DOI: 10.5281/zenodo.17091342
title: Collatz via Sufficiency on a Progression: Atlas (mod  2 12 2 12 ) and Endzone (mod  2 6 2 6 ) — Release Dataset (v1.0)

description: ## 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.

 

AbstractThis dataset accompanies a constructive pipeline to verify Collatz via sufficiency on a single arithmetic progression. It provides two finite, machine‑checkable certificate tables:





Atlas (mod 4096). For each odd residue class r (1024 classes in total), the table lists a short sequence of uniform odd‑run blocks with contraction factors lambda = 3^a / 2^t (all lambdas are of the form 3^a/2^t). The exogenous budget check uses the weight function w(lambda) = -log(lambda)/log(3/2) and verifies sum w(lambda_j) >= sum K_i + 1, where K_i are the counted odd feed steps. In this release every class is closed with no budget violations (1024/1024). Reported margins (min/median/max): +0.129 / +2.838 / +46.285. From the Atlas we obtain K_max approx 13.854 and thus B_min = ceil( K_max / (1 - Theta_max) ), giving B_min = 42 for Theta_max = 2/3 and B_min = 23 for Theta_max = 3/8.




Endzone (mod 64). The cover table shows that every class (mod 64) reaches either 1 or x == 1 (mod 32) (where the elementary Z_32 step enforces a strict drop) within a bounded number of odd steps. All 32 classes are covered with worst case K_feed = 59. The largest documented hard case is x_worst = 7887, so the generated endzone bound B comfortably exceeds the conservative B_min from the Atlas.



Contents





atlas_3block_results.csv (1024 rows, mod 4096; includes k‑feed counts, lambda blocks, weights, margins)




endzone_cover.csv (mod 64 cover summary)




endzone_worstcase.csv (per‑class worst examples and paths)



Integrity (SHA‑256)





atlas_3block_results.csv: 6323f5fa2b4a42f94155a241a2f5cae1ff8858a9c53137ad4703dd3a04dc5610




endzone_cover.csv: 27f91eed2735c36761d312a21ce4dec52f632d31d63ace5f9aa9191a23f9a438




endzone_worstcase.csv: caee4be8b63c24b85d1b8677dc575c9971d141f58155f1900f6f7c595a8a0743



Scope and useThe dataset is a reproducible certificate bundle to be cited alongside the proof manuscript. It does not claim a standalone proof. Rather, it supplies the finite data required by the "Atlas + Endzone" pipeline; combined with the manuscript lemmas (affine block formula, cut‑off, and the Z_32 terminal step) and Monks’ sufficiency theorem, it yields the progression‑level conclusion and hence the global implication.