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This work aims to reinterpret the Collatz conjecture through topological principles rather than purely number-theoretic approaches.

July 14, 2026Open Access

PFUSRC-080 Topological Morphogenesis of the Collatz Conjecture — From 3n+1 Iteration to 45° Biconical Interlayer Oscillation: Tracing a Number-Theoretic Problem to Its Geometric Boundary

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This work aims to reinterpret the Collatz conjecture through topological principles rather than purely number-theoretic approaches.
Utilizes the PFUSRC topological morphogenesis framework for analysis.
Examines numerical trajectories and their relationships to the minimal closed loop.
Establishes a comparison with existing results in analytic number theory.
Demonstrates that all numerical paths converge to the same topological origin.
Identifies two concepts of infinity: one mathematical and one topological, defined by curvature anchor points.
Highlights significant differences in iteration paths for specific numerical examples, revealing their topological implications.

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Repositions the Collatz conjecture as a topological convergence problem, implying new insights into well-known number-theoretic challenges.

Zhenmin Wang (2026) studied this question.

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Repositions the Collatz conjecture as a topological convergence problem, implying new insights into well-known number-theoretic challenges.