Fixes thinking signature validation errors

Addresses an issue where thinking signature validation fails due to model mapping and empty internal registry.

- Implements a fallback mechanism in the router to use the global model registry when the internal registry is empty. This ensures that models registered via API keys are correctly resolved even without local provider configurations.
- Modifies `GetModelGroup` to use registry-based grouping in addition to name pattern matching, covering cases where models are registered with API keys but lack provider names in their names.
- Updates signature validation to compare model groups instead of exact model names.

These changes resolve thinking signature validation errors and improve the accuracy of model resolution.

internal/routing/router_test.go

@@ -5,6 +5,7 @@ import (
 	"testing"
 
 	"github.com/router-for-me/CLIProxyAPI/v6/internal/config"
+	globalRegistry "github.com/router-for-me/CLIProxyAPI/v6/internal/registry"
 	"github.com/router-for-me/CLIProxyAPI/v6/sdk/cliproxy/executor"
 	"github.com/stretchr/testify/assert"
 )
@@ -113,3 +114,89 @@ func TestRouter_Resolve_NoProviders(t *testing.T) {
 	assert.Equal(t, "unknown-model", decision.ResolvedModel)
 	assert.Empty(t, decision.Candidates)
 }
+
+// === Global Registry Fallback Tests (T-027) ===
+// These tests verify that when the internal registry is empty,
+// the router falls back to the global model registry.
+// This is the core fix for the thinking signature 400 error.
+
+func TestRouter_GlobalRegistryFallback_LocalProvider(t *testing.T) {
+	// This test requires registering a model in the global registry.
+	// We use a model that's already registered via api-key config in production.
+	// For isolated testing, we can skip if global registry is not populated.
+	
+	globalReg := globalRegistry.GetGlobalRegistry()
+	modelCount := globalReg.GetModelCount("claude-sonnet-4-20250514")
+	
+	if modelCount == 0 {
+		t.Skip("Global registry not populated - run with server context")
+	}
+	
+	// Empty internal registry
+	emptyRegistry := NewRegistry()
+	cfg := &config.Config{}
+	router := NewRouter(emptyRegistry, cfg)
+	
+	req := RoutingRequest{
+		RequestedModel:      "claude-sonnet-4-20250514",
+		PreferLocalProvider: true,
+	}
+	decision := router.ResolveV2(req)
+	
+	// Should find provider from global registry
+	assert.Equal(t, RouteTypeLocalProvider, decision.RouteType)
+	assert.Equal(t, "claude-sonnet-4-20250514", decision.ResolvedModel)
+	assert.False(t, decision.ShouldProxy)
+}
+
+func TestRouter_GlobalRegistryFallback_ModelMapping(t *testing.T) {
+	// This test verifies that model mapping works with global registry fallback.
+	
+	globalReg := globalRegistry.GetGlobalRegistry()
+	modelCount := globalReg.GetModelCount("claude-opus-4-5-thinking")
+	
+	if modelCount == 0 {
+		t.Skip("Global registry not populated - run with server context")
+	}
+	
+	// Empty internal registry
+	emptyRegistry := NewRegistry()
+	cfg := &config.Config{
+		AmpCode: config.AmpCode{
+			ModelMappings: []config.AmpModelMapping{
+				{From: "claude-opus-4-5-20251101", To: "claude-opus-4-5-thinking"},
+			},
+		},
+	}
+	router := NewRouter(emptyRegistry, cfg)
+	
+	req := RoutingRequest{
+		RequestedModel:      "claude-opus-4-5-20251101",
+		PreferLocalProvider: true,
+	}
+	decision := router.ResolveV2(req)
+	
+	// Should find mapped model from global registry
+	assert.Equal(t, RouteTypeModelMapping, decision.RouteType)
+	assert.Equal(t, "claude-opus-4-5-thinking", decision.ResolvedModel)
+	assert.False(t, decision.ShouldProxy)
+}
+
+func TestRouter_GlobalRegistryFallback_AmpCreditsWhenNotFound(t *testing.T) {
+	// Empty internal registry
+	emptyRegistry := NewRegistry()
+	cfg := &config.Config{}
+	router := NewRouter(emptyRegistry, cfg)
+	
+	// Use a model that definitely doesn't exist anywhere
+	req := RoutingRequest{
+		RequestedModel:      "nonexistent-model-12345",
+		PreferLocalProvider: true,
+	}
+	decision := router.ResolveV2(req)
+	
+	// Should fall back to AMP credits proxy
+	assert.Equal(t, RouteTypeAmpCredits, decision.RouteType)
+	assert.Equal(t, "nonexistent-model-12345", decision.ResolvedModel)
+	assert.True(t, decision.ShouldProxy)
+}