),
+                2e-7);
+    std::array<double, 3> basis{};
+    basis[c] = 1.;
+    constexpr double coordinate_h = 1e-4;
+    const auto positive = shell.EvaluateExternalDrillingConstraint(
+        0, phi + coordinate_h * fesa::Vector3{basis}, velocity, force, rate,
+        acceleration);
+    const auto negative = shell.EvaluateExternalDrillingConstraint(
+        0, phi - coordinate_h * fesa::Vector3{basis}, velocity, force, rate,
+        acceleration);
+    ASSERT_TRUE(positive.HasValue());
+    ASSERT_TRUE(negative.HasValue());
+    for (std::size_t j = 0; j < 3; ++j)
+      EXPECT_NEAR(
+          actual.Value().hessian(j, c),
+          (positive.Value().gradient[j] - negative.Value().gradient[j]) /
+              (2. * coordinate_h),
+          1e-7);
+  }
+  const auto& n = rotation.Value();
+  EXPECT_NEAR(actual.Value().value, -n.drill_null.Dot(force), 1e-14);
+  fesa::Vector3 n_dot{};
+  std::array<double, 3> values{};
+  for (std::size_t i = 0; i < 3; ++i)
+    for (std::size_t j = 0; j < 3; ++j)
+      values[i] += n.null_gradient(i, j) * velocity[j];
+  n_dot = fesa::Vector3{values};
+  EXPECT_NEAR(actual.Value().directional_first,
+              -n_dot.Dot(force) - n.drill_null.Dot(rate), 1e-14);
+  EXPECT_NEAR(actual.Value().directional_second,
+              -n.null_directional_second.Dot(force) - 2. * n_dot.Dot(rate) -
+                  n.drill_null.Dot(acceleration),
+              1e-14);
+  for (std::size_t c = 0; c < 3; ++c) {
+    double expected = 0.;
+    for (std::size_t i = 0; i < 3; ++i)
+      expected -= n.null_gradient(i, c) * force[i];
+    EXPECT_NEAR(actual.Value().gradient[c], expected, 1e-14);
+  }
+}
+
+TEST(Mitc4DrillingSelection,
+     ModesAreImmutableReferenceInputsAndPreservePhysicalResponse) {
+  const auto nodes = Nodes();
+  const auto direct = ProductionShell(nodes);
+  const auto legacy = LegacyShell(nodes);
+  EXPECT_EQ(direct.DrillingMode(), fesa::Mitc4DrillingMode::kDirectSpring);
+  EXPECT_EQ(legacy.DrillingMode(),
+            fesa::Mitc4DrillingMode::kLegacyCorotatedTwist);
+  EXPECT_STREQ(fesa::Mitc4DrillingModeName(direct.DrillingMode()),
+               "direct-initial-director-spring");
+  EXPECT_STREQ(fesa::Mitc4DrillingModeName(legacy.DrillingMode()),
+               "legacy-corotated-twist");
+  const auto a =
+      fesa::nonlinear_mitc4_internal::ConfigurationSnapshot::Read(direct);
+  const auto b =
+      fesa::nonlinear_mitc4_internal::ConfigurationSnapshot::Read(legacy);
+  EXPECT_EQ(a.values, b.values);
+  EXPECT_NE(a.drilling_mode, b.drilling_mode);
+  const auto direction = ToVector(Direction());
+  const auto r =
+      fesa::EvaluateInternalResidualAndTangent(direct, Trial(), &direction);
+  const auto l =
+      fesa::EvaluateInternalResidualAndTangent(legacy, Trial(), &direction);
+  ASSERT_TRUE(r.HasValue());
+  ASSERT_TRUE(l.HasValue());
+  EXPECT_DOUBLE_EQ(r.Value().physical_strain_energy,
+                   l.Value().physical_strain_energy);
+  EXPECT_NE(r.Value().drilling_energy, l.Value().drilling_energy);
+  for (std::size_t i = 0; i < 24; ++i) {
+    EXPECT_DOUBLE_EQ(r.Value().physical_force[i], l.Value().physical_force[i]);
+    for (std::size_t j = 0; j < 24; ++j)
+      EXPECT_NEAR(
+          r.Value().internal_tangent(i, j) - r.Value().drilling_tangent(i, j),
+          l.Value().internal_tangent(i, j) - l.Value().drilling_tangent(i, j),
+          1e-14);
+  }
+  for (std::size_t gp = 0; gp < 4; ++gp)
+    EXPECT_EQ(r.Value().recovery.gauss_points[gp].section_resultant,
+              l.Value().recovery.gauss_points[gp].section_resultant);
+  const fesa::ShellSection section{"Section", .2, 0, {"spring.inp", 1}};
+  const fesa::LinearElasticMaterial material{
+      "Material", 120., .25, {"spring.inp", 2}};
+  const auto linear = fesa::Mitc4Shell::Create(
+      NodePointers(nodes),
+      {{{0., 0., 1.}, {0., 0., 1.}, {0., 0., 1.}, {0., 0., 1.}}}, section,
+      material);
+  ASSERT_TRUE(linear.HasValue());
+  EXPECT_EQ(linear.Value().DrillingMode(), direct.DrillingMode());
+  const auto alternate = fesa::mitc4_drilling_internal::TestAccess::WithMode(
+      linear.Value(), fesa::Mitc4DrillingMode::kLegacyCorotatedTwist);
+  const auto k1 = linear.Value().Stiffness();
+  const auto k2 = alternate.Stiffness();
+  ASSERT_TRUE(k1.HasValue());
+  ASSERT_TRUE(k2.HasValue());
+  for (std::size_t i = 0; i < 24; ++i)
+    for (std::size_t j = 0; j < 24; ++j)
+      EXPECT_DOUBLE_EQ(k1.Value().stabilized_global24(i, j),
+                       k2.Value().stabilized_global24(i, j));
+}
+
+TEST(Mitc4DrillingSelection, DirectRejectsInvalidScaleAndNonfiniteTrial) {
+  const auto nodes = Nodes();
+  const fesa::ShellSection section{"Section", .2, 0, {"spring.inp", 1}};
+  for (double youngs_modulus : {1e-320, (std::numeric_limits<double>::max)()}) {
+    const fesa::LinearElasticMaterial material{
+        "Material", youngs_modulus, .25, {"spring.inp", 2}};
+    const auto invalid = fesa::NonlinearMitc4Shell::Create(
+        NodePointers(nodes), Frames(), section, material);
+    ASSERT_FALSE(invalid.HasValue());
+    EXPECT_EQ(invalid.GetStatus().Diagnostics()[0].code,
+              youngs_modulus < 1.0 ? "invalid-nonlinear-shell-drilling"
+                                  : "invalid-shell-material");
+  }
+  const auto shell = ProductionShell(nodes);
+  for (double value : {std::numeric_limits<double>::quiet_NaN(),
+                       std::numeric_limits<double>::infinity()}) {
+    auto trial = Trial();
+    trial.rotation_vector[0] = {value, 0., 0.};
+    EXPECT_FALSE(
+        fesa::EvaluateInternalResidualAndTangent(shell, trial).HasValue());
+  }
+  const auto valid = fesa::EvaluateInternalResidualAndTangent(shell, {});
+  ASSERT_TRUE(valid.HasValue());
+  EXPECT_DOUBLE_EQ(valid.Value().drilling_energy, 0.);
+}
+
+TEST(Mitc4DrillingSelection, DirectRetainsPositiveSubnormalSpringScale) {
+  const auto nodes = Nodes();
+  const fesa::ShellSection section{"Section", .2, 0, {"spring.inp", 1}};
+  unsigned accepted = 0;
+  for (double youngs_modulus :
+       {1e-315, 1e-316, 1e-317, 1e-318, 2e-318, 3e-318, 1e-319}) {
+    const fesa::LinearElasticMaterial material{
+        "Material", youngs_modulus, .25, {"spring.inp", 2}};
+    const auto linear = fesa::Mitc4Shell::Create(
+        NodePointers(nodes),
+        {{{0., 0., 1.}, {0., 0., 1.}, {0., 0., 1.}, {0., 0., 1.}}}, section,
+        material);
+    ASSERT_TRUE(linear.HasValue());
+    const auto stiffness = linear.Value().Stiffness();
+    const auto shell = fesa::NonlinearMitc4Shell::Create(
+        NodePointers(nodes), Frames(), section, material);
+    if (!stiffness.HasValue()) {
+      EXPECT_FALSE(shell.HasValue());
+      continue;
+    }
+    ASSERT_TRUE(shell.HasValue());
+    ++accepted;
+    fesa::NonlinearMitc4TrialDofs trial{};
+    trial.rotation_vector[0] = {0., 0., 1.};
+    const auto actual =
+        fesa::EvaluateInternalResidualAndTangent(shell.Value(), trial);
+    ASSERT_TRUE(actual.HasValue());
+    // Scale is already validated. No later half-scale rounding may change K.
+    const double kd = stiffness.Value().drilling_stiffness;
+    EXPECT_EQ(actual.Value().drilling_tangent(5, 5), kd);
+    EXPECT_EQ(actual.Value().drilling_force[5], kd);
+    trial.rotation_vector[0] = {0., 0., 2.};
+    const auto double_angle =
+        fesa::EvaluateInternalResidualAndTangent(shell.Value(), trial);
+    ASSERT_TRUE(double_angle.HasValue());
+    // U(2) = 2*kd is representable even for the least positive spring scale.
+    EXPECT_EQ(double_angle.Value().drilling_energy, 2. * kd);
+    EXPECT_EQ(double_angle.Value().drilling_force[5], 2. * kd);
+  }
+  EXPECT_GT(accepted, 0U);
+}
+
+TEST(Mitc4DrillingSelection, LegacyHeadFrozenEvidence) {
+  const auto nodes = Nodes();
+  const auto shell = LegacyShell(nodes);
+  const auto direction = ToVector(Direction());
+  const auto response =
+      fesa::EvaluateInternalResidualAndTangent(shell, Trial(), &direction);
+  ASSERT_TRUE(response.HasValue());
+  const auto& r = response.Value();
+  std::array<std::uint64_t, 8> hashes{};
+  hashes.fill(14695981039346656037ULL);
+  const auto add = [&](std::size_t channel, double value) {
+    std::uint64_t bits{};
+    std::memcpy(&bits, &value, sizeof(bits));
+    for (unsigned b = 0; b < 8; ++b) {
+      hashes[channel] ^= (bits >> (8 * b)) & 255ULL;
+      hashes[channel] *= 1099511628211ULL;
+    }
+  };
+  add(0, r.drilling_energy);
+  for (std::size_t i = 0; i < 24; ++i) {
+    add(1, r.drilling_force[i]);
+    add(4, r.force_directional_second[i]);
+    for (std::size_t j = 0; j < 24; ++j) {
+      add(2, r.drilling_tangent(i, j));
+      add(3, r.drilling_metric(i, j));
+    }
+  }
+  for (std::size_t n = 0; n < 4; ++n) {
+    add(5, r.drilling_constraint[n]);
+    for (std::size_t i = 0; i < 24; ++i) {
+      add(5, r.drilling_constraint_gradient(n, i));
+      add(7, r.drilling_constraint_third_directional_gradient[n][i]);
+      for (std::size_t j = 0; j < 24; ++j)
+        add(6, r.drilling_constraint_hessian[n](i, j));
+    }
+  }
+  // Captured before implementation from HEAD
+  // 52e321e15c70377d4318aace3f3bc64b3ea1a65c, native MSVC x64 Debug. Entire
+  // energy/force/tangent/metric/directional/psi inventories are pinned
+  // independently, including the historical polar1 constraint inconsistency. Do
+  // not regenerate these from the selected mode.
+  constexpr std::array<std::uint64_t, 8> frozen{
+      16395275265220000061ULL, 12405324468590059764ULL, 79034762627498281ULL,
+      7305417493946306304ULL,  7191018337857616990ULL,  4845391414006668707ULL,
+      11613163243225266145ULL, 3872161451216566265ULL};
+  EXPECT_EQ(hashes, frozen);
+}
+
 }  // namespace