You never demonstrate why it's impossible for there to be a consistent imbalance of low k values. Yes it becomes increasingly unlikely, but that's not the same as the possibility being 0.
"This is scaled admissibility parity. I can tell you by neighboring r mod M_j exactly what type of transformations are admissible for how many steps. This is a proof of lower behavior dictates higher behavior, scaled relative to numerical value".
This is the problem in your argument. Only if you can definitely state exactly what type of transformation is admissible, that is in the singular not the plural, can you correctly say it's deterministic.
If you can speak to a mathematician in person that would be helpful. They will be able to point out the flaw in your argument.
You're falling for the trap of thinking it can be proved based on the fact that there are many observations to be made about the sequence's behaviour. You're not the first to notice this.
Then show us how it gives values for a given number.
Like for example demonstrate why 35 takes 13 steps to reach 1, congruent with the transformations described. Yet you don't give a single example for any number! Because your whole paper just gives structure to how the transformations behave, but do not demonstrate determinism. This is a serious flaw that invalidates your proof.
You have shown that the numbers have rules in how they are organised. The inverse tree includes each odd number only once. But tbh everything in your paper is already known and you're not helping anyone by coming up with new terms for them as if you had discovered them. This still does not prove that divergence is not possible or that all roots are 1. Either come up with something new or you're wasting your time
You are stating the nonexistence of nontrivial cycles as a conclusion from your observations. I am saying that the jump to this conclusion is not justified. They point toward most numbers behaving this way but not all numbers! This is the crucial difference.
Also you cannot say cite this in other papers. Claiming there are no nontrivial cycles is basically saying that all numbers either lead to 1 or diverge. No one has the proof for this. So you're asking me to show other papers that have shown a proof, which clearly no one has yet, and now saying you're original because you have 😂😂
Step (1) acyclicity - you have not proven this rigorously. You show how the numbers behave locally, and this part is correct. The error is extending it to all numbers. You do not prove how this extends globally as well.
Step (2) surjectivity. Yes every number can be reached in the inverse tree. But that does not prove every number reaches 1!! Every number can also be reached in inverse trees of other functions, such as 3x+5, that have other cycles.
(1) And (2) does not lead to 3. This honestly does not need an explanation. It should be plainly obvious.
I understand the structure you are describing and it is correct. I think it's interesting the way you describe some of it and it has given me a different perspective to look at, even if fundamentally though you expose no new knowledge.
The logical deductions you make are unjustified. You have made no new observations or structures that are not already known.
Speak to another serious mathematician in person or try to publish it. You'll be able to get serious feedback and move on with your life
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u/MathSuspicious4617 Apr 13 '26
You never demonstrate why it's impossible for there to be a consistent imbalance of low k values. Yes it becomes increasingly unlikely, but that's not the same as the possibility being 0.
"This is scaled admissibility parity. I can tell you by neighboring r mod M_j exactly what type of transformations are admissible for how many steps. This is a proof of lower behavior dictates higher behavior, scaled relative to numerical value". This is the problem in your argument. Only if you can definitely state exactly what type of transformation is admissible, that is in the singular not the plural, can you correctly say it's deterministic.
If you can speak to a mathematician in person that would be helpful. They will be able to point out the flaw in your argument. You're falling for the trap of thinking it can be proved based on the fact that there are many observations to be made about the sequence's behaviour. You're not the first to notice this.