diff --git a/veza-backend-api/cmd/api/main.go b/veza-backend-api/cmd/api/main.go
index 489998299..a142568ed 100644
--- a/veza-backend-api/cmd/api/main.go
+++ b/veza-backend-api/cmd/api/main.go
@@ -46,6 +46,11 @@ import (
 // @in header
 // @name Authorization
 
+// @securityDefinitions.apikey ApiKeyAuth
+// @in header
+// @name X-API-Key
+// @description Developer API key (obtain from Developer Portal). Format: vza_xxxxx
+
 func main() {
 	// Charger les variables d'environnement
 	// NOTE: Do not write to stderr to avoid broken pipe errors with systemd journald
diff --git a/veza-backend-api/internal/api/router.go b/veza-backend-api/internal/api/router.go
index 190e0de79..b95cae1fd 100644
--- a/veza-backend-api/internal/api/router.go
+++ b/veza-backend-api/internal/api/router.go
@@ -290,6 +290,18 @@ func (r *APIRouter) Setup(router *gin.Engine) error {
 
 	// Groupe API v1 (nouveau frontend React)
 	v1 := router.Group("/api/v1")
+
+	// v0.12.8: API key rate limiting — applied to all v1 routes
+	// Only affects requests authenticated via X-API-Key (JWT requests pass through)
+	apiKeyRateLimiter := middleware.NewAPIKeyRateLimiter(middleware.DefaultAPIKeyRateLimiterConfig())
+	v1.Use(apiKeyRateLimiter.Middleware())
+
+	// v0.12.8: API key scope enforcement — check read/write scopes on API key requests
+	if r.config != nil && r.config.AuthMiddleware != nil {
+		apiKeySvc := services.NewAPIKeyService(r.db.GormDB, r.logger)
+		v1.Use(middleware.RequireAPIKeyScope(apiKeySvc))
+	}
+
 	{
 		// Auth routes first so r.authService is set for admin unlock in setupCoreProtectedRoutes
 		if err := r.setupAuthRoutes(v1); err != nil {
diff --git a/veza-backend-api/internal/middleware/api_key_rate_limiter.go b/veza-backend-api/internal/middleware/api_key_rate_limiter.go
new file mode 100644
index 000000000..7d8971fd1
--- /dev/null
+++ b/veza-backend-api/internal/middleware/api_key_rate_limiter.go
@@ -0,0 +1,189 @@
+package middleware
+
+import (
+	"net/http"
+	"strconv"
+	"sync"
+	"time"
+
+	"veza-backend-api/internal/models"
+
+	"github.com/gin-gonic/gin"
+)
+
+// APIKeyRateLimiterConfig defines rate limits for API key authenticated requests.
+// Limits are per API key (not per IP) to give each developer their own quota.
+type APIKeyRateLimiterConfig struct {
+	// ReadLimit is the max number of read (GET) requests per window per key
+	ReadLimit int
+	// WriteLimit is the max number of write (POST/PUT/DELETE) requests per window per key
+	WriteLimit int
+	// Window is the sliding window duration
+	Window time.Duration
+}
+
+// DefaultAPIKeyRateLimiterConfig returns default limits: 1000 reads/hour, 200 writes/hour
+func DefaultAPIKeyRateLimiterConfig() *APIKeyRateLimiterConfig {
+	return &APIKeyRateLimiterConfig{
+		ReadLimit:  1000,
+		WriteLimit: 200,
+		Window:     time.Hour,
+	}
+}
+
+type apiKeyEntry struct {
+	timestamps []time.Time
+}
+
+// APIKeyRateLimiter rate-limits requests authenticated via API key.
+// It tracks read and write operations separately, keyed by API key ID.
+type APIKeyRateLimiter struct {
+	config      *APIKeyRateLimiterConfig
+	readStore   map[string]*apiKeyEntry
+	writeStore  map[string]*apiKeyEntry
+	mu          sync.Mutex
+	stop        chan struct{}
+}
+
+// NewAPIKeyRateLimiter creates a new API key rate limiter
+func NewAPIKeyRateLimiter(config *APIKeyRateLimiterConfig) *APIKeyRateLimiter {
+	if config == nil {
+		config = DefaultAPIKeyRateLimiterConfig()
+	}
+	rl := &APIKeyRateLimiter{
+		config:     config,
+		readStore:  make(map[string]*apiKeyEntry),
+		writeStore: make(map[string]*apiKeyEntry),
+		stop:       make(chan struct{}),
+	}
+	go rl.cleanup()
+	return rl
+}
+
+// Middleware returns a Gin middleware that enforces API key rate limits.
+// It only applies to requests authenticated via API key (context has "api_key" set).
+// JWT-authenticated requests pass through without additional limiting.
+func (rl *APIKeyRateLimiter) Middleware() gin.HandlerFunc {
+	return func(c *gin.Context) {
+		// Only rate-limit API key requests
+		apiKeyVal, exists := c.Get("api_key")
+		if !exists {
+			c.Next()
+			return
+		}
+
+		// Extract key ID for per-key tracking
+		key, ok := apiKeyVal.(*models.APIKey)
+		if !ok {
+			c.Next()
+			return
+		}
+		keyID := key.ID.String()
+
+		isWrite := c.Request.Method != http.MethodGet && c.Request.Method != http.MethodHead && c.Request.Method != http.MethodOptions
+
+		var limit int
+		var store map[string]*apiKeyEntry
+		if isWrite {
+			limit = rl.config.WriteLimit
+			store = rl.writeStore
+		} else {
+			limit = rl.config.ReadLimit
+			store = rl.readStore
+		}
+
+		rl.mu.Lock()
+		now := time.Now()
+		cutoff := now.Add(-rl.config.Window)
+
+		entry, ok := store[keyID]
+		if !ok {
+			entry = &apiKeyEntry{}
+			store[keyID] = entry
+		}
+
+		// Prune expired timestamps
+		valid := make([]time.Time, 0, len(entry.timestamps))
+		for _, t := range entry.timestamps {
+			if t.After(cutoff) {
+				valid = append(valid, t)
+			}
+		}
+
+		if len(valid) >= limit {
+			entry.timestamps = valid
+			rl.mu.Unlock()
+
+			resetTime := now.Add(rl.config.Window).Unix()
+			retryAfter := int(rl.config.Window.Seconds())
+
+			c.Header("X-RateLimit-Limit", strconv.Itoa(limit))
+			c.Header("X-RateLimit-Remaining", "0")
+			c.Header("X-RateLimit-Reset", strconv.FormatInt(resetTime, 10))
+			c.Header("Retry-After", strconv.Itoa(retryAfter))
+			c.JSON(http.StatusTooManyRequests, gin.H{
+				"success": false,
+				"error": gin.H{
+					"code":        "RATE_LIMIT_EXCEEDED",
+					"message":     "API key rate limit exceeded. Please try again later.",
+					"retry_after": retryAfter,
+					"limit":       limit,
+					"remaining":   0,
+					"reset":       resetTime,
+				},
+			})
+			c.Abort()
+			return
+		}
+
+		valid = append(valid, now)
+		entry.timestamps = valid
+		remaining := limit - len(valid)
+		rl.mu.Unlock()
+
+		c.Header("X-RateLimit-Limit", strconv.Itoa(limit))
+		c.Header("X-RateLimit-Remaining", strconv.Itoa(remaining))
+		c.Header("X-RateLimit-Reset", strconv.FormatInt(now.Add(rl.config.Window).Unix(), 10))
+
+		c.Next()
+	}
+}
+
+// Stop signals the cleanup goroutine to exit
+func (rl *APIKeyRateLimiter) Stop() {
+	close(rl.stop)
+}
+
+func (rl *APIKeyRateLimiter) cleanup() {
+	ticker := time.NewTicker(5 * time.Minute)
+	defer ticker.Stop()
+
+	for {
+		select {
+		case <-ticker.C:
+			rl.mu.Lock()
+			cutoff := time.Now().Add(-rl.config.Window)
+			pruneStore(rl.readStore, cutoff)
+			pruneStore(rl.writeStore, cutoff)
+			rl.mu.Unlock()
+		case <-rl.stop:
+			return
+		}
+	}
+}
+
+func pruneStore(store map[string]*apiKeyEntry, cutoff time.Time) {
+	for key, entry := range store {
+		valid := make([]time.Time, 0, len(entry.timestamps))
+		for _, t := range entry.timestamps {
+			if t.After(cutoff) {
+				valid = append(valid, t)
+			}
+		}
+		if len(valid) == 0 {
+			delete(store, key)
+		} else {
+			entry.timestamps = valid
+		}
+	}
+}
diff --git a/veza-backend-api/internal/middleware/api_key_rate_limiter_test.go b/veza-backend-api/internal/middleware/api_key_rate_limiter_test.go
new file mode 100644
index 000000000..a7897b3ba
--- /dev/null
+++ b/veza-backend-api/internal/middleware/api_key_rate_limiter_test.go
@@ -0,0 +1,216 @@
+package middleware
+
+import (
+	"net/http"
+	"net/http/httptest"
+	"testing"
+	"time"
+
+	"veza-backend-api/internal/models"
+
+	"github.com/gin-gonic/gin"
+	"github.com/google/uuid"
+)
+
+func init() {
+	gin.SetMode(gin.TestMode)
+}
+
+func TestAPIKeyRateLimiter_PassthroughWithoutAPIKey(t *testing.T) {
+	rl := NewAPIKeyRateLimiter(DefaultAPIKeyRateLimiterConfig())
+	defer rl.Stop()
+
+	router := gin.New()
+	router.Use(rl.Middleware())
+	router.GET("/test", func(c *gin.Context) {
+		c.JSON(http.StatusOK, gin.H{"ok": true})
+	})
+
+	// Request without api_key in context — should pass through
+	w := httptest.NewRecorder()
+	req, _ := http.NewRequest("GET", "/test", nil)
+	router.ServeHTTP(w, req)
+
+	if w.Code != http.StatusOK {
+		t.Errorf("expected 200, got %d", w.Code)
+	}
+}
+
+func TestAPIKeyRateLimiter_EnforcesReadLimit(t *testing.T) {
+	config := &APIKeyRateLimiterConfig{
+		ReadLimit:  3,
+		WriteLimit: 2,
+		Window:     time.Minute,
+	}
+	rl := NewAPIKeyRateLimiter(config)
+	defer rl.Stop()
+
+	keyID := uuid.New()
+	apiKey := &models.APIKey{ID: keyID, UserID: uuid.New(), Name: "test"}
+
+	router := gin.New()
+	// Simulate auth middleware setting api_key
+	router.Use(func(c *gin.Context) {
+		c.Set("api_key", apiKey)
+		c.Next()
+	})
+	router.Use(rl.Middleware())
+	router.GET("/test", func(c *gin.Context) {
+		c.JSON(http.StatusOK, gin.H{"ok": true})
+	})
+
+	// First 3 requests should pass
+	for i := 0; i < 3; i++ {
+		w := httptest.NewRecorder()
+		req, _ := http.NewRequest("GET", "/test", nil)
+		router.ServeHTTP(w, req)
+		if w.Code != http.StatusOK {
+			t.Errorf("request %d: expected 200, got %d", i+1, w.Code)
+		}
+	}
+
+	// 4th request should be rate limited
+	w := httptest.NewRecorder()
+	req, _ := http.NewRequest("GET", "/test", nil)
+	router.ServeHTTP(w, req)
+	if w.Code != http.StatusTooManyRequests {
+		t.Errorf("4th request: expected 429, got %d", w.Code)
+	}
+
+	// Check rate limit headers
+	if w.Header().Get("X-RateLimit-Limit") != "3" {
+		t.Errorf("expected X-RateLimit-Limit=3, got %s", w.Header().Get("X-RateLimit-Limit"))
+	}
+	if w.Header().Get("X-RateLimit-Remaining") != "0" {
+		t.Errorf("expected X-RateLimit-Remaining=0, got %s", w.Header().Get("X-RateLimit-Remaining"))
+	}
+}
+
+func TestAPIKeyRateLimiter_EnforcesWriteLimit(t *testing.T) {
+	config := &APIKeyRateLimiterConfig{
+		ReadLimit:  100,
+		WriteLimit: 2,
+		Window:     time.Minute,
+	}
+	rl := NewAPIKeyRateLimiter(config)
+	defer rl.Stop()
+
+	keyID := uuid.New()
+	apiKey := &models.APIKey{ID: keyID, UserID: uuid.New(), Name: "test"}
+
+	router := gin.New()
+	router.Use(func(c *gin.Context) {
+		c.Set("api_key", apiKey)
+		c.Next()
+	})
+	router.Use(rl.Middleware())
+	router.POST("/test", func(c *gin.Context) {
+		c.JSON(http.StatusOK, gin.H{"ok": true})
+	})
+
+	// First 2 POST requests should pass
+	for i := 0; i < 2; i++ {
+		w := httptest.NewRecorder()
+		req, _ := http.NewRequest("POST", "/test", nil)
+		router.ServeHTTP(w, req)
+		if w.Code != http.StatusOK {
+			t.Errorf("request %d: expected 200, got %d", i+1, w.Code)
+		}
+	}
+
+	// 3rd POST should be rate limited
+	w := httptest.NewRecorder()
+	req, _ := http.NewRequest("POST", "/test", nil)
+	router.ServeHTTP(w, req)
+	if w.Code != http.StatusTooManyRequests {
+		t.Errorf("3rd POST: expected 429, got %d", w.Code)
+	}
+}
+
+func TestAPIKeyRateLimiter_SeparateKeysHaveSeparateLimits(t *testing.T) {
+	config := &APIKeyRateLimiterConfig{
+		ReadLimit:  2,
+		WriteLimit: 2,
+		Window:     time.Minute,
+	}
+	rl := NewAPIKeyRateLimiter(config)
+	defer rl.Stop()
+
+	key1 := &models.APIKey{ID: uuid.New(), UserID: uuid.New(), Name: "key1"}
+	key2 := &models.APIKey{ID: uuid.New(), UserID: uuid.New(), Name: "key2"}
+
+	makeRouter := func(apiKey *models.APIKey) *gin.Engine {
+		r := gin.New()
+		r.Use(func(c *gin.Context) {
+			c.Set("api_key", apiKey)
+			c.Next()
+		})
+		r.Use(rl.Middleware())
+		r.GET("/test", func(c *gin.Context) {
+			c.JSON(http.StatusOK, gin.H{"ok": true})
+		})
+		return r
+	}
+
+	router1 := makeRouter(key1)
+	router2 := makeRouter(key2)
+
+	// Exhaust key1's limit
+	for i := 0; i < 2; i++ {
+		w := httptest.NewRecorder()
+		req, _ := http.NewRequest("GET", "/test", nil)
+		router1.ServeHTTP(w, req)
+	}
+
+	// key1 should be rate limited
+	w := httptest.NewRecorder()
+	req, _ := http.NewRequest("GET", "/test", nil)
+	router1.ServeHTTP(w, req)
+	if w.Code != http.StatusTooManyRequests {
+		t.Errorf("key1 3rd request: expected 429, got %d", w.Code)
+	}
+
+	// key2 should still work
+	w = httptest.NewRecorder()
+	req, _ = http.NewRequest("GET", "/test", nil)
+	router2.ServeHTTP(w, req)
+	if w.Code != http.StatusOK {
+		t.Errorf("key2 1st request: expected 200, got %d", w.Code)
+	}
+}
+
+func TestAPIKeyRateLimiter_ReturnsRateLimitHeaders(t *testing.T) {
+	config := &APIKeyRateLimiterConfig{
+		ReadLimit:  10,
+		WriteLimit: 5,
+		Window:     time.Hour,
+	}
+	rl := NewAPIKeyRateLimiter(config)
+	defer rl.Stop()
+
+	apiKey := &models.APIKey{ID: uuid.New(), UserID: uuid.New(), Name: "test"}
+
+	router := gin.New()
+	router.Use(func(c *gin.Context) {
+		c.Set("api_key", apiKey)
+		c.Next()
+	})
+	router.Use(rl.Middleware())
+	router.GET("/test", func(c *gin.Context) {
+		c.JSON(http.StatusOK, gin.H{"ok": true})
+	})
+
+	w := httptest.NewRecorder()
+	req, _ := http.NewRequest("GET", "/test", nil)
+	router.ServeHTTP(w, req)
+
+	if w.Header().Get("X-RateLimit-Limit") != "10" {
+		t.Errorf("expected X-RateLimit-Limit=10, got %s", w.Header().Get("X-RateLimit-Limit"))
+	}
+	if w.Header().Get("X-RateLimit-Remaining") != "9" {
+		t.Errorf("expected X-RateLimit-Remaining=9, got %s", w.Header().Get("X-RateLimit-Remaining"))
+	}
+	if w.Header().Get("X-RateLimit-Reset") == "" {
+		t.Error("expected X-RateLimit-Reset header to be set")
+	}
+}
diff --git a/veza-backend-api/internal/middleware/api_key_scope.go b/veza-backend-api/internal/middleware/api_key_scope.go
new file mode 100644
index 000000000..4901f75de
--- /dev/null
+++ b/veza-backend-api/internal/middleware/api_key_scope.go
@@ -0,0 +1,66 @@
+package middleware
+
+import (
+	"net/http"
+
+	"veza-backend-api/internal/models"
+	"veza-backend-api/internal/services"
+
+	"github.com/gin-gonic/gin"
+)
+
+// RequireAPIKeyScope returns a Gin middleware that enforces API key scopes.
+// For API key authenticated requests, it verifies the key has the required scope.
+// JWT-authenticated requests pass through (they already use RBAC).
+//
+// Scope mapping:
+//   - GET/HEAD/OPTIONS → "read"
+//   - POST/PUT/PATCH/DELETE → "write"
+//   - "admin" scope implies both "read" and "write"
+func RequireAPIKeyScope(apiKeyService *services.APIKeyService) gin.HandlerFunc {
+	return func(c *gin.Context) {
+		apiKeyVal, exists := c.Get("api_key")
+		if !exists {
+			// Not an API key request (JWT auth) — pass through
+			c.Next()
+			return
+		}
+
+		key, ok := apiKeyVal.(*models.APIKey)
+		if !ok {
+			c.JSON(http.StatusInternalServerError, gin.H{
+				"success": false,
+				"error": gin.H{
+					"code":    "INTERNAL_ERROR",
+					"message": "Invalid API key context",
+				},
+			})
+			c.Abort()
+			return
+		}
+
+		var requiredScope string
+		switch c.Request.Method {
+		case http.MethodGet, http.MethodHead, http.MethodOptions:
+			requiredScope = "read"
+		default:
+			requiredScope = "write"
+		}
+
+		if !apiKeyService.HasScope(key, requiredScope) {
+			c.JSON(http.StatusForbidden, gin.H{
+				"success": false,
+				"error": gin.H{
+					"code":    "INSUFFICIENT_SCOPE",
+					"message": "API key does not have the required scope: " + requiredScope,
+					"required_scope": requiredScope,
+					"key_scopes":     key.Scopes,
+				},
+			})
+			c.Abort()
+			return
+		}
+
+		c.Next()
+	}
+}
diff --git a/veza-backend-api/internal/middleware/api_key_scope_test.go b/veza-backend-api/internal/middleware/api_key_scope_test.go
new file mode 100644
index 000000000..b1ddcde91
--- /dev/null
+++ b/veza-backend-api/internal/middleware/api_key_scope_test.go
@@ -0,0 +1,149 @@
+package middleware
+
+import (
+	"net/http"
+	"net/http/httptest"
+	"testing"
+
+	"veza-backend-api/internal/models"
+	"veza-backend-api/internal/services"
+
+	"github.com/gin-gonic/gin"
+	"github.com/google/uuid"
+	"github.com/lib/pq"
+	"go.uber.org/zap"
+)
+
+func TestRequireAPIKeyScope_PassthroughWithoutAPIKey(t *testing.T) {
+	svc := services.NewAPIKeyService(nil, zap.NewNop())
+
+	router := gin.New()
+	router.Use(RequireAPIKeyScope(svc))
+	router.GET("/test", func(c *gin.Context) {
+		c.JSON(http.StatusOK, gin.H{"ok": true})
+	})
+
+	w := httptest.NewRecorder()
+	req, _ := http.NewRequest("GET", "/test", nil)
+	router.ServeHTTP(w, req)
+
+	if w.Code != http.StatusOK {
+		t.Errorf("expected 200, got %d", w.Code)
+	}
+}
+
+func TestRequireAPIKeyScope_AllowsReadScopeOnGET(t *testing.T) {
+	svc := services.NewAPIKeyService(nil, zap.NewNop())
+
+	apiKey := &models.APIKey{
+		ID:     uuid.New(),
+		UserID: uuid.New(),
+		Name:   "test",
+		Scopes: pq.StringArray{"read"},
+	}
+
+	router := gin.New()
+	router.Use(func(c *gin.Context) {
+		c.Set("api_key", apiKey)
+		c.Next()
+	})
+	router.Use(RequireAPIKeyScope(svc))
+	router.GET("/test", func(c *gin.Context) {
+		c.JSON(http.StatusOK, gin.H{"ok": true})
+	})
+
+	w := httptest.NewRecorder()
+	req, _ := http.NewRequest("GET", "/test", nil)
+	router.ServeHTTP(w, req)
+
+	if w.Code != http.StatusOK {
+		t.Errorf("expected 200, got %d", w.Code)
+	}
+}
+
+func TestRequireAPIKeyScope_DeniesWriteWithReadOnlyScope(t *testing.T) {
+	svc := services.NewAPIKeyService(nil, zap.NewNop())
+
+	apiKey := &models.APIKey{
+		ID:     uuid.New(),
+		UserID: uuid.New(),
+		Name:   "test",
+		Scopes: pq.StringArray{"read"},
+	}
+
+	router := gin.New()
+	router.Use(func(c *gin.Context) {
+		c.Set("api_key", apiKey)
+		c.Next()
+	})
+	router.Use(RequireAPIKeyScope(svc))
+	router.POST("/test", func(c *gin.Context) {
+		c.JSON(http.StatusOK, gin.H{"ok": true})
+	})
+
+	w := httptest.NewRecorder()
+	req, _ := http.NewRequest("POST", "/test", nil)
+	router.ServeHTTP(w, req)
+
+	if w.Code != http.StatusForbidden {
+		t.Errorf("expected 403, got %d", w.Code)
+	}
+}
+
+func TestRequireAPIKeyScope_AllowsWriteWithWriteScope(t *testing.T) {
+	svc := services.NewAPIKeyService(nil, zap.NewNop())
+
+	apiKey := &models.APIKey{
+		ID:     uuid.New(),
+		UserID: uuid.New(),
+		Name:   "test",
+		Scopes: pq.StringArray{"read", "write"},
+	}
+
+	router := gin.New()
+	router.Use(func(c *gin.Context) {
+		c.Set("api_key", apiKey)
+		c.Next()
+	})
+	router.Use(RequireAPIKeyScope(svc))
+	router.POST("/test", func(c *gin.Context) {
+		c.JSON(http.StatusOK, gin.H{"ok": true})
+	})
+
+	w := httptest.NewRecorder()
+	req, _ := http.NewRequest("POST", "/test", nil)
+	router.ServeHTTP(w, req)
+
+	if w.Code != http.StatusOK {
+		t.Errorf("expected 200, got %d", w.Code)
+	}
+}
+
+func TestRequireAPIKeyScope_AdminScopeAllowsAll(t *testing.T) {
+	svc := services.NewAPIKeyService(nil, zap.NewNop())
+
+	apiKey := &models.APIKey{
+		ID:     uuid.New(),
+		UserID: uuid.New(),
+		Name:   "test",
+		Scopes: pq.StringArray{"admin"},
+	}
+
+	router := gin.New()
+	router.Use(func(c *gin.Context) {
+		c.Set("api_key", apiKey)
+		c.Next()
+	})
+	router.Use(RequireAPIKeyScope(svc))
+	router.DELETE("/test", func(c *gin.Context) {
+		c.JSON(http.StatusOK, gin.H{"ok": true})
+	})
+
+	w := httptest.NewRecorder()
+	req, _ := http.NewRequest("DELETE", "/test", nil)
+	router.ServeHTTP(w, req)
+
+	if w.Code != http.StatusOK {
+		t.Errorf("expected 200, got %d (admin should have write access)", w.Code)
+	}
+}
diff --git a/veza-backend-api/openapi.yaml b/veza-backend-api/openapi.yaml
index 1bb999e8d..d402fef82 100644
--- a/veza-backend-api/openapi.yaml
+++ b/veza-backend-api/openapi.yaml
@@ -3429,7 +3429,13 @@ paths:
       - Webhook
 securityDefinitions:
   BearerAuth:
+    description: "JWT Bearer token. Format: Bearer {token}"
     in: header
     name: Authorization
     type: apiKey
+  ApiKeyAuth:
+    description: "Developer API key. Format: vza_xxxxx (obtain from Developer Portal)"
+    in: header
+    name: X-API-Key
+    type: apiKey
 swagger: "2.0"