The Torah, and the Torah only, defines what it means to keep or break the Sabbath. Here's what it teaches.
Sabbath must be observed from sunset on Friday to sunset on Saturday - “from evening to evening shall you keep your Sabbath” (Leviticus 23:32)
No work can be done on the Sabbath. It is wholly a day of rest - “Six days shall work be done, but the seventh day is a Sabbath of solemn rest, holy to the LORD.” (Exodus 31:15)
If you turn your furnace on during the winter on the Sabbath, you're a Sabbath breaker - “You shall kindle no fire in all your dwelling places on the Sabbath day.” (Exodus 35:3)
If you bake or boil food on the Sabbath, you're a Sabbath breaker - “On the sixth day they gathered twice as much bread, two omers each. And when all the leaders of the congregation came and told Moses, he said to them, “This is what the LORD has commanded: ‘Tomorrow is a day of solemn rest, a holy Sabbath to the LORD; bake what you will bake and boil what you will boil, and all that is left over lay aside to be kept till the morning.” (Exodus 16:22–23)
If you travel far from your home, you're a Sabbath breaker - “Remain each of you in his place; let no one go out of his place on the seventh day.” (Exodus 16:29)
You don't keep the Sabbath unless you enforce the Sabbath with the death penalty - “Whoever does any work on the Sabbath day shall be put to death.” (Exodus 31:15)
“While the people of Israel were in the wilderness, they found a man gathering sticks on the Sabbath day. And those who found him gathering sticks brought him to Moses and Aaron and to all the congregation. They put him in custody, because it had not been made clear what should be done to him. And the LORD said to Moses, “The man shall be put to death; all the congregation shall stone him with stones outside the camp.” (Numbers 15:32–35)
You don't keep the Sabbath unless your priest sacrifices two lambs every Sabbath - “On the Sabbath day, two male lambs a year old without blemish, and two tenths of an ephah of fine flour for a grain offering, mixed with oil, and its drink offering: this is the burnt offering of every Sabbath, besides the regular burnt offering and its drink offering.” (Numbers 28:9–10)
Based on how the Torah defines what it means to keep the Sabbath, who can say that they're a Sabbath Keeper?