feat: add eigen2 frequency pipeline and fail-closed validation

Implement MITC4 mass, constrained whitening, MKL FEAST, modal HDF5, and deterministic Value comparison. MSVC Debug builds; 394 of 395 tests pass. Original-model all-c residual and the documented S3 static contract conflict remain unresolved; this is an implementation checkpoint, not feature acceptance.

include/fesa/solvers/eigen/mkl_feast_eigen_solver.h

@@ -0,0 +1,83 @@
+#ifndef FESA_SOLVERS_EIGEN_MKL_FEAST_EIGEN_SOLVER_H_
+#define FESA_SOLVERS_EIGEN_MKL_FEAST_EIGEN_SOLVER_H_
+
+#include <cstddef>
+#include <cstdint>
+#include <string>
+#include <vector>
+
+#include "fesa/core/status.h"
+#include "fesa/math/matrix.h"
+
+namespace fesa {
+
+class SparseMatrix;
+
+/// @brief Records one deterministic private-backend invocation.
+struct FeastBackendCall {
+  std::size_t ordinal;
+  std::string kind;
+  std::string purpose;
+  double lower;
+  double upper;
+  std::size_t allocated_m0;
+  int info;
+  bool count_available;
+  std::size_t count;
+  bool loop_available;
+  int loop;
+  bool epsout_available;
+  double epsout;
+  std::string outcome;
+  std::string decision_reason;
+};
+
+/// @brief Owns the complete validated FEAST interval result before public N
+/// selection.
+struct FeastEigenResult {
+  std::size_t requested_modes;
+  std::vector<double> eigenvalues;
+  Matrix eigenvectors;
+  double operator_scale;
+  std::vector<std::size_t> column_ids;
+  std::vector<bool> backend_res_available;
+  std::vector<double> backend_res;
+  std::vector<double> normalized_eigenvalues;
+  std::vector<double> whitened_residuals;
+  double gram_error;
+  std::vector<FeastBackendCall> backend_calls;
+  std::vector<std::int64_t> base_fpm;
+  std::string runtime_version;
+  std::string integer_abi;
+  std::size_t thread_count;
+  std::uint64_t seed;
+  double enclosure_lower;
+  double enclosure_upper;
+  double solve_lower;
+  double solve_upper;
+  std::string upper_search_termination;
+};
+
+/// @brief Solves a whitened real-symmetric eigenproblem with oneMKL FEAST.
+class MklFeastEigenSolver final {
+ public:
+  /// @brief Computes all validated interval pairs for a requested lowest-mode
+  /// prefix.
+  /// @param whitened_operator Symmetric physical-lambda operator after
+  /// whitening.
+  /// @param requested_modes Number of lowest modes eventually exposed by the
+  /// caller.
+  /// @param zero_operator_scale Positive physical scale used only when A is
+  /// exactly zero.
+  /// @return Sorted all-c eigenpairs in physical lambda units or a solver
+  /// failure.
+  /// @note The implementation fixes oneMKL local thread count to one during
+  /// every call.
+  Result<FeastEigenResult> Solve(const SparseMatrix& whitened_operator,
+                                 std::size_t requested_modes,
+                                 double zero_operator_scale) const;
+};
+
+}  // namespace fesa
+
+#endif  // FESA_SOLVERS_EIGEN_MKL_FEAST_EIGEN_SOLVER_H_