Where We Stand on the Collatz Conjecture: Research Map and Explainer

An English interactive 3D/2D research map with 356 nodes and 532 relationships, a four-minute explanatory video, timed subtitles, primary source notes, and a selection of internally reviewed reports. This is the public research snapshot of 16 September 2026.

The full Collatz conjecture remains unproved. Green marks internal checking within stated assumptions, including conditional lemmas and limitations; it does not mean external peer review or a percentage solved. The video credits Terras, Everett, Bernstein, Lagarias and Tao, and distinguishes published contributions from this project. The latest restricted-family reduction in this snapshot concerns a first coefficient certificate of degree below 4d under stated hypotheses. Actual coefficient bounds, the global denominator estimate and universal coverage remain open.

Authors: Khamit Kadyrbekov and Daniyal Kadirbekov. AI assistance is disclosed. No improvement over Tao or established novelty of all map entries is claimed.

Interactive map: https://kadyrbekovhamit-cyber.github.io/collatz-research-map/
English video with subtitles: https://youtu.be/Xmxrv8oOIls
Source repository: https://github.com/kadyrbekovhamit-cyber/collatz-research-map
Project page: https://www.gero.uz/research/collatz-map/