GERO / OPEN RESEARCH ATLAS

Collatz, in colour.

Explore the arguments, the corrections, and the questions still open.
By Khamit Kadyrbekov and his son Daniyal Kadirbekov.

Full conjecture remains open
DRAG TO ROTATE · CLICK TO INSPECT
356 / 532nodes / relationships

Snapshot: 16 September 2026 · Colour tour: 18 September 2026. Coordinates aid navigation; they are not mathematical distances. Colours are categories, not confidence scores or a percentage solved. This is a research record, not a formally verified proof graph. The vivid palette is inspired by molecular visualizations; no AlphaFold data or confidence metric is used.

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English synthetic narration · no autoplay · subtitles included. Download subtitles · Watch on YouTube.

The history behind the map

1976–1977 / TERRAS & EVERETT

Almost-everywhere descent in natural density.

1996 / BERNSTEIN & LAGARIAS

Exact 2-adic coding of the dynamics.

2019 · PUBLISHED 2022 / TAO

Almost bounded orbit minima in logarithmic density. Universal convergence remains open.

2026 / THIS PROJECT

Conditional arguments, explicit corrections, and missing obligations recorded together.

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Useful feedback identifies the node or report, the precise assumption or calculation, and a counterexample or earlier source where possible. Visualization feedback is welcome too: which view makes the unresolved dependencies clearer?