So how do we establish that LENR has been replicated? We are surrounded by hyperskeptics, whom I have no real interest in appeasing because their standard, if it were applied to any other branch of science, would send us back to some kind of stone age.
I recommend you ignore the hyperskeptics. I engage with them here only to keep in practices, as an exercise in rhetorical target practice.
I recommend you concentrate instead on trying to persuade open minded people who are sincerely interested in the subject. There are apparently a large number of such people. Although the numbers seem to be dropping off. See:
http://lenr-canr.org/wordpress/?page_id=1213
Aiming for an ordinary skeptic, it seems reasonable to me to accept the first hundred or so replications by the "who's who of electrochemistry" as accepted, those >150 peer reviewd replications collected by Britz, > 180 labs, and the 14,700 replication
People do not like to be told they have to read many papers to evaluate cold fusion. So I usually suggest they read McKubre, starting with his review, then one of his publications:
http://lenr-canr.org/acrobat/McKubreMCHcoldfusionb.pdf
http://lenr-canr.org/acrobat/McKubreMCHisothermala.pdf
These are well-written, and they are understandable. They are easier to understand than, say, Fleischmann. Fleischmann presents stronger evidence of more dramatic effects at higher power, but his methods are harder to understand.
As I often say, McKubre presents the best evidence. If this does not convince you, the other papers probably will not convince you either, so you might as well drop the subject. I am not hiding any better evidence. I am not holding back more convincing papers.
This is ordinary scientific research, published in peer-reviewed mainstream journals. If it were any subject other than cold fusion, no scientist on earth would question the validity of it. In my opinion, all opposition to cold fusion is either political or emotional. There are no legitimate scientific grounds to doubt it. (I dismiss Shanahan as a crackpot for reasons I need not reiterate, except that for some reason he wants me to mention him every time I make this assertion, so I do this here as a courtesy.)
Since there is no rational, scientific reason to reject cold fusion, we cannot hope that an appeal to rationality, science, evidence, replications, thermodynamics, or any other conventional evidence will convince the opposition. With regard to this subject, they are not playing by the rules, although they may when it comes to other subjects. So, I suggest we ignore them. Concentrate on convincing people who do play by the rules, and who do understand science. Based on the number and variety of readers at LENR-CANR.org, I believe there is "goodwill, and latent support" for the field, as I describe here, on pages 5 - 7:
http://lenr-canr.org/acrobat/RothwellJthefuturem.pdf
There is another good reason to start off by recommending the McKubre review, as I do on the front page at LENR-CANR and in the blurb for my video. It separates the sheep from the goats. It takes no great effort to read this paper. Anyone with a scientific education can understand it. You may not agree with it, but it is easy to understand. When you suggest this, a person who is sincerely interested will say "thanks" and read the paper. Whereas the hyperskeptics and trolls will not read it. The Real Roger Barker will dismiss it. Mary Yugo will kvetch and moan that it is too ha-a-a-a-ard so it must be wrong. These people are either uninterested or incapable of understanding cold fusion, so you need not waste time on them. When they ask the same stupid questions again and again, and they keep demanding you "give them proof," feel free to say, "read McKubre" and leave it at that. (In other words, blow them off by saying Read The F**** Manual.)