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March 7, 2026Open Access

VII. Structure of entries to C1 and the rigid regime

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Authors

MBMiguel Cerdá Bennassar

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Overview

Technical note identifies a boundary in the dynamics of the Collatz conjecture, suggesting new avenues for resolution.

Key Points

  • The aim is to pinpoint the obstacle in the 2-adic argument related to the Collatz conjecture.
  • Identified the rigid regime where dynamics are autonomous.
  • Reformulated the obstacle as 2-adic convergence.
  • Defined a sufficient condition for closing the argument based on parameterization.
  • Confirmed that infinite orbits in ℕ enter a rigid regime where initial conditions are irrelevant.
  • Established a natural condition involving bi-Lipschitz regularity to close the argument.
  • Clarified the distinctions between established proofs and remaining unresolved issues.

Cite This Study

Miguel Cerdá Bennassar (2026) studied this question.

synapsesocial.com/papers/69abc2455af8044f7a4ebae4https://doi.org/10.5281/zenodo.18879276
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