November 9, 2025Open Access

A 2-adic Density Lemma in the Odd Trajectory of the Collatz Map

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Analysis reveals relative density patterns in odd numbers within Collatz trajectories, indicating unique dynamics in number families.

Relative density for odd numbers is shown to be 1/2^(r-1), revealing unique patterns in arithmetic progressions.
Key finding includes the association of numerical families, leading all odd numbers to a common global attractor.
Observational analysis connects the Collatz dynamics with 4-adic families, demonstrating convergence behavior.
Insights from this framework highlight the significance of the density concept, potentially impacting probabilistic models.

Miguel Cerda Bennassar (2025) studied this question.

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