Why there are no mappings to infinity under the Collatz map (and similar)

TL;DR

This paper explores why the Collatz conjecture and similar mappings do not lead to infinite sequences, providing insights into their behavior and potential reasons for the conjecture's unresolved status.

Contribution

It offers a theoretical explanation for the absence of infinite mappings in the Collatz conjecture and its generalizations, advancing understanding of their dynamics.

Findings

No evidence of mappings to infinity under Collatz and similar functions.

Theoretical reasoning suggests inherent constraints prevent infinite trajectories.

Supports the conjecture that all sequences eventually reach 1.

Abstract

Following up on earlier work, I suggest why there are no mappings to infinity under the Collatz conjecture, nor under other mappings of the generalization $3n+p$, where $p$ is odd.