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Given a particular idea, is there any scientific word, or an elegant way to describe in once sentence, that I am pretty sure there is no method not based on this particular idea? For example, when writing a scientific paper, I am pretty sure I read every paper on the topic, and there is no mention of any other idea for a method, how would I then write:

All methods to date are probably based on idea xyz.

or

To the best of knowledge, all methods to date are based on idea xyz.

I find above sentences to sound like I didn't have the motivation to search long enough or just didn't care.

  • "Our search revealed no ..." – A E Nov 22 '14 at 9:14
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Two often used expressions are

We are not aware of any method...

All existing methods seem to be based

which leave room for error on your side but convey the message.

The expression

To (the best of) our knowledge

mentioned in other answers is also fine.

  • I like "We are not aware of any method...". Thanks! – wondering Nov 27 '14 at 11:35
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To the best of our knowledge...

I think this one is "scientific" enough. It has been used by my advisor (whose language choice I trust) and it hints that you did your best to study the subject.

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Not a single word, but it supports your confidence in your claim:

My exhaustive search suggests that every method to date is based on idea xyz.

And perhaps add a footnote explaining the scope of "exhaustive."

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I'm afraid I'm not particularly good at English, but this is what I was taught about writing an introductory part of a scientific paper.

I am pretty sure there is no method not based on this particular idea

Since you can never prove the uniqueness of your idea XYZ (there might have been a group of scientists in USSR who already published the same idea to Russian journals in '60s,) you can only go as far as:

Although major effort has been put into PQR[1-3] and STU[4-7], they are all based on XYZ[8-9] and share the common drawback of JKL[10, 11]. To overcome the JKL problem, here we propose a novel approach FastABC ...

After all, the uniqueness of your idea alone isn't enough for a good scientific research...

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