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A short constructive proof of the middle levels theorem

Contribution grade

Combinatorics · Scoped scientific or research-capability contribution

Reference score10,000Provisional editorial estimate of this exact contribution; its grade is assessed separately.

What changed

A constructive proof joins a cycle factor through explicitly described six-cycles to obtain a Hamilton cycle in the middle levels of an odd-dimensional cube.

Scientific scope

A constructive proof joins a cycle factor through explicitly described six-cycles to obtain a Hamilton cycle in the middle levels of an odd-dimensional cube. Scope limitation: This is the 2018 short proof, following the earlier proof credited by its authors. WRS retains the complete version-2 narrative and checks finite instances through n=6. Finite checks do not prove the theorem for all n or the asymptotic lower bound on the number of cycles. The earlier PDF-ingestion experiment remains a separate historical object.

Evidence

Assessment uses the catalogue-linked source evidence for the stated contribution. This is the 2018 short proof, following the earlier proof credited by its authors. WRS retains the complete version-2 narrative and checks finite instances through n=6. Finite checks do not prove the theorem for all n or the asymptotic lower bound on the number of cycles. The earlier PDF-ingestion experiment remains a separate historical object.

Contributors

Provisional WRS assessment, edition 2026-10-16.1. Independent expert calibration is pending. This grade does not certify correctness or assign ownership.

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