diff --git a/include/fesa/core/diagnostic.hpp b/include/fesa/core/diagnostic.hpp
new file mode 100644
index 0000000..68909d3
--- /dev/null
+++ b/include/fesa/core/diagnostic.hpp
@@ -0,0 +1,31 @@
+#pragma once
+
+#include <optional>
+#include <string>
+
+#include <fesa/core/source_location.hpp>
+
+namespace fesa {
+
+enum class DiagnosticStage {
+    io,
+    syntax,
+    semantic,
+    model,
+    equation,
+    solver,
+    results,
+    validation
+};
+
+enum class Severity { warning, error };
+
+struct Diagnostic final {
+    DiagnosticStage stage;
+    Severity severity;
+    std::string code;
+    std::string message;
+    std::optional<SourceLocation> source;
+};
+
+}  // namespace fesa
diff --git a/include/fesa/core/entity_id.hpp b/include/fesa/core/entity_id.hpp
new file mode 100644
index 0000000..1328959
--- /dev/null
+++ b/include/fesa/core/entity_id.hpp
@@ -0,0 +1,28 @@
+#pragma once
+
+#include <compare>
+#include <cstdint>
+#include <stdexcept>
+
+namespace fesa {
+
+template <class Tag>
+class EntityId final {
+public:
+    explicit constexpr EntityId(const std::int64_t value) : value_{value} {
+        if (value < 0) {
+            throw std::invalid_argument{"EntityId value must not be negative."};
+        }
+    }
+
+    [[nodiscard]] constexpr std::int64_t value() const noexcept {
+        return value_;
+    }
+
+    auto operator<=>(const EntityId&) const = default;
+
+private:
+    std::int64_t value_;
+};
+
+}  // namespace fesa
diff --git a/include/fesa/core/source_location.hpp b/include/fesa/core/source_location.hpp
new file mode 100644
index 0000000..815469a
--- /dev/null
+++ b/include/fesa/core/source_location.hpp
@@ -0,0 +1,14 @@
+#pragma once
+
+#include <cstddef>
+#include <filesystem>
+
+namespace fesa {
+
+struct SourceLocation final {
+    std::filesystem::path file;
+    std::size_t line;
+    std::size_t column;
+};
+
+}  // namespace fesa
diff --git a/include/fesa/core/status.hpp b/include/fesa/core/status.hpp
new file mode 100644
index 0000000..0bdd52e
--- /dev/null
+++ b/include/fesa/core/status.hpp
@@ -0,0 +1,14 @@
+#pragma once
+
+#include <vector>
+
+#include <fesa/core/diagnostic.hpp>
+
+namespace fesa {
+
+struct Status final {
+    bool succeeded;
+    std::vector<Diagnostic> diagnostics;
+};
+
+}  // namespace fesa
diff --git a/include/fesa/core/vec3.hpp b/include/fesa/core/vec3.hpp
new file mode 100644
index 0000000..272f8dd
--- /dev/null
+++ b/include/fesa/core/vec3.hpp
@@ -0,0 +1,18 @@
+#pragma once
+
+#include <cmath>
+
+namespace fesa {
+
+struct Vec3 final {
+    double x;
+    double y;
+    double z;
+};
+
+[[nodiscard]] inline bool is_finite(const Vec3 value) noexcept {
+    return std::isfinite(value.x) && std::isfinite(value.y) &&
+           std::isfinite(value.z);
+}
+
+}  // namespace fesa
diff --git a/tests/CMakeLists.txt b/tests/CMakeLists.txt
index a2a5538..bb4f70d 100644
--- a/tests/CMakeLists.txt
+++ b/tests/CMakeLists.txt
@@ -36,3 +36,24 @@ set_property(
     PROPERTY ENVIRONMENT_MODIFICATION
         ${FESA_DEPENDENCY_RUNTIME_MODIFICATIONS}
 )
+
+add_executable(fesa_core_value_tests
+    unit/core/diagnostic_test.cpp
+    unit/core/entity_id_test.cpp
+    unit/core/status_test.cpp
+    unit/core/vec3_test.cpp
+)
+
+target_compile_features(fesa_core_value_tests PRIVATE cxx_std_20)
+target_compile_options(fesa_core_value_tests PRIVATE /W4 /permissive- /EHsc)
+
+target_link_libraries(fesa_core_value_tests
+    PRIVATE
+        fesa_core
+        GTest::gtest_main
+)
+
+add_test(
+    NAME CoreValueTypes
+    COMMAND "$<TARGET_FILE:fesa_core_value_tests>"
+)
diff --git a/tests/unit/core/diagnostic_test.cpp b/tests/unit/core/diagnostic_test.cpp
new file mode 100644
index 0000000..290fb3f
--- /dev/null
+++ b/tests/unit/core/diagnostic_test.cpp
@@ -0,0 +1,38 @@
+#include <filesystem>
+#include <optional>
+#include <string>
+
+#include <gtest/gtest.h>
+
+#include <fesa/core/diagnostic.hpp>
+
+namespace {
+
+TEST(Diagnostic, PreservesSourceLocation) {
+    const fesa::Diagnostic diagnostic{
+        fesa::DiagnosticStage::syntax,
+        fesa::Severity::error,
+        "ABAQUS_INVALID_NODE",
+        "Node data is incomplete.",
+        fesa::SourceLocation{
+            std::filesystem::path{"models/beam.inp"}, 42, 9}};
+
+    ASSERT_TRUE(diagnostic.source.has_value());
+    EXPECT_EQ(
+        diagnostic.source->file, std::filesystem::path{"models/beam.inp"});
+    EXPECT_EQ(diagnostic.source->line, 42U);
+    EXPECT_EQ(diagnostic.source->column, 9U);
+}
+
+TEST(Diagnostic, AllowsDiagnosticsWithoutSourceLocation) {
+    const fesa::Diagnostic diagnostic{
+        fesa::DiagnosticStage::solver,
+        fesa::Severity::warning,
+        "SOLVER_RESIDUAL",
+        "Residual is above the reporting threshold.",
+        std::nullopt};
+
+    EXPECT_FALSE(diagnostic.source.has_value());
+}
+
+}  // namespace
diff --git a/tests/unit/core/entity_id_test.cpp b/tests/unit/core/entity_id_test.cpp
new file mode 100644
index 0000000..9817a40
--- /dev/null
+++ b/tests/unit/core/entity_id_test.cpp
@@ -0,0 +1,36 @@
+#include <cstdint>
+#include <stdexcept>
+#include <type_traits>
+
+#include <gtest/gtest.h>
+
+#include <fesa/core/entity_id.hpp>
+
+namespace {
+
+struct NodeTag;
+struct ElementTag;
+
+using NodeId = fesa::EntityId<NodeTag>;
+using ElementId = fesa::EntityId<ElementTag>;
+
+static_assert(std::is_constructible_v<NodeId, std::int64_t>);
+static_assert(!std::is_convertible_v<std::int64_t, NodeId>);
+static_assert(!std::is_convertible_v<NodeId, ElementId>);
+
+TEST(EntityId, PreservesValueAndSupportsTypedOrdering) {
+    constexpr NodeId first{7};
+    constexpr NodeId second{11};
+
+    static_assert(first.value() == 7);
+    static_assert(first < second);
+
+    EXPECT_EQ(first.value(), 7);
+    EXPECT_LT(first, second);
+}
+
+TEST(EntityId, RejectsNegativeValues) {
+    EXPECT_THROW((NodeId{-1}), std::invalid_argument);
+}
+
+}  // namespace
diff --git a/tests/unit/core/status_test.cpp b/tests/unit/core/status_test.cpp
new file mode 100644
index 0000000..32a0ca4
--- /dev/null
+++ b/tests/unit/core/status_test.cpp
@@ -0,0 +1,35 @@
+#include <filesystem>
+#include <vector>
+
+#include <gtest/gtest.h>
+
+#include <fesa/core/status.hpp>
+
+namespace {
+
+TEST(CoreStatus, PreservesFailureDiagnostics) {
+    const fesa::Status status{
+        false,
+        {fesa::Diagnostic{
+            fesa::DiagnosticStage::model,
+            fesa::Severity::error,
+            "MODEL_NONFINITE_VECTOR",
+            "A vector component is not finite.",
+            fesa::SourceLocation{
+                std::filesystem::path{"models/invalid.inp"}, 8, 3}}}};
+
+    EXPECT_FALSE(status.succeeded);
+    ASSERT_EQ(status.diagnostics.size(), 1U);
+    EXPECT_EQ(status.diagnostics.front().code, "MODEL_NONFINITE_VECTOR");
+    ASSERT_TRUE(status.diagnostics.front().source.has_value());
+    EXPECT_EQ(status.diagnostics.front().source->line, 8U);
+}
+
+TEST(CoreStatus, RepresentsSuccessWithoutDiagnostics) {
+    const fesa::Status status{true, {}};
+
+    EXPECT_TRUE(status.succeeded);
+    EXPECT_TRUE(status.diagnostics.empty());
+}
+
+}  // namespace
diff --git a/tests/unit/core/vec3_test.cpp b/tests/unit/core/vec3_test.cpp
new file mode 100644
index 0000000..92e4420
--- /dev/null
+++ b/tests/unit/core/vec3_test.cpp
@@ -0,0 +1,20 @@
+#include <limits>
+
+#include <gtest/gtest.h>
+
+#include <fesa/core/vec3.hpp>
+
+namespace {
+
+TEST(CoreVec3, ReportsOnlyFiniteVectorsAsFinite) {
+    EXPECT_TRUE(fesa::is_finite(fesa::Vec3{1.0, -2.0, 0.0}));
+
+    const double infinity = std::numeric_limits<double>::infinity();
+    const double nan = std::numeric_limits<double>::quiet_NaN();
+
+    EXPECT_FALSE(fesa::is_finite(fesa::Vec3{infinity, 0.0, 0.0}));
+    EXPECT_FALSE(fesa::is_finite(fesa::Vec3{0.0, -infinity, 0.0}));
+    EXPECT_FALSE(fesa::is_finite(fesa::Vec3{0.0, 0.0, nan}));
+}
+
+}  // namespace