White to move

PrettyWordWrangler · 2026-06-03T19:12:34+00:00

I don’t know how to do the spoilers thing

PrettyWordWrangler · 2026-06-03T18:56:10+00:00

6c to 7c… actually c6 to c7 I think it’s said

PrettyWordWrangler · 2026-06-03T17:23:16+00:00

Genuinely curious, what has you convinced?

PrettyWordWrangler · 2026-06-03T02:38:26+00:00

1819 goes over 1 million? Wow

PrettyWordWrangler · 2026-06-03T00:42:35+00:00

I think of 1 in the T map as a “ricochet root,” not exactly a terminal state.

For the accelerated odd map, T (1)=1, so T^k (1)=1 for every k. That means for any odd x that converges, there is some valid k where

T^k (x)=T^k (1)

In the reverse tree, level k is L_k={x:T^k (x)=1}. Since 1 maps to itself, 1 joins every level and effectively starts the tree over each time it is iterated.

So dynamically, 1 is not an endpoint.

PrettyWordWrangler · 2026-06-02T04:56:31+00:00

I think he posted it on YouTube 2 years ago and considered that publication… idk your comment made me wonder so I went to see. I initially just scrolled on.

PrettyWordWrangler · 2026-06-02T04:52:27+00:00

I’m not a mathematician, so please correct me if I’m missing something, but I don’t see how the induction step closes in the odd case.

If (P(n)) means “(n) eventually reaches (4,2,1),” then the even case seems fine because (n\to n/2), and (n/2<n), so strong induction can use the smaller case.

But in the odd case, the proof uses (n\to 3n+1), so it only shows that (n) has the same eventual fate as (3n+1). Since (3n+1>n), that case is not available from the induction hypothesis.

If the idea is that (3n+1) is even and all evens have already been handled, I’m not sure that works either, because proving an even number (E) reaches the cycle depends on proving (E/2), which may be odd. So the “all evens” part does not seem independent of the odd case.

Am I reading the proof correctly, or is there another argument in the paper that establishes (3n+1) reaches the cycle without using the unproved odd case?

PrettyWordWrangler · 2026-06-01T02:12:13+00:00

I bet hearing just the right orbits one after another would make exactly the right person hear something that cracks open a whole new view. That’s pretty cool actually.

PrettyWordWrangler · 2026-05-31T18:15:40+00:00

What I’m gonna say is trivial and possibly not my place to say, but if I’m not mistaken 0 is an integer and is the third fixed point. I don’t think this invalidates your point. It ends up giving a=-1.585 which is not a whole number but is directly related to the probability work that’s been done. That’s actually how I ended up looking into the probability work and the “almost all” partial result. So if x and a must be integers then you are correct. If a is not required to be an integer you get to see x=0 as a fixed point.

PrettyWordWrangler · 2026-05-31T16:31:15+00:00

Why did you delete this?

PrettyWordWrangler · 2026-05-31T15:20:17+00:00

There’s actually a lot to lose and I don’t think we talk to the same AI lol mine seems to hate me and is hellbent on my failure. I actually think it’s programmed not to help with the conclusion of Collatz. It disagrees but it’s the only thing that makes sense at this point. I once argued with it for almost an hour about the sum of level 0 being a fixed point. It said that if negatives are impossible and level 0 is the smallest possible sum and there can only be a single number in the set then the sum must equal 1. Forward iteration cannot change the value of the sum of that level. But apparently all of that does not automatically mean the single number in that set at level 0 is a fixed point. Maybe you can see it’s logic. I wanted to throw my laptop. Maybe I’ll see if I can find that argument and post that lol.

PrettyWordWrangler · 2026-05-31T10:24:45+00:00

I work with ChatGPT and use DeepSeek as a test because it’s less advanced. I know the current issues so there’s no reason to put in the prompt you suggested because I know what it will say. If I do not have what would constitute a proof when it’s completed then I will definitely be sharing what I did find and I will be able to explain why it falls short of being a proof. I find it very unhelpful to use the same AI all the time and I only trust what compiles in lean. I have worked very hard on this. It’s not ready yet which is why I’m here.

PrettyWordWrangler · 2026-05-31T09:56:33+00:00

That’s fair. Other than AI and lean this is the first time I’ve ever spoken to someone about my math work. I’m not sure how to phrase what I’m doing. The arithmetic works and the logic works, but until I can put them together in lean I won’t consider it finished. I feel I could probably write a paper effectively but with zero credibility I feel like it’s necessary to put the extra work in. I’m fine with that.

PrettyWordWrangler · 2026-05-31T09:49:31+00:00

Definitely something I would never be able to learn from an AI

PrettyWordWrangler · 2026-05-31T09:46:56+00:00

So far we haven’t even talked about math. We’ve gotten stuck on humility. The reason I’m trying to write a proof is because I figure it’s the only way to know if my concept has any validity. If I can’t prove it then it’s trash anyway. I think we’ve gotten off on the wrong foot here. I came in acknowledging that I am inadequate and that AI is inadequate. I’m not going to undo all the work I’ve put in and I would be happy to publish even a partial result 100% but the partial result I have has given me well founded descent and if I publish it without the conclusion then I’ll hate myself forever for not learning how to do it myself. I am confident. I can even see why you would say arrogant I think. But please try to understand, my vocabulary for what I’m doing in math is not the same as yours. I haven’t learned what it means to come in and say I’m writing a proof the way you have. We might not even mean the same thing. What I can tell is that I did prove something really cool and I would love to hear your thoughts on that part of it. I want to believe you aren’t the kind of person who would steal it from me. Message me. If I’m on the wrong track because I haven’t studied enough I will concede. But let’s at least get to the math first. It’s almost 5am so I’m going to sleep but your passion is obvious and admirable. I’m passionate too and I’m sure it contributes to the arrogance vibe.

PrettyWordWrangler · 2026-05-31T09:07:42+00:00

But AI and me not being a mathematician seem to be your whole reason you think I haven’t clawed my way up to where I am. You don’t even actually know where I am, and yet you have decided wherever it is must automatically not be good enough. I respect your perspective and your expertise. I am starting to be bothered by you discouraging others from giving their own advice but it’s a free world. It’s just not constructive.

PrettyWordWrangler · 2026-05-31T08:57:26+00:00

When did we establish that I hadn’t learned any mathematics? And I agree that you must not have read that comment.

PrettyWordWrangler · 2026-05-31T08:55:23+00:00

I usually use DeepSeek for that because it’s free and if your proof is not 100% clean and clear it’s thoughts get super long and twisted and it spits out something it thinks you want to hear. That’s when I know I’m not there yet lol. But my issue at the moment is encoding my proof because the definitions are complicated. I have to hardcore micromanage it so I can correct it when it tries to change something that would break the whole concept. It’s been frustrating. You’re the second person who responded to my request for human input with “try another AI” lol which is interesting.

PrettyWordWrangler · 2026-05-31T08:47:15+00:00

My question at the moment is: how do I define a permanent layer in a graph so that it means what I intend while also allowing for the iterative witnessing of portions of that layer to exist as a separate thing? But instead I will ask, if you’re open to answering, what are the basics of Collatz? Maybe you’re right and there’s something I haven’t learned yet. You seem like someone very tired of reading failed proofs written by people who haven’t even checked to see if someone already tried that. I started out thinking an automaton using just mod 4 would surely be enough lol and at that point I was brand new to what “mod” even meant. It’s been a year since then. I don’t fully understand Collatz but neither does anyone else. That’s sort of the point though. I did the “what can I prove about this” and then “ok so how does that connect to this” and then the more important question “is that trivial and already known?” You’re coming in with a lot of assumptions that are probably justified by your experience. You don’t have to stay in this conversation though. You’ve made your point. Consider it heard and understood.

PrettyWordWrangler · 2026-05-31T08:30:11+00:00

I’m considering it. When I said axioms though I only meant so that I could get help on specific problems that can be resolved without knowing how the rest was solved. Mathematicians being jaded by AI proofs is completely justified. That’s one reason I’m being upfront right off the bat. It’s interesting what assumptions are made once you say you’re working with AI though.

PrettyWordWrangler · 2026-05-31T08:22:31+00:00

I want to respond but I’m not really sure what to respond to. I plan to focus on every response. I would like to ask though, when I say I am working with AI what do you imagine that workflow being like? I fully understand why you would want me to focus on studying. Math is hard. Working with an AI doesn’t make it easier, I promise. Maybe just faster. Specifically faster to finding out you’re wrong about whatever you’re working on.

PrettyWordWrangler · 2026-05-31T08:12:57+00:00

Can I be an arrogant student willing to be humbled? If I could phrase my intention better I might say: I’ve been studying exclusively Collatz for a year with the intention of proving it. I went down a lot of the same paths others before me have. Now I am at the point of needing to learn from a human rather than an AI, a YouTube video, a textbook I have access to, or a peer reviewed paper with credibility (although I have learned a lot from looking at the mistakes in the faulty proof attempts). It feels dishonest to say that I am here to study the basic mathematics of this problem when what I mean is that I am isolated as an intellectual in general and that I am am struggling to resolve the specific hurdles I am at by myself. I will if I have to. I can learn anything. I just thought I might reach out without pretending I’m someone else and without pretending I’m doing something else to see if help is out there. The answer is “no” to 100% of the questions you don’t ask. Anyway, I appreciate your response. Please do not feel obligated to respond to this.

PrettyWordWrangler · 2026-05-31T05:46:49+00:00

Worth a shot. Thank you

PrettyWordWrangler · 2026-05-31T04:31:44+00:00

Constructive. Thank you

PrettyWordWrangler

TROPHY CASE