Is EntityManager obtained via @PersistenceContext in CDI in Java EE application server thread-safe?

Question

• I know that EntityManager instantiated by myself is not thread-safe.
• I know that EntityManager injected via @PersistenceContext in EJB behaves like hread-safe, because EJB container serializes access to EJB beans.
• I know that in EJB injected EntityManager is really a proxy.
• I know that when I inject EntityManager via @PersistenceContext to @Dependent CDI bean and inject that bean to EJB, it behaves like thread-safe because of covering EJB (I believe that in this case EntityManager is proxy too).

But:

• What happens when I inject EntityManager via @PersistenceContext to CDI bean and use this bean directly for example in Servlet? I believe that this EntityManager is a proxy, so does this proxy guarantee thread safety?

Edit: Similar question Java CDI @PersistenceContext and thread safety does't solve my problem, because accepted answer shows EJB examples, not CDI examples.

Edit: I checked source code of WildFly application server and it looks that WildFly uses thread-safe proxy in CDI. This proxy selects real EntityManager when needed. Real EntityManagers are kept in special structure - stack of maps of EntityManagers in ThreadLocal.

Answer 1

https://www.javacodegeeks.com/2013/06/jpa-2-entitymanagers-transactions-and-everything-around-it.html says:

The biggest benefit of using Transaction Scoped Entity Manager is that it is stateless. This also makes the Transaction Scoped EntityManager threadsafe and thus virtually maintenance free

also pro JPA book says:

a transaction-scoped entity manager is stateless, meaning that it can be safely stored on any Java EE component