2101.08060
The Collatz Problem generalized to 3x + k
Franz Wegner
correctmedium confidence
- Category
- Not specified
- Journal tier
- Specialist/Solid
- Processed
- Sep 28, 2025, 12:55 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
Both the paper and the model use the same core conjugacy Syr_k(kx) = k·Syr_1(x) for odd k with 3∤k to transport Tao’s Syracuse-distribution framework from k=1 to general k, yielding P_{k,n}(y) = P_{1,n}(k^{-1}y) and the k-independence of the oscillation Osc_{m,n}. The model’s derivation mirrors Wegner’s equations (35)→(37) and the oscillation argument, with only minor presentational differences.
Referee report (LaTeX)
\textbf{Recommendation:} minor revisions
\textbf{Journal Tier:} specialist/solid
\textbf{Justification:}
The paper gives a short, correct, and useful observation: an exact conjugacy transports Tao’s Syracuse-iterate distribution from k=1 to all k in D, implying k-independence of the oscillation. The model solution reproduces the same argument. Minor improvements in exposition (up-front hypotheses, a one-line justification of the permutation/bijection step, and a more explicit link from the conjugacy to the distribution identity) would polish the presentation.