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/io/hdf5/eigen_hdf5_results_writer.h

@@ -0,0 +1,24 @@
+#ifndef FESA_IO_HDF5_EIGEN_HDF5_RESULTS_WRITER_H_
+#define FESA_IO_HDF5_EIGEN_HDF5_RESULTS_WRITER_H_
+
+#include <filesystem>
+#include <vector>
+
+#include "fesa/results/eigen_results_writer.h"
+
+namespace fesa {
+
+/// @brief Atomically writes validated linear-frequency HDF5 results.
+class EigenHdf5ResultsWriter final : public EigenResultsWriter {
+ public:
+  /// @brief Serializes an accepted modal state after closed-file self-check.
+  /// @return An output failure when the candidate cannot be validated or
+  /// finalized; an existing final file is then preserved.
+  Status Write(const std::filesystem::path& output_path, const Domain& domain,
+               const EigenAnalysisState& state,
+               const std::vector<Diagnostic>& diagnostics) override;
+};
+
+}  // namespace fesa
+
+#endif  // FESA_IO_HDF5_EIGEN_HDF5_RESULTS_WRITER_H_