Work

The Type-C Integer-Gap Lemma for Periodic Collatz Blocks

Year: 2026

Type: preprint

Abstract: This record fixes the Type-C local rigidity component used in the author’s ongoing research toward a proof of the Collatz conjecture.The paper establishes an exact block decomposition, exact block transport, the Type U / Type C / Type D classification, and proves the Type-C Integer-Gap Lemma. As a consequence, every Type-C block is shown to be strictly descending except for the trivial fixed point. This work is intended as a reusable component for subsequent global analysis and does not claim a complete proof of the Collatz conjecture.

Source: Zenodo (CERN European Organization for Nuclear Research)

DOI: 10.5281/zenodo.21768280

Author: Kawanishi, Yoshihito

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7172294987

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