Implement private HHT field convergence policy and oracle tests

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_