It's science. We have no idea what the truth is, and an inherent part of seeking it is that we'll propose ideas that are incomplete or wrong.

Oh come on. The author of the Git Re-Basin paper is a scientist acting in good faith based on the results they believe they have observed. Chill out and let the scientific process play out. Nobody here is acting out of malevolence, except maybe you for stirring the pot and putting that author through unnecessary pain. I've been there as a junior scientist getting beaten up on OpenReview. That was bad enough without a live audience on Reddit commenting on it.

(I'm a professor at a major CS program.) Applying to a PhD program is applying to a job. You have to:

1. Describe what job you're applying to (i.e., what you want to work on). I have to think this is a worthwhile and relevant enough job to be interested in potentially admitting you.
2. Make the case that you (and especially/uniquely you compared to the broader pool) are qualified to perform that job. (Your background, your research experience, your letters.) I have to think you're (especially/uniquely) qualified to admit you.

In fact, it's applying to more than a job. When I hire researchers at my company, I definitely don't expect them to stay for 5+ years, and I know that I can tell them to leave in the rare/unfortunate circumstance that it's not a good fit. For a PhD applicant, I'm making the commitment to hire you and keep you employed for five years no matter what. That's a really high bar, and it should be if I want both of us to be successful.

And, strangely, despite this significant commitment, the PhD admissions process is often lower-touch than a job interview. I get to see a personal statement and some letters of reference, and I might get to interview you, but certainly not at the level of rigor of an industry job.

Bottom line: from my point of view as a faculty member, PhD admissions is a job application, except the stakes are even higher because the commitment is bigger. If you have a mediocre GPA and a tiny bit of irrelevant research experience, I can see why that doesn't cut it.

So what do you do?

1. You need to have a clear sense of the job you want to apply to. That means reading papers, watching talks, attending conferences where possible, and developing specific research interest and specific opinions on what we should be doing scientifically that we're not doing. This is all stuff that you can hypothetically do on your own, but it goes much better with a community. Coming to lab meetings for a local university lab is great. Attending talks from the ML Collective is also great. There are organizations like the ML Collective that you can get involved in so that you have a research community no matter where you are or where you work. The result of this effort won't be lines on a CV: it'll be a really compelling statement of purpose that lays out the important work you think needs to be done and that you want to accomplish. This isn't a contract that you'll work on that one thing, but it's a way to convince me of the existence of a path through your PhD that can lead to success.
2. You need to be qualified to do that job. This is the harder part - what you understandably appear to be struggling with. The most direct way to get this experience would be to do a full-time master's, especially at a place that offers funded master's degrees (Princeton, Cornell, CMU, and MILA come to mind as places with many or all funded master's degree students, but there are probably many others). You don't need a publication, and you definitely don't need five. (Publications can actually be unhelpful if you're nth author on something unrelated to what you want to work on or if you have so many publications that it's unclear what your focus is.) The important part is having meaningful research maturity and the technical expertise necessary to get started on the job you've described (and letters from reputable people - who have worked with enough students to have a basis for comparison - to back that up). All of the students I admitted last year were in master's programs but didn't have first-author publications. But their experiences in their master's programs (and the letters backing that up) convinced me they were mature researchers with big ideas and the technical skills to pursue them. This will be reflected in your CV, your letters, and your statement of purpose. Short of doing a full-time master's, research experiences through work or part-time with a lab can also work. And, at the end of the day, you may need to consider changing jobs to something that will allow you to accumulate the experiences you need.

Finally, you should ask yourself whether a PhD is what you want/need. There are plenty of ways to get a PhD's worth of experience in industry research roles without needing to make the sacrifices attendant to a PhD. At least, if you don't want a job (like being a professor) that requires a PhD.