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What would a mathematical research project look like as a three dimensional

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map?

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This is GERO's public Collatz research snapshot: three hundred fifty six

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nodes, connected by five hundred thirty two relationships.

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Rotate it, inspect an argument, and see where a route stops.

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The full Collatz conjecture remains unproved.

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The rule is simple: halve an even number; multiply an odd number by three and

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add one.

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The claim is that every positive start reaches one.

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Terras and Everett established almost everywhere descent in natural density.

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Bernstein and Lagarias developed exact two adic coding.

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These achievements explain structure, while leaving the universal question

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open.

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Terence Tao's major advance controls orbit minima.

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For any bound tending to infinity, however slowly, almost every start

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eventually falls below that bound, in logarithmic density.

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This does not establish that every start reaches one.

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A map must keep that distinction visible: an impressive theorem and a

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complete solution are different claims.

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Our colours describe categories, not a probability that Collatz is solved.

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Blue marks internally checked arguments within their stated assumptions.

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Cyan identifies selected published references.

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Amber marks open obligations.

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This is a navigation layout, not a mathematical distance or a formal proof

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graph.

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The data snapshot is from September sixteenth, twenty twenty six.

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Research history also includes corrections.

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The coral node records an error in an earlier route: a proposed common

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infimum gap could not hold.

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Preserving that correction matters.

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A useful map should make failed assumptions discoverable, alongside the

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arguments that survived internal checking.

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Independent review remains a separate step.

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In the public snapshot, one restricted branch reduces a first coefficient

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certificate to degree below four d, under explicit hypotheses.

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Bounds for the actual coefficients remain missing.

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So does coverage of arbitrary Collatz trajectories.

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Closing a local branch would be progress, but would not by itself establish

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the conjecture.

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One sufficient route is universal descent: every odd start greater than one

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must eventually fall below itself.

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We have not proved that statement.

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We are Khamit Kadyrbekov and his son, Daniyal Kadirbekov.

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We have been working on this project for several months with artificial

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intelligence assistance.

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Explore the map and leave a specific correction, missing assumption, or

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relevant source.