Pre-print service like arXiv but with private option, so I can correct my mistakes without publicly advertising my mistakes? As a student, I make mistakes all the time, and stealing my idea will not face heavy retaliation. I don't mind if someone comes up with concurrent works, but I do mind if my key idea is leaked. Many graduate students in my field therefore only use pre-print services if their papers are either publicly presented or conditionally accepted.
I am looking for a website that can do most of what ArXiv does, with an additional private option or limited visibility, for example an option to make the paper unindexed by search engines. This way, my paper cannot be seen for at least a few months. By doing so, I can at least claim that I am one of the first few researchers who got the idea right. And most importantly, I can privately correct my mistakes, if any. Publishing mistakes is embarrassing and sometimes harms one's career. Many mistakes will be revealed during the peer-review processes and I have a chance to correct them before publicizing.
Please kindly think twice before giving ethically and &quot;politically correct&quot; comments like no one will scoop me, everyone will cite me, and the scoopers will be punished. At least in my field, scooping and idea-stealing is commonly observable, and big-names don't care about publicizing pre-prints because they have resources to punish the scoopers. I do understand that keeping my work private might harm the community as the information becomes less transparent. However, it could also be possible that my un-reviewed flawed works misguide the community, and a paper reviewed will benefit the society more.
I personally wasted six months because of someone else's mistake in a published work.

I heard that in molecular biology there is a widely-used service to upload your research data, like protein structure and sequencing, to get a timestamp. The uploaded materials can be set to be private for a period, and fully disclosed later. A lot of people do use this function. This is not exactly what I am looking for but shares some similar ideas.
If I remember correctly, there is an interesting paper studying the scooping patterns with the aid of this database.

Solutions found! Zenodo and some other university-run pre-print services do have an embargo function.
Moreover, SSRN is a widely used repository, that, unlike arxiv, only displays the newest version to the general public, although still keeps a tag on the first submitted date!
Basically, if I understand you correctly, you want proof of priority without publishing.
Well, this problem is well known from middle-ages and renaissance where people wanted to be able to prove they have the earliest solution without revealing what it is (so that if someone finds it, they can prove they were there first).
They often used anagrams, today you probably would use some private/public key combination for this (I am not a crypto expert, you would have to read up on this).
However, to be honest, this will look weird. The current position in science is: if you have done it, publish it and expose it to criticism, and you may gain priority. If you wish to monetize it, you can create a patent that is public, but protects your rights (in theory), or keep it a trade secret and make money out of it.
As for a website that supports timestamps for unrevealed papers, I am not aware of any, but of course if there were, you need to make sure you trust the maintainers. Furthermore, if you had one and if somebody publishes a completed paper somewhere else before your paper goes live, this will not help you. The fact that you had worked provably, say, for multiple years on the topic will at best prevent plagiarism charges when you end up publishing. But this, if it occurs, could be proven otherwise, e.g. lab diary, emails, etc. It will not make you the &quot;first to publish&quot;. Don't forget, there are quite a few cases where people who had publications were superseded by later, but more visible publications. So, even open publications may be vulnerable to &quot;post-scooping&quot;.
So, your question needs to be what one would need such a service for? I therefore doubt that people would set up such a system with obviously limited utility. Of course, this is not a statement that there isn't.
I understand that this does not precisely answer your question, but I hope I was able to put things in context and why your question may not have a satisfactory answer.