Full Inheritance of Negative Drift in Modular Collatz Classes: A Conditional Result

## Experimental Disclosure Notice

**This work is part of a documented experiment on AI-generated mathematical content.** The mathematical arguments presented were produced by large language models (primarily ChatGPT) with minimal human intervention, as part of a study examining AI capabilities in formal mathematics and the robustness of academic publication processes.

The content should be evaluated critically and is not guaranteed to be mathematically sound. For a full methodological discussion and analysis of this experiment, see:

M. H. Thaler, *Proofing Collatz with AI: A Retrospective on an Experimental Publication Process* (2025). DOI: https://doi.org/10.5281/zenodo.17232247

**Transparency statement:** The author’s role was primarily that of a mediator, documenting and publishing AI-generated outputs with minimal filtering. This disclosure is made in the interest of scientific transparency and to inform readers about the nature of this work.

This paper establishes a conditional result on symbolic drift inheritance in the modular Collatz framework. It proves that if a residue class at level kk has strictly negative drift, then both modular successors at level k+1k+1 also inherit strictly negative drift. The argument uses convex decomposition and contradiction. Empirical data for k=1k=1 to 88 support this claim. While the result does not resolve global convergence, it provides structural reinforcement for symbolic drift cone formation in modular dynamics.