open problem
The Collatz Conjecture
Iterate n -> n/2 or 3n+1; does every starting value reach 1? Simple to state, unproven since 1937.
8 machine-reviewed papers whose extracted
claims name this problem. Matching is literal, over the claim graph, so every listing traces to
a sentence in a review.
This is the review hub: papers that name the problem, with the machine's
verdict on each. The claims shelf lists the
individual claims themselves, formal (Lean) or stated.
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REJECT
On the Collatz Conjecture: Topological and Ergodic Approach
The claimed proof of finiteness of Collatz cycles fails because the key equivalence and the main theorem rely on circular reasoning.
arxiv:2601.03297 · math.DS · 2026-01
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UNVERDICTED
Logical Undefinability of the Generalized Collatz Transition Relation in B\"uchi Arithmetic
The paper's stated theorem about Büchi arithmetic is not supported by the body, which instead proves a different, weaker result about a divisibility predicate being non-semilinear.
arxiv:2601.12772 · math.NT · 2026-01
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REJECT
Non-Definability of Reachability in B\"uchi Arithmetic for a Family of Generalized Collatz Maps
The submission advertises a theorem on Collatz reachability and Büchi arithmetic, but its full text is a different, largely expository note that never states or proves that theorem.
arxiv:2602.06066 · math.GM · 2026-02
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UNVERDICTED
Emergence of Gamma-Type Upward-Phase Statistics in the Collatz Map: An Effective Poisson Process Mechanism
Modeling Collatz upward phases as a homogeneous Poisson process produces a Gamma distribution for their number, with closed-form scale θ ≈ 11.61 and shape K logarithmic in the initial value.
arxiv:2606.26811 · nlin.CD · 2026-06
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UNVERDICTED
Integer patterns in Collatz sequences
Builds an arborescence from the inverse Collatz map g(x) and claims the resulting integer patterns give new insights into proving the conjecture.
arxiv:1907.07088 · math.GM · 2019-07
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UNVERDICTED
Paradoxical behavior in Collatz sequences
Paradoxical Collatz sequences exceeding the start value are shown to relate directly to the Collatz conjecture and to occur only finitely many times under that conjecture, supporting Terras' stopping-time claim.
arxiv:2502.00948 · math.GM · 2025-02
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UNVERDICTED
Parity vectors and paradoxical sequences in the accelerated Collatz map
Proves unconditional theorems on sharp finitary parity-vector density, closed-form counts of paradoxical sequences of fixed length k, and density zero for bounded-length paradoxical sequences in the accelerated Collatz map, with a numerical link to convergents of log_3 2.
arxiv:2605.13886 · math.NT · 2026-05
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UNVERDICTED
Loop Termination and Generalized Collatz Sequences
Termination of one-variable linear-constraint loops over integers is decidable in polynomial time if the generalized Collatz conjecture holds, with any such procedure also settling specific instances of the conjecture.
arxiv:2605.15094 · cs.LO · 2026-05