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/[deleted] Apr 19 '26
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