>>>> I find it utterly hard to believe that any full-time professional, even in America, is employed without having any piece of paper signed by their employer -- and they a copy signed by him -- that states basically "John Doe and Corporation X agree that John shall work full-time for X, and receive a salary of $Y per month".

I never signed such a thing. Roughly a quarter century ago, I received a job offer letter with a salary level. I verbally accepted the offer. But my salary is much different today, and there's nothing with my signature on it to that effect. It's very loose and informal. The payroll software knows. This is at a huge and well managed company.

I have no doubt that the company's ability to cut my pay is constrained by regulations, like they probably have to inform me in advance. One of my employers once announced a furlough and temporary pay cut when there was a financial disaster. Nothing was signed.

About counting hours, this is a US thing. We have two classes of employees, depending on whether they are entitled to overtime pay or not. Most professionals are not. There are criteria for classifying employees, and one of them is whether they are required to work a specific number of hours.

Sure a company can say something if I show up 3 hours a month: "You're fired." Or they can cite a specific shortcoming in my performance. What I think is a sub-plot of this thread is that measuring this performance and tying it to a relative workload is not always straightforward.

Note that I'm not a lawyer, this is not legal advice. A lot of it sounds strange because it is strange.