The mechanism of the Enneagram is nine core fears and the strategies that compensate for them: every type is a whole way of operating grown to avoid one thing. A One is avoiding 'I am bad, I am wrong', and the compensating strategy is to get everything right first — hence the inner critic, checking around the clock.
Ones belong to the body centre (Eight, Nine, One), whose shared undertone is anger; a One's way of handling it is to press it down and convert it into 'should'. You rarely blow up, but you have principles, and principles are anger made polite.
Where you'll recognise it: a typo bothers you, other people's sloppiness tires you more than it tires them, and 'good enough' is very hard to say. Running well, a One is the person with the highest quality: reliable, upright, doing things properly and completely. Stuck, the inner critic takes over — harsh on yourself, disappointed in others, rigid. Under stress the line runs to Four (sinking into emotion and self-doubt); in growth it runs to Seven (finally allowing yourself some ease). For a One, loosening isn't decline — it's the cure.