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Dataset of trajectories and sample code to generate trajectoroies
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[2025-10-15v4]A Unified Proof of the Collatz Conjecture The Invariant Structure of the $3n+1$ Problem: Generalization to All Integers via Phase Expression Theory and Universal Structural Limits.pdf
Note:The latest version of the manuscript has been uploaded to zenodo: https://doi.org/10.5281/zenodo.17394543 This paper presents a \textbf{unified and constructive framework} th
Figshare2025-10-20 更新190
Results of arc-fractal sequences with 2 arcs (Heighway and Lévy) and 3 arcs (arrowhead and crab).
† Even though it has been discussed in the text in Sec. 1.2.2 and shown in [27, p. 265], it turns out that at a particular level, the sequences for arc-fractal with even n have 2n types of symbols whi
NIAID Data Ecosystem90
[2025-10-13v3]A Unified Proof of the Collatz Conjecture The Invariant Structure of the $3n+1$ Problem: Generalization to All Integers via Phase Expression Theory and Universal Structural Limits.pdf
This paper presents a \textbf{unified and constructive framework} that resolves the long-standing open problem, the \textbf{Collatz Conjecture} ($3n+1$), over all non-zero integers (positive and negat
DataCite Commons2025-10-15 更新60
[2025-10-15v4]A Unified Proof of the Collatz Conjecture The Invariant Structure of the $3n+1$ Problem: Generalization to All Integers via Phase Expression Theory and Universal Structural Limits.pdf
Note:The latest version of the manuscript has been uploaded to zenodo: https://doi.org/10.5281/zenodo.17394543 This paper presents a \textbf{unified and constructive framework} th
DataCite Commons2025-10-20 更新100
The complete list of two-dimensional rotation-symmetric number-conserving septenary cellular automata
This dataset contains a complete list of all 30144 two-dimensional rotation-symmetric number-con-serving cellular automata with the state set {0,1,2,3,4,5,6} based on adjacent cells only, i.e. with th
DataCite Commons2022-08-30 更新90
