diff --git a/msvc/fesa_solver.vcxproj b/msvc/fesa_solver.vcxproj
index 3ab073a..9d64409 100644
--- a/msvc/fesa_solver.vcxproj
+++ b/msvc/fesa_solver.vcxproj
@@ -16,6 +16,7 @@
     <ClCompile Include="..\src\fesa\analysis\hht_dynamic_algebra.cpp" />
     <ClInclude Include="..\src\fesa\analysis\hht_development_probe.h" />
     <ClCompile Include="..\src\fesa\analysis\hht_dynamic_assembly.cpp" />
+    <ClCompile Include="..\src\fesa\analysis\hht_field_convergence.cpp" />
     <ClCompile Include="..\src\fesa\analysis\hht_reduced_operators.cpp" />
     <ClCompile Include="..\src\fesa\analysis\hht_reduced_procedure.cpp" />
     <ClCompile Include="..\src\fesa\analysis\hht_dynamic_procedure.cpp" />
diff --git a/msvc/fesa_unit_tests.vcxproj b/msvc/fesa_unit_tests.vcxproj
index 80e95ee..21ccaa7 100644
--- a/msvc/fesa_unit_tests.vcxproj
+++ b/msvc/fesa_unit_tests.vcxproj
@@ -21,6 +21,7 @@
     <ClCompile Include="..\tests\unit\analysis\hht_temporal_verification_test.cpp" />
     <ClCompile Include="..\tests\unit\analysis\hht_dynamic_algebra_test.cpp" />
     <ClCompile Include="..\tests\unit\analysis\hht_development_probe_test.cpp" />
+    <ClCompile Include="..\tests\unit\analysis\hht_field_convergence_test.cpp" />
     <ClCompile Include="..\tests\unit\analysis\hht_reduced_shell_test.cpp" />
     <ClCompile Include="..\tests\unit\analysis\hht_dynamic_procedure_test.cpp" />
     <ClCompile Include="..\tests\unit\analysis\nonlinear_analysis_state_test.cpp" />
diff --git a/src/fesa/CMakeLists.txt b/src/fesa/CMakeLists.txt
index 804c94a..7f70e0b 100644
--- a/src/fesa/CMakeLists.txt
+++ b/src/fesa/CMakeLists.txt
@@ -9,6 +9,7 @@ add_library(
     analysis/hht_dynamic_algebra.cpp
     analysis/hht_development_probe.h
     analysis/hht_dynamic_assembly.cpp
+    analysis/hht_field_convergence.cpp
     analysis/hht_reduced_operators.cpp
     analysis/hht_reduced_procedure.cpp
     analysis/hht_dynamic_procedure.cpp
diff --git a/src/fesa/analysis/hht_field_convergence.cpp b/src/fesa/analysis/hht_field_convergence.cpp
new file mode 100644
index 0000000..c887db0
--- /dev/null
+++ b/src/fesa/analysis/hht_field_convergence.cpp
@@ -0,0 +1,166 @@
+#include "analysis/hht_field_convergence.h"
+
+#include <algorithm>
+#include <cmath>
+#include <limits>
+
+namespace fesa::hht_field_convergence {
+namespace {
+constexpr double kRn = .005, kCn = .01, kRp = .02, kEpsilon = 1e-5;
+constexpr double kZeroCorrection = .001, kLinear = 1e-8;
+constexpr double kInactive = 1e-5, kSmallTranslation = 1e-8;
+bool Nonnegative(double x) { return std::isfinite(x) && x >= 0; }
+bool ValidOptional(const std::optional<double>& x) {
+  return !x || Nonnegative(*x);
+}
+bool ValidHistory(const History& h) {
+  return Nonnegative(h.nonzero_sum) && Nonnegative(h.maximum_sum) &&
+      h.nonzero_count <= h.maximum_count &&
+      (h.nonzero_count != 0 || h.nonzero_sum == 0) &&
+      (h.maximum_count != 0 || h.maximum_sum == 0);
+}
+}  // namespace
+
+Evaluation Evaluate(const std::array<FieldInput, 2>& fields,
+                    const std::array<History, 2>& committed,
+                    std::size_t iteration, double reference_length) {
+  Evaluation result;
+  result.status = Status::Failure(FailureCategory::kSolver,
+      {{Severity::kError, "invalid-state", {}, {}, {}, "Invalid field convergence arithmetic or input."}});
+  result.pending = committed;
+  if (!std::isfinite(reference_length) || reference_length <= 0) return result;
+  for (std::size_t a = 0; a < 2; ++a) {
+    const auto& f = fields[a];
+    const auto& h = committed[a];
+    auto& out = result.fields[a];
+    if (!ValidHistory(h) || !Nonnegative(f.residual) || !Nonnegative(f.increment) ||
+        !ValidOptional(f.correction) || !ValidOptional(f.previous_residual) ||
+        !ValidOptional(f.older_residual)) return result;
+    if (f.flux.empty()) {
+      if (f.active) { result.status = Status::Failure(FailureCategory::kSolver,
+          {{Severity::kError, "invalid-flux-population", {}, {}, {}, "Empty active flux population."}}); return result; }
+      continue;
+    }
+    const double historic_maximum = h.maximum_count == 0 ? 0 :
+        h.maximum_sum / static_cast<double>(h.maximum_count);
+    const double cutoff = kInactive * historic_maximum;
+    double maximum = 0;
+    for (const auto& x : f.flux) {
+      if (!std::isfinite(x.internal) || !std::isfinite(x.inertia)) return result;
+      const double total = x.internal + x.inertia;
+      if (!std::isfinite(total)) return result;
+      maximum = std::max(maximum, std::abs(total));
+    }
+    out.maximum_flux = maximum;
+    const bool filter = maximum >= .1 * historic_maximum;
+    double sum = 0;
+    std::size_t count = 0;
+    for (const auto& x : f.flux) {
+      const double b = std::abs(x.internal + x.inertia);
+      if (!filter || b >= cutoff) {
+        sum += b;
+        if (!std::isfinite(sum)) return result;
+        ++count;
+      }
+    }
+    if (count == 0) { result.status = Status::Failure(FailureCategory::kSolver,
+          {{Severity::kError, "invalid-flux-population", {}, {}, {}, "Empty active flux population."}}); return result; }
+    const double spatial = sum / static_cast<double>(count);
+    out.spatial_flux = spatial;
+    if (h.nonzero_count == std::numeric_limits<std::uint64_t>::max() ||
+        h.maximum_count == std::numeric_limits<std::uint64_t>::max()) return result;
+    const double base = h.nonzero_count == 0 ? .01 :
+        h.nonzero_sum / static_cast<double>(h.nonzero_count);
+    const double next_sum = h.nonzero_sum + spatial;
+    const double next_maximum = h.maximum_sum + maximum;
+    if (!Nonnegative(next_sum) || !Nonnegative(next_maximum)) return result;
+    const double included = next_sum / static_cast<double>(h.nonzero_count + 1);
+    const bool eligible = spatial > kEpsilon * (h.nonzero_count == 0 ? base : included);
+    const double raw = eligible ? included : base;
+    if (!std::isfinite(raw) || raw <= 0) return result;
+    out.time_average_flux = raw;
+    out.residual_scale = raw;
+    auto& pending = result.pending[a];
+    if (eligible) { pending.nonzero_sum = next_sum; ++pending.nonzero_count; }
+    pending.maximum_sum = next_maximum;
+    ++pending.maximum_count;
+  }
+  // Both conversions read raw means, never a converted peer scale.
+  if (fields[0].active && fields[1].active) {
+    const double force = *result.fields[0].time_average_flux;
+    const double moment = *result.fields[1].time_average_flux;
+    const std::array<double, 2> converted{moment / reference_length, reference_length * force};
+    for (std::size_t a = 0; a < 2; ++a) {
+      if (!Nonnegative(converted[a])) return result;
+      auto& out = result.fields[a];
+      if (*out.spatial_flux <= *out.time_average_flux &&
+          *out.time_average_flux < converted[a]) out.residual_scale = converted[a];
+    }
+  }
+  bool all_linear = iteration >= 1;
+  for (std::size_t a = 0; a < 2; ++a) {
+    if (!fields[a].active) continue;
+    const double scale = *result.fields[a].residual_scale;
+    if (!std::isfinite(scale) || scale <= 0) return result;
+    const double ratio = fields[a].residual / scale;
+    if (!Nonnegative(ratio)) return result;
+    all_linear = all_linear && ratio <= kLinear;
+  }
+  bool all_pass = true;
+  for (std::size_t a = 0; a < 2; ++a) {
+    const auto& f = fields[a];
+    if (!f.active) continue;
+    auto& out = result.fields[a];
+    const double scale = *out.residual_scale;
+    const double ratio = f.residual / scale;
+    if (all_linear) {
+      out.branch = Branch::kLinear;
+      out.residual_threshold = kLinear;
+      out.residual_pass = true; out.field_pass = true;
+      continue;
+    }
+    const bool zero = *out.spatial_flux <= kEpsilon * scale;
+    bool nonquadratic = false;
+    if (!zero && iteration > 9 && f.previous_residual && f.older_residual &&
+        *f.older_residual > *f.previous_residual && *f.previous_residual > f.residual && f.residual > 0) {
+      const double recent = f.residual / *f.previous_residual;
+      const double older = *f.previous_residual / *f.older_residual;
+      if (!Nonnegative(recent) || !Nonnegative(older)) return result;
+      nonquadratic = recent >= older;
+    }
+    out.branch = zero ? Branch::kZeroFlux :
+        (nonquadratic ? Branch::kNonquadratic : Branch::kNormal);
+    const double residual_threshold = zero ? kEpsilon : (nonquadratic ? kRp : kRn);
+    out.residual_threshold = residual_threshold;
+    out.residual_pass = ratio <= residual_threshold;
+    if (zero && *out.residual_pass) { out.field_pass = true; continue; }
+    if (!zero && iteration >= 1 && a == 0 && f.increment < kSmallTranslation * reference_length) {
+      out.field_pass = out.residual_pass;
+    } else {
+      const double correction_threshold = zero ? kZeroCorrection : kCn;
+      out.correction_threshold = correction_threshold;
+      const double bound = correction_threshold * f.increment;
+      if (!Nonnegative(bound)) return result;
+      if (iteration >= 1 && f.correction) out.correction_pass = *f.correction <= bound;
+      if (!zero && !nonquadratic && iteration >= 2 && f.correction &&
+          f.previous_residual && f.older_residual) {
+        const double denominator = std::min(*f.previous_residual, *f.older_residual);
+        if (denominator > 0) {
+          const double quotient = f.residual / denominator;
+          if (!Nonnegative(quotient)) return result;
+          const double estimate = quotient * *f.correction;
+          if (!Nonnegative(estimate)) return result;
+          out.estimated_correction = estimate;
+          out.correction_pass = out.correction_pass.value_or(false) || estimate <= bound;
+        }
+      }
+      out.field_pass = zero ? out.correction_pass.value_or(false) :
+          (*out.residual_pass && out.correction_pass.value_or(false));
+    }
+    all_pass = all_pass && *out.field_pass;
+  }
+  result.field_pass = all_pass;
+  result.status = Status::Ok();
+  return result;
+}
+}  // namespace fesa::hht_field_convergence
diff --git a/src/fesa/analysis/hht_field_convergence.h b/src/fesa/analysis/hht_field_convergence.h
new file mode 100644
index 0000000..e4123c6
--- /dev/null
+++ b/src/fesa/analysis/hht_field_convergence.h
@@ -0,0 +1,52 @@
+#ifndef FESA_ANALYSIS_HHT_FIELD_CONVERGENCE_H_
+#define FESA_ANALYSIS_HHT_FIELD_CONVERGENCE_H_
+
+#include <array>
+#include <cstddef>
+#include <cstdint>
+#include <optional>
+#include <vector>
+
+#include "fesa/core/status.h"
+
+namespace fesa::hht_field_convergence {
+inline constexpr const char* kPolicyId = "abaqus2025-field-on-fesa-v1";
+// Ordered element rows first, then external source entries (including explicit zero).
+// External entries use internal=value, inertia=0. No assembled cancellation here.
+struct FluxOccurrence { double internal = 0.0; double inertia = 0.0; };
+struct History {
+  double nonzero_sum = 0.0;
+  std::uint64_t nonzero_count = 0;
+  double maximum_sum = 0.0;
+  std::uint64_t maximum_count = 0;
+};
+struct FieldInput {
+  bool active = false;  // At least one free full DOF of this field.
+  std::vector<FluxOccurrence> flux;
+  double residual = 0.0;  // max |I+fint-F| on full free endpoint DOFs, fi=1.
+  double increment = 0.0; // max |q_trial-q_last_accepted| in fixed full u/phi chart.
+  std::optional<double> correction; // max |q_trial-q_previous_selected|, i>=1.
+  std::optional<double> previous_residual;
+  std::optional<double> older_residual;
+};
+enum class Branch { kNotEvaluated, kLinear, kZeroFlux, kNonquadratic, kNormal };
+struct FieldResult {
+  std::optional<double> spatial_flux, maximum_flux, time_average_flux, residual_scale;
+  std::optional<double> estimated_correction, residual_threshold, correction_threshold;
+  std::optional<bool> residual_pass, correction_pass, field_pass;
+  Branch branch = Branch::kNotEvaluated;
+};
+struct Evaluation {
+  Status status = Status::Failure(FailureCategory::kSolver, {});
+  bool field_pass = false;
+  std::array<FieldResult, 2> fields;
+  // Pure pending snapshot: procedure owns exactly-once commit after every gate/output.
+  std::array<History, 2> pending;
+};
+// Index 0: force/translation; index 1: generalized moment/total rotation phi.
+Evaluation Evaluate(const std::array<FieldInput, 2>& fields,
+                    const std::array<History, 2>& committed,
+                    std::size_t iteration, double reference_length);
+}  // namespace fesa::hht_field_convergence
+
+#endif  // FESA_ANALYSIS_HHT_FIELD_CONVERGENCE_H_
diff --git a/tests/CMakeLists.txt b/tests/CMakeLists.txt
index 1e77eac..9c4a638 100644
--- a/tests/CMakeLists.txt
+++ b/tests/CMakeLists.txt
@@ -15,6 +15,7 @@ add_executable(
     unit/analysis/hht_temporal_verification_test.cpp
     unit/analysis/hht_dynamic_algebra_test.cpp
     unit/analysis/hht_development_probe_test.cpp
+    unit/analysis/hht_field_convergence_test.cpp
     unit/analysis/hht_reduced_shell_test.cpp
     unit/analysis/hht_dynamic_procedure_test.cpp
     unit/analysis/nonlinear_analysis_state_test.cpp
diff --git a/tests/unit/analysis/hht_field_convergence_test.cpp b/tests/unit/analysis/hht_field_convergence_test.cpp
new file mode 100644
index 0000000..fd7b8b8
--- /dev/null
+++ b/tests/unit/analysis/hht_field_convergence_test.cpp
@@ -0,0 +1,232 @@
+#include "analysis/hht_field_convergence.h"
+#include <gtest/gtest.h>
+#include <cmath>
+#include <limits>
+namespace fesa::hht_field_convergence {
+namespace {
+using Inputs = std::array<FieldInput, 2>;
+using Histories = std::array<History, 2>;
+Inputs Normal() {
+  Inputs f{}; f[0].active = true; f[0].flux = {{2.0, 0.0}};
+  f[0].residual = .01; f[0].increment = 1; f[0].correction = .01;
+  return f;
+}
+TEST(HhtFieldConvergence, SignedElementTotalAndSourcePopulationOracle) {
+  auto f = Normal(); f[0].flux.assign(30, {});
+  f[0].flux[0] = {8, -6}; f[0].flux[1] = {-2, 0};
+  f[0].flux[24] = {3, 0}; f[0].flux[27] = {-3, 0};
+  Histories h{}; h[0].maximum_sum = 10; h[0].maximum_count = 1;
+  auto r = Evaluate(f, h, 1, 2); ASSERT_TRUE(r.status.IsOk());
+  EXPECT_DOUBLE_EQ(*r.fields[0].spatial_flux, 2.5);
+  r = Evaluate(f, {}, 1, 2); ASSERT_TRUE(r.status.IsOk());
+  EXPECT_DOUBLE_EQ(*r.fields[0].spatial_flux, 1.0/3.0);
+}
+TEST(HhtFieldConvergence, NormalBoundaryAndInitialCorrectionMissing) {
+  auto f = Normal(); auto r = Evaluate(f, {}, 1, 2);
+  ASSERT_TRUE(r.status.IsOk()); EXPECT_TRUE(r.field_pass);
+  f[0].residual = std::nextafter(.005 * 2, INFINITY);
+  r = Evaluate(f, {}, 1, 2); ASSERT_TRUE(r.status.IsOk()); EXPECT_FALSE(r.field_pass);
+  f = Normal(); r = Evaluate(f, {}, 0, 2);
+  ASSERT_TRUE(r.status.IsOk()); EXPECT_FALSE(r.field_pass);
+  EXPECT_FALSE(r.fields[0].correction_pass.has_value());
+}
+TEST(HhtFieldConvergence, ScalarPopulationThresholdAndReactivation) {
+  auto f=Normal(); Histories h{}; h[0].maximum_sum=100; h[0].maximum_count=1;
+  f[0].flux={{0,0},{.001,0},{10,0}};
+  auto r=Evaluate(f,h,1,2); ASSERT_TRUE(r.status.IsOk());
+  EXPECT_DOUBLE_EQ(*r.fields[0].spatial_flux,5.0005);
+  f[0].flux[2].internal=std::nextafter(10.,0.);
+  r=Evaluate(f,h,1,2); ASSERT_TRUE(r.status.IsOk());
+  EXPECT_DOUBLE_EQ(*r.fields[0].spatial_flux,(.001+std::nextafter(10.,0.))/3);
+  f[0].flux={{0,0},{0,0}}; r=Evaluate(f,h,1,2); ASSERT_TRUE(r.status.IsOk());
+  EXPECT_DOUBLE_EQ(*r.fields[0].spatial_flux,0);
+}
+TEST(HhtFieldConvergence, InitialAverageAndNonzeroEligibilityBoundary) {
+  auto f=Normal(); const double edge=1e-5*.01;
+  for (double x:{std::nextafter(edge,0.),edge,std::nextafter(edge,INFINITY)}) {
+    f[0].flux={{x,0}}; auto r=Evaluate(f,{},0,2); ASSERT_TRUE(r.status.IsOk());
+    EXPECT_DOUBLE_EQ(*r.fields[0].time_average_flux,x>edge?x:.01);
+    EXPECT_EQ(r.pending[0].nonzero_count,x>edge?1U:0U);
+    EXPECT_EQ(r.pending[0].maximum_count,1U);
+  }
+}
+TEST(HhtFieldConvergence, PendingHistoryIsRecomputedAndRollbackIsPure) {
+  auto f=Normal(); Histories h{}; h[0]={10,1,4,1};
+  f[0].flux={{30,0}}; auto a=Evaluate(f,h,1,2); ASSERT_TRUE(a.status.IsOk());
+  EXPECT_DOUBLE_EQ(*a.fields[0].time_average_flux,20);
+  f[0].flux={{70,0}}; auto b=Evaluate(f,h,2,2); ASSERT_TRUE(b.status.IsOk());
+  EXPECT_DOUBLE_EQ(*b.fields[0].time_average_flux,40);
+  EXPECT_DOUBLE_EQ(b.pending[0].nonzero_sum,80);
+  EXPECT_DOUBLE_EQ(b.pending[0].maximum_sum,74);
+  EXPECT_EQ(b.pending[0].maximum_count,2U);
+  EXPECT_DOUBLE_EQ(h[0].nonzero_sum,10); EXPECT_EQ(h[0].nonzero_count,1U);
+  f[0].flux={{0,0}}; auto z=Evaluate(f,h,1,2); ASSERT_TRUE(z.status.IsOk());
+  EXPECT_EQ(z.pending[0].nonzero_count,1U); EXPECT_EQ(z.pending[0].maximum_count,2U);
+  EXPECT_DOUBLE_EQ(z.pending[0].maximum_sum,4);
+}
+TEST(HhtFieldConvergence, RawScaleConversionIsSimultaneousAndUnitConsistent) {
+  auto f=Normal(); Histories h{}; h[0]={3,1,3,1}; h[1]={.3,1,.3,1};
+  f[0].flux={{3,0}}; f[1].active=true; f[1].flux={{.1,0}};
+  auto r=Evaluate(f,h,1,2); ASSERT_TRUE(r.status.IsOk());
+  EXPECT_DOUBLE_EQ(*r.fields[0].residual_scale,3);
+  EXPECT_DOUBLE_EQ(*r.fields[1].time_average_flux,.2);
+  EXPECT_DOUBLE_EQ(*r.fields[1].residual_scale,6);
+  f[1].active=false; r=Evaluate(f,h,1,2); ASSERT_TRUE(r.status.IsOk());
+  EXPECT_EQ(r.fields[1].branch,Branch::kNotEvaluated);
+  EXPECT_FALSE(r.fields[1].field_pass.has_value());
+}
+TEST(HhtFieldConvergence, EstimatedCorrectionHasRealHistoryAndNormalOnly) {
+  auto f=Normal(); f[0].flux={{400,0}}; f[0].residual=2;
+  f[0].correction=.04; f[0].previous_residual=4; f[0].older_residual=8;
+  auto r=Evaluate(f,{},2,2); ASSERT_TRUE(r.status.IsOk());
+  EXPECT_DOUBLE_EQ(*r.fields[0].estimated_correction,.02); EXPECT_FALSE(r.field_pass);
+  f[0].residual=1; r=Evaluate(f,{},2,2); ASSERT_TRUE(r.status.IsOk());
+  EXPECT_DOUBLE_EQ(*r.fields[0].estimated_correction,.01); EXPECT_TRUE(r.field_pass);
+  f[0].older_residual=0; r=Evaluate(f,{},2,2); ASSERT_TRUE(r.status.IsOk());
+  EXPECT_FALSE(r.fields[0].estimated_correction.has_value()); EXPECT_FALSE(r.field_pass);
+  f[0].older_residual=8; r=Evaluate(f,{},1,2); ASSERT_TRUE(r.status.IsOk());
+  EXPECT_FALSE(r.fields[0].estimated_correction.has_value()); EXPECT_FALSE(r.field_pass);
+}
+TEST(HhtFieldConvergence, NonquadraticIterationAndRateBoundaries) {
+  auto f=Normal(); f[0].flux={{100,0}}; f[0].residual=2;
+  f[0].previous_residual=4; f[0].older_residual=8;
+  auto r=Evaluate(f,{},9,2); ASSERT_TRUE(r.status.IsOk());
+  EXPECT_EQ(r.fields[0].branch,Branch::kNormal); EXPECT_FALSE(r.field_pass);
+  r=Evaluate(f,{},10,2); ASSERT_TRUE(r.status.IsOk());
+  EXPECT_EQ(r.fields[0].branch,Branch::kNonquadratic); EXPECT_TRUE(r.field_pass);
+  EXPECT_FALSE(r.fields[0].estimated_correction.has_value());
+  f[0].older_residual=16; f[0].residual=1;
+  r=Evaluate(f,{},10,2); ASSERT_TRUE(r.status.IsOk()); EXPECT_EQ(r.fields[0].branch,Branch::kNonquadratic);
+  f[0].residual=.5; r=Evaluate(f,{},10,2); ASSERT_TRUE(r.status.IsOk());
+  EXPECT_EQ(r.fields[0].branch,Branch::kNormal);
+  f[0].residual=4; r=Evaluate(f,{},10,2); ASSERT_TRUE(r.status.IsOk());
+  EXPECT_EQ(r.fields[0].branch,Branch::kNormal);
+}
+TEST(HhtFieldConvergence, ZeroFluxUsesResidualOrActualCorrectionAtBoundary) {
+  auto f=Normal(); Histories h{}; h[0]={2,1,2,1};
+  f[0].flux={{0,0}}; f[0].residual=1e-5*2; f[0].correction.reset();
+  auto r=Evaluate(f,h,0,2); ASSERT_TRUE(r.status.IsOk()); EXPECT_TRUE(r.field_pass);
+  EXPECT_EQ(r.fields[0].branch,Branch::kZeroFlux); EXPECT_FALSE(r.fields[0].correction_pass.has_value());
+  f[0].residual=std::nextafter(1e-5*2,INFINITY);
+  r=Evaluate(f,h,0,2); ASSERT_TRUE(r.status.IsOk()); EXPECT_FALSE(r.field_pass);
+  f[0].correction=.001; r=Evaluate(f,h,1,2); ASSERT_TRUE(r.status.IsOk()); EXPECT_TRUE(r.field_pass);
+  f[0].correction=std::nextafter(.001,INFINITY);
+  r=Evaluate(f,h,1,2); ASSERT_TRUE(r.status.IsOk()); EXPECT_FALSE(r.field_pass);
+  f[0].increment=0; f[0].correction=0;
+  r=Evaluate(f,h,1,2); ASSERT_TRUE(r.status.IsOk()); EXPECT_TRUE(r.field_pass);
+}
+TEST(HhtFieldConvergence, LinearRequiresEveryActiveFieldAndAnActualIteration) {
+  auto f=Normal(); f[1]=f[0]; f[1].flux={{4,0}};
+  f[0].residual=2e-8; f[1].residual=4e-8; f[0].correction.reset(); f[1].correction.reset();
+  auto r=Evaluate(f,{},1,2); ASSERT_TRUE(r.status.IsOk()); EXPECT_TRUE(r.field_pass);
+  EXPECT_EQ(r.fields[0].branch,Branch::kLinear); EXPECT_EQ(r.fields[1].branch,Branch::kLinear);
+  f[1].residual=std::nextafter(4e-8,INFINITY);
+  r=Evaluate(f,{},1,2); ASSERT_TRUE(r.status.IsOk()); EXPECT_FALSE(r.field_pass);
+  EXPECT_EQ(r.fields[0].branch,Branch::kNormal);
+  f[1].residual=4e-8; r=Evaluate(f,{},0,2); ASSERT_TRUE(r.status.IsOk()); EXPECT_FALSE(r.field_pass);
+}
+TEST(HhtFieldConvergence, SmallTranslationExemptionIsStrictAndNeverRotational) {
+  auto f=Normal(); f[0].increment=std::nextafter(2e-8,0.); f[0].correction=1;
+  auto r=Evaluate(f,{},1,2); ASSERT_TRUE(r.status.IsOk()); EXPECT_TRUE(r.field_pass);
+  EXPECT_FALSE(r.fields[0].correction_pass.has_value());
+  f[0].increment=2e-8; r=Evaluate(f,{},1,2); ASSERT_TRUE(r.status.IsOk()); EXPECT_FALSE(r.field_pass);
+  f[1]=f[0]; f[0].active=false; f[1].increment=0; f[1].correction=0;
+  r=Evaluate(f,{},1,2); ASSERT_TRUE(r.status.IsOk()); EXPECT_TRUE(r.field_pass);
+  f[1].correction=std::numeric_limits<double>::denorm_min();
+  r=Evaluate(f,{},1,2); ASSERT_TRUE(r.status.IsOk()); EXPECT_FALSE(r.field_pass);
+}
+TEST(HhtFieldConvergence, InvalidAndOverflowNeverBecomeMissingOrPassing) {
+  const double inf=std::numeric_limits<double>::infinity();
+  const double nan=std::numeric_limits<double>::quiet_NaN();
+  const double max=std::numeric_limits<double>::max();
+  for(double x:{0.,-1.,inf,nan}) EXPECT_FALSE(Evaluate(Normal(),{},1,x).status.IsOk());
+  for(double x:{-1.,inf,nan}) {
+    auto f=Normal(); f[0].residual=x; EXPECT_FALSE(Evaluate(f,{},1,2).status.IsOk());
+    f=Normal(); f[0].correction=x; EXPECT_FALSE(Evaluate(f,{},1,2).status.IsOk());
+    f=Normal(); f[0].older_residual=x; EXPECT_FALSE(Evaluate(f,{},2,2).status.IsOk());
+    f=Normal(); f[0].flux={{x,0}};
+    if(x!=-1.) EXPECT_FALSE(Evaluate(f,{},1,2).status.IsOk());
+  }
+  auto f=Normal(); f[0].flux.clear(); EXPECT_FALSE(Evaluate(f,{},1,2).status.IsOk());
+  f=Normal(); f[0].flux={{max,max}}; EXPECT_FALSE(Evaluate(f,{},1,2).status.IsOk());
+  f=Normal(); f[0].flux={{max,0},{max,0}}; EXPECT_FALSE(Evaluate(f,{},1,2).status.IsOk());
+  f=Normal(); f[0].older_residual=std::numeric_limits<double>::denorm_min();
+  f[0].previous_residual=1; EXPECT_FALSE(Evaluate(f,{},2,2).status.IsOk());
+  Histories h{}; h[0]={max,1,max,1}; f=Normal(); f[0].flux={{max,0}}; EXPECT_FALSE(Evaluate(f,h,1,2).status.IsOk());
+  h={}; h[0].maximum_count=std::numeric_limits<std::uint64_t>::max();
+  EXPECT_FALSE(Evaluate(Normal(),h,1,2).status.IsOk());
+  h={}; h[0]={0,1,0,1}; f=Normal(); f[0].flux={{0,0}};
+  EXPECT_FALSE(Evaluate(f,h,1,2).status.IsOk());
+  f=Normal(); f[0].residual=1e200; f[0].correction=1e200;
+  f[0].older_residual=1; f[0].previous_residual=1;
+  const auto overflow=Evaluate(f,{},2,2);
+  EXPECT_FALSE(overflow.status.IsOk()); EXPECT_FALSE(overflow.field_pass);
+  f=Normal(); f[1]=f[0]; f[0].flux={{max,0}};
+  EXPECT_FALSE(Evaluate(f,{},1,2).status.IsOk());
+  Inputs inactive{}; auto r=Evaluate(inactive,{},0,2); ASSERT_TRUE(r.status.IsOk());
+  EXPECT_TRUE(r.field_pass); EXPECT_FALSE(r.fields[0].field_pass.has_value());
+}
+TEST(HhtFieldConvergence, DecisionThresholdsBelowEqualAboveWithoutTolerance) {
+  auto f=Normal();
+  for(double x:{std::nextafter(.01,0.),.01,std::nextafter(.01,INFINITY)}) {
+    f[0].correction=x; auto r=Evaluate(f,{},1,2); ASSERT_TRUE(r.status.IsOk());
+    EXPECT_EQ(r.field_pass,x<=.01);
+  }
+  for(double x:{std::nextafter(.01,0.),.01,std::nextafter(.01,INFINITY)}) {
+    f=Normal(); f[0].residual=x; auto r=Evaluate(f,{},1,2); ASSERT_TRUE(r.status.IsOk());
+    EXPECT_EQ(r.field_pass,x<=.01);
+  }
+  for(double x:{std::nextafter(2.,0.),2.,std::nextafter(2.,INFINITY)}) {
+    f=Normal(); f[0].flux={{100,0}}; f[0].residual=x;
+    f[0].previous_residual=4; f[0].older_residual=8;
+    auto r=Evaluate(f,{},10,2); ASSERT_TRUE(r.status.IsOk());
+    // For below 2 the detector selects normal; equality/above selects Rp.
+    EXPECT_EQ(r.field_pass,x==2.);
+  }
+}
+TEST(HhtFieldConvergence, MixedIncidenceRetainsEveryElementScalarOccurrence) {
+  auto f=Normal(); f[0].flux={{6,0},{-2,0},{-1,0},{9,0},{0,0}};
+  // Three occurrences can share one global DOF and one belong to another.
+  // Node averaging would produce 6, signed assembly would produce 3 and 9.
+  auto r=Evaluate(f,{},1,2); ASSERT_TRUE(r.status.IsOk());
+  EXPECT_DOUBLE_EQ(*r.fields[0].spatial_flux,3.6);
+  EXPECT_DOUBLE_EQ(*r.fields[0].maximum_flux,9);
+}
+
+TEST(HhtFieldConvergence, RemainingThresholdsHaveAdjacentRepresentableBoundaries) {
+  for (double x:{std::nextafter(.001,0.),.001,std::nextafter(.001,INFINITY)}) {
+    auto f=Normal(); Histories h{}; h[0]={2,1,2,1};
+    f[0].flux={{0,0}}; f[0].residual=.1; f[0].correction=x;
+    auto r=Evaluate(f,h,1,2); ASSERT_TRUE(r.status.IsOk());
+    EXPECT_EQ(r.field_pass,x<=.001);
+  }
+  for (double x:{std::nextafter(2e-5,0.),2e-5,std::nextafter(2e-5,INFINITY)}) {
+    auto f=Normal(); Histories h{}; h[0]={2,1,2,1};
+    f[0].flux={{0,0}}; f[0].residual=x; f[0].correction.reset();
+    auto r=Evaluate(f,h,0,2); ASSERT_TRUE(r.status.IsOk());
+    EXPECT_EQ(r.field_pass,x<=2e-5);
+  }
+  for (double x:{std::nextafter(2e-8,0.),2e-8,std::nextafter(2e-8,INFINITY)}) {
+    auto f=Normal(); f[0].increment=x; f[0].correction=1;
+    auto r=Evaluate(f,{},1,2); ASSERT_TRUE(r.status.IsOk());
+    EXPECT_EQ(r.field_pass,x<2e-8);
+    f=Normal(); f[0].residual=x; f[0].correction.reset();
+    r=Evaluate(f,{},1,2); ASSERT_TRUE(r.status.IsOk());
+    EXPECT_EQ(r.fields[0].branch,x<=2e-8?Branch::kLinear:Branch::kNormal);
+  }
+  for (double x:{std::nextafter(.001,0.),.001,std::nextafter(.001,INFINITY)}) {
+    auto f=Normal(); Histories h{}; h[0]={0,0,100,1};
+    f[0].flux={{0,0},{x,0},{10,0}};
+    auto r=Evaluate(f,h,1,2); ASSERT_TRUE(r.status.IsOk());
+    EXPECT_DOUBLE_EQ(*r.fields[0].spatial_flux,x<.001?10:(10+x)/2);
+  }
+  for (double x:{std::nextafter(2.,0.),2.,std::nextafter(2.,INFINITY)}) {
+    auto f=Normal(); f[0].flux={{100,0}}; f[0].residual=x;
+    f[0].previous_residual=4; f[0].older_residual=16;
+    auto r=Evaluate(f,{},10,2); ASSERT_TRUE(r.status.IsOk());
+    EXPECT_EQ(r.fields[0].branch,Branch::kNonquadratic);
+    EXPECT_EQ(r.field_pass,x<=2);
+  }
+}
+} // namespace
+} // namespace fesa::hht_field_convergence