Nice writeup and nitpicking is very much welcomed - it serves only to improve everyone's understanding, but you make false claims right off the bat during your nitpick, which achieves the opposite.
> To expand on the above: is differs from == only when the considered expression contains a null.
Not True which is clear from my examples, but to reiterate:
```
SELECT (5 = TRUE) AS ' == ', (5 IS TRUE) AS ' IS '
-- == | IS
-- -------|------------
-- 0 | 1
```
Nowhere in that statement did NULL appear and yet "IS" produced different results than "==" did.
Not disagreeing with the theory btw - big fan of Codd myself, but reality rarely conforms to ideals.