Does the field have a cornerstone forum where amateurs mingle with pros? For example, there are several professional astronomers and astronauts on Reddit, and telescope builders on CloudyNights.com. Atmospheric optics has atoptics.org.uk. The chess community has lichess.org. Places like that could be a good place to post about your idea without going into the technical specifics. Hopefully, other members of the community would let you know if you're going down a promising path, and refer you to a specific pro/academic to further discuss your idea.
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You could ask if some researcher active in the field would be willing to co-author. This would come with the additional benefit of possibly improving the paper's quality, besides just publishing it.
You could try finding a conference related to the topic of your findings and, from there, look for associated workshops or similar that might fit the topic and submit your paper there. These can have lower barriers of entry and better chances of getting accepted than the actual conferences and might be more open to "outsiders", although I don't know about that for sure. This way you might be able to get something published as part of the conference proceedings.
Or, try finding someone who's recognized as a member of the scientific community and who'd be willing to co-author the paper and go from there. No idea how to go about that though.
Why arxiv?
If you want to engage your ideas with academics why not just contact some directly?
arXiv is the standard for researcheres in my field to publish their works as an open collective. I'd like to formally offer it to the scientific community to both prove myself as a proper member of the field even if I never had formal education and maybe get a bit of clout added to a resume portfolio if its real and game-changing.
I know how academics are though so im keeping expectations in check, have to have some healthy skepticism to keep myself in check about this in case its not or only passingly noteworthy.
I have my own website where I do in-depth technical writing and im a community leader in some social media places so worst case scenario ill just add a section to my website and post on the social media places about it. If I make use of the findings to enhance my own systems then Ive proven to myself and the community who adopts them that it works as a functional useful system which is arguably more important and which may snowball.
You could put it up on ResearchGate first to get eyes across it and potentially get an endorsement. Then reach out to the endorser to get sponsored for arXiv.
The other option is to submit it for peer review. You’d need to to look up the best pathway based on your field.
Make it easy to understand and repeatable. If you do not have the education credentials, it may take a little more finesse. Finding a conference is a great idea. Make some personal contacts with someone putting on a workshop. Depending on the field, they may be in need of papers. I am happy to help with any questions on the overall process or formatting. I have a published paper, so I have an idea of some of the struggles. My wife has put on many workshops in the AI field and is often complaining of how hard it is to find quality content to have presented.
But still,it is uncommon for research papers to be published with a single author. It is common practice to reach out to peers to have your discoveries peerreviewed. They might be able to help you elevate your discovery to a higher level and more maturity. They might also be a doorway to help you publish.
It's not the norm to publish alone, but it's not really uncommon either. Peer review is conducted when you publish, regardless of how many authors are listed on the article. The reviewers are typically selected by the journal, and are anonymous to the person submitting the paper.