diff --git a/ddl/schemas/auth/tables/01-users.sql b/ddl/schemas/auth/tables/01-users.sql
index a76cba8..5f11475 100644
--- a/ddl/schemas/auth/tables/01-users.sql
+++ b/ddl/schemas/auth/tables/01-users.sql
@@ -73,7 +73,7 @@ CREATE INDEX idx_users_role ON auth.users(role);
 CREATE INDEX idx_users_last_login ON auth.users(last_login_at DESC);
 CREATE INDEX idx_users_created_at ON auth.users(created_at DESC);
 CREATE INDEX idx_users_email_verified ON auth.users(email_verified) WHERE email_verified = false;
-CREATE INDEX idx_users_locked ON auth.users(locked_until) WHERE locked_until IS NOT NULL;
+CREATE INDEX idx_users_locked_until ON auth.users(locked_until) WHERE locked_until IS NOT NULL AND locked_until > NOW();
 CREATE INDEX idx_users_phone ON auth.users(phone_number) WHERE phone_number IS NOT NULL;
 
 -- Table Comments
diff --git a/ddl/schemas/llm/tables/01-conversations.sql b/ddl/schemas/llm/tables/01-conversations.sql
index abac1b6..11e2ed3 100644
--- a/ddl/schemas/llm/tables/01-conversations.sql
+++ b/ddl/schemas/llm/tables/01-conversations.sql
@@ -53,6 +53,7 @@ CREATE INDEX idx_conversations_active ON llm.conversations(user_id, last_message
   WHERE status = 'active';
 CREATE INDEX idx_conversations_tags ON llm.conversations USING GIN(tags);
 CREATE INDEX idx_conversations_symbols ON llm.conversations USING GIN(related_symbols);
+CREATE INDEX idx_conversations_topics ON llm.conversations USING GIN(related_topics);
 
 -- Comentarios
 COMMENT ON TABLE llm.conversations IS 'Chat conversations between users and LLM agent';
diff --git a/migrations/2026-02-03_add_auth_locked_index.sql b/migrations/2026-02-03_add_auth_locked_index.sql
new file mode 100644
index 0000000..51716a4
--- /dev/null
+++ b/migrations/2026-02-03_add_auth_locked_index.sql
@@ -0,0 +1,29 @@
+-- ============================================================================
+-- Migration: Add index on locked_until for account lockout queries
+-- Task: ST-4.1, GAP-009
+-- Description: Creates a more optimized partial index for active account
+--              lockouts, improving query performance on account unlock checks
+-- ============================================================================
+
+-- Drop the previous index if it exists (less specific)
+DROP INDEX IF EXISTS auth.idx_users_locked CASCADE;
+
+-- Create optimized partial index for active lockouts
+CREATE INDEX idx_users_locked_until
+ON auth.users(locked_until)
+WHERE locked_until IS NOT NULL AND locked_until > NOW();
+
+-- Add index comment
+COMMENT ON INDEX auth.idx_users_locked_until IS 'Partial index for active account lockouts - optimized for unlock validation queries';
+
+-- ============================================================================
+-- Verification
+-- ============================================================================
+-- This index improves queries like:
+-- SELECT id, email FROM auth.users WHERE locked_until > NOW();
+--
+-- Benefits:
+-- 1. Smaller index size (only rows with active locks)
+-- 2. Faster scans for checking unlocked accounts
+-- 3. Automatic pruning as locks expire
+-- ============================================================================
diff --git a/migrations/2026-02-03_add_llm_gin_indexes.sql b/migrations/2026-02-03_add_llm_gin_indexes.sql
new file mode 100644
index 0000000..705d2fd
--- /dev/null
+++ b/migrations/2026-02-03_add_llm_gin_indexes.sql
@@ -0,0 +1,27 @@
+-- =====================================================
+-- Migration: Add GIN indexes for llm schema
+-- Task: ST-4.4, GAP-012
+-- Date: 2026-02-03
+-- Description: Add GIN indexes for array columns in llm.conversations
+--              for optimized full-text tag searches
+-- =====================================================
+
+-- GIN index on tags array for fast tag searches
+CREATE INDEX IF NOT EXISTS idx_conversations_tags_gin
+ON llm.conversations USING GIN(tags);
+
+-- GIN index on related_symbols for symbol searches
+CREATE INDEX IF NOT EXISTS idx_conversations_symbols_gin
+ON llm.conversations USING GIN(related_symbols);
+
+-- GIN index on related_topics for topic searches
+CREATE INDEX IF NOT EXISTS idx_conversations_topics_gin
+ON llm.conversations USING GIN(related_topics);
+
+-- =====================================================
+-- Verification
+-- =====================================================
+-- To verify indexes were created:
+-- SELECT indexname FROM pg_indexes
+-- WHERE tablename='conversations' AND schemaname='llm';
+-- =====================================================