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Midpoint Cuts

Abstract

Midpoint cuts isolate the local upper pairings and identify the four unpaired endpoints on each side.

Theorem 1.1 (Four local endpoints).

Lean statement: D5/S3/Combinatorics/SemiMeanderSecondDiagonal/Stage1.leftCut_four_endpoint_pairing_shape

Proof. Machine-checked in Lean as D5/S3/Combinatorics/SemiMeanderSecondDiagonal/Stage1.leftCut_four_endpoint_pairing_shape (✓ std3). ∎

Source. Repository-derived.

Acknowledgement. Hunter Hogan (2026). OEIS A400429, semi-meanders by crossings and winding number. URL: https://oeis.org/A400429.

Commentary.

At winding n minus four, the left cut has four endpoints in local upper pairs; their noncrossing shape has the classified alternatives.

References