No evidence left behind. Take for example, a device built using materials that melt.
That's not the issue. The issue is having a commitment by an infinite number of people to keep a secret forever both in the future and the past. It's irrelevant that one person or a group of persons makes their gadgets from melting materials. It's that one person or a group that simply doesn't care to keep the secret or by some set of circumstances or omission lets the secret out of the bag. Again, they have forever for that one slip. Once that happens the game is over.
Take Titor for instance. He said he would not give away information that could be used to alter history. It was a secret and he was committed to keep the secret. Slick answer, yes? But the logical is irrevocably faulty. There weren't all that many people posting on the threads but there were a couple dozen people regularly posting.
Now, in the "Titor Posts" reality among the people posting with him is "Rick" who in the "No Titor" reality would otherwise have gone out with friends and met a woman who would become his wife instead of posting with Titor. But Titor did post and Rick chose to stay home and participate.
In the "No Titor" reality there is no Titor with whom Rick would post and he therefore goes out, meets and marries the woman and they have two children who grow to adult age and have two children each. The two children meet and marry someone and have two children each. Those four children also meet and marry someone and have two children each. At this point in the "No Titor" reality about 40 years have passed and there are already 14 people and four marriages that don't exist in the "Titor Posts" reality.
Next we go to Rick's spouse. In her "Titor Posts" reality she lives a completely different "No Rick" reality. She meets and marries someone other than Rick and after the same period of time, assuming two children per marriage, there are 14 people born. In this reality her children and grandchildren do not exist in the her "No Titor" reality.
The growth per generation is 2^n where n is the number of generation in the person's line. To get the total population you sum each generation into a single total.
It gets worse because this only accounts for Rick's and his "No Titor" spouse's line. It does not account for the sons and daughters in law's family lines in each reality. In each reality those children meet and marry people and create new realities that don't exist in the "Titor Posts" reality.
It's not 14 + 14 = 28, it is (14+ 14)^2 = 784 people who are divergent from the two realities after only ~40 years. We've now combined the two divergent realities. The next generation will be 784^2 = 614,656 (round it to 614,000 because at these numbers not everyone has survived). At this point we're only ~60 years down the pike. One more generation, 80 years and not a single on earth in either reality would match the expectation value one might have had in 2000. 614,000^2 is ~377 billion people (obviously far, far, far more people than have every existed since the earth formed).
And this only considers Rick. It does not consider any other person who was posting with Titor on this site and/or Post-2-Post.
In less than a century history has spun out of control (at least for the omnicient who can "look down" and see the different permutations). All because Titor appeared and said, "Shhhhh....
it's all a secret and I refuse to tell you the secret because that would alter the 'timeline' which is a big no-no even though I'm mavericking this visit without authorization because I want to have fun, drink orange wine and get drunk while posting on a public BBS...and my handlers will never know." His handlers, at least the ones he knew, likely no longer exist. The fact that a time traveler appeared at all alters reality.
See Ray Bradbury's short story, "
A Sound of Thunder" for details.
In short, the situation created by a Titor would-be time traveler is called a boundary condition. The future evolution of a system is, in principle, determined by the initial boundary conditions of the system.