The Collatz Conjecture

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The Collatz Conjecture

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Latest research edition

October 22, 2026

Binary Base-Map Proof Development

Proved Set and base-family results, exact connections between families, and the remaining global theorem needed to complete the argument.

Research update: established partial results; complete Collatz proof remains open.

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Dated edition of the research manuscript, including work recorded through August 21, 2026.

Cover of Binary Base-Map Proof Development, October 22, 2026 View the dated research PDF ↗

Proof Completed May 28 2025

Finished Proof

Proof I have been working on for 4 years.

NOTE: Reviewing the stated errors to resolve them.

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Formal Proof

I used A.I. to format the formal proof.  The 2nd document is proof without any A.I.

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Collatz Conjecture Proof of thoughts

Prior to the AI formatting the formal proof, this work was completed. Some individuals preferred to review my work without any AI involvement.

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Collatz Conjecture

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