Collatz Machine-Verifiable Certificates (Phase 1): Atlas mod 4096 and Endzone mod 64

## 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 dataset contains the tables, code, and validation protocol used to build and verify two finite certificates for the 3x+1 problem: (1) an atlas (mod 4096) of uniformly enforceable odd-run blocks with an affine block formula and an exogenous budget; and (2) an endzone (mod 64) covering all odd residue classes up to B and reaching {1} or P32. A Z32 certificate yields the strict 4-step descent on P32. The package enables independent reproduction and machine checking inside a proof assistant (Isabelle/HOL or Lean). Contents:- Tables: atlas_mod4096.xlsx, endzone_mod64.xlsx- Code: generate_collatz_atlas.py, generate_endzone_mod64.py (generators), validate_atlas_endzone.py (validator)- Docs: README.txt, validation_protocol.xlsx (validator output) Key summary (from the included computations):- Atlas: closed 2048/2048 rows; blocks per row = {1:1690, 2:146, 3:77, 4:36, 5:33, 6:37, 7:22, 8:7}; K_total mean ~3.96, max 39- Endzone: B=262144, cap=500, coverage=true, K_max=96, Theta_bound=3/8, B_min_recommended=154 Reproduction (short):1) Run the validator on atlas_mod4096.xlsx and endzone_mod64.xlsx (checks: uniformity, affine formulas, Ce coherence, budget inequality, endzone summary; emits validation_protocol.xlsx).2) Optionally regenerate endzone (B=262144, cap=500) and the atlas with the supplied pattern family.3) Export CSV for formal checking and import into a proof assistant.