diff --git a/internal/builder/mirror.go b/internal/builder/mirror.go
index 83307fe..f5d5fb7 100644
--- a/internal/builder/mirror.go
+++ b/internal/builder/mirror.go
@@ -186,7 +186,7 @@ func (r Registry) MirrorImage(ctx context.Context, from, repository string) (str
 	// on the first merge that rebuilt a whole catalogue (2026-09-28), and every module whose base
 	// lives there failed on a copy it did not need.
 	if strings.HasPrefix(where.reference, "sha256:") {
-		held, err := r.has(ctx, "http://"+r.Address+"/v2/"+repository+"/manifests/"+where.reference)
+		held, err := r.has(ctx, "http://"+r.Address+"/v2/"+repository+"/manifests/"+where.reference, manifestAccept)
 		if err != nil {
 			return "", fmt.Errorf("asking %s whether it holds %s: %w", r.Address, from, err)
 		}
diff --git a/internal/builder/mirror_test.go b/internal/builder/mirror_test.go
index 7f8adbd..9a17b18 100644
--- a/internal/builder/mirror_test.go
+++ b/internal/builder/mirror_test.go
@@ -104,6 +104,14 @@ func (m *theMeshsRegistry) handler() http.Handler {
 		defer m.mu.Unlock()
 		switch {
 		case r.Method == http.MethodHead && strings.Contains(r.URL.Path, "/manifests/"):
+			// **As strictly as a real registry.** A manifest is answered only in a media type the
+			// caller named; a request with no Accept is answered as if nothing were there. The fake
+			// used to answer regardless, which is why it could not catch a check that asked without
+			// one — and the mesh copied every base again (2026-09-28).
+			if !strings.Contains(r.Header.Get("Accept"), "manifest") && !strings.Contains(r.Header.Get("Accept"), "index") {
+				w.WriteHeader(http.StatusNotFound)
+				return
+			}
 			if _, ok := m.manifests[r.URL.Path[strings.LastIndex(r.URL.Path, "/")+1:]]; ok {
 				w.WriteHeader(http.StatusOK)
 			} else {
diff --git a/internal/builder/registry.go b/internal/builder/registry.go
index 481ce53..fd277d0 100644
--- a/internal/builder/registry.go
+++ b/internal/builder/registry.go
@@ -122,11 +122,23 @@ func (r Registry) PublishArchive(ctx context.Context, repository string, body []
 	return final, nil
 }
 
-func (r Registry) has(ctx context.Context, url string) (bool, error) {
+// has is whether this registry already holds what is at that URL.
+//
+// **A manifest HEAD must say what it accepts.** A registry answers a manifest request only in a media
+// type the caller named, and a bare HEAD — no Accept at all — is answered 404 for a manifest it holds
+// perfectly well. Measured against the mesh's own registry (2026-09-28): the same digest answered 200
+// with the manifest media types and 404 without them, so a check written without them concluded the
+// registry held nothing, copied every base again, and exhausted the public hub's pull limit. A blob
+// needs no Accept, which is why this went unnoticed: the same helper was right for blobs and wrong
+// for manifests.
+func (r Registry) has(ctx context.Context, url string, accept ...string) (bool, error) {
 	request, err := http.NewRequestWithContext(ctx, http.MethodHead, url, nil)
 	if err != nil {
 		return false, err
 	}
+	for _, media := range accept {
+		request.Header.Set("Accept", media)
+	}
 	response, err := r.client().Do(request)
 	if err != nil {
 		return false, fmt.Errorf("cannot reach the registry at %s: %w", r.Address, err)