postgresql is not strictly serializable/externally consistent

for example this will commit under serializable:

    create table counters(counter int);

    insert into counters(counter) values(1);

    BEGIN TRANSACTION ISOLATION LEVEL serializable; 
    select sum(counter) from counters; 
    /* insert sum into counters. wait until committing next transaction before executing the insert */
    insert into counters(counter) values(1);
    COMMIT;

    /* this transaction should commit before doing the insert in the above transaction and after the above transaction has calculated the sum */
    BEGIN TRANSACTION ISOLATION LEVEL serializable; 
    insert into counters(counter) values(10);
    COMMIT;

both transactions commit and the final table looks like:

1, 10, 1

which is possible if the first transaction committed first, and then the second transaction committed. but it is possible for another client to see the table as: [1], [1, 10], [1, 1, 10] which is a sequence of states which should not be possible. if you see [1], [1, 10] then you should see [1, 10, 11] as the last state. hence it violates external consistency.