a broken arm on shabbos afternon is NOT a sakana,”
It most CERTAINLY IS! None of us is qualified unless we are doctors, to determine if that broken bone might lead to sepsis, or further injury (certainly extreme pain), or any of a myriad of things. Even a SAFEK (doubt) of sakanas nefashos is docheh shabbos.
Why on earth would you or anyone else think that a broken bone is not a serious sakana, PARTICULARLY in a child or elderly person? We are not talking about a mildly-sprained ankle. But any part of the body that becomes swollen and black and blue due to severe injury, has the potential for gangrene and other types of infection. That’s not a loophole. The halacha IS to get to a doctor.