Prefix Reconstruction

Abstract

Prefix data reconstructs the two half matchings and joins their unmatched endpoints in rank order.

Theorem 1.1 (Crossing arches follow rank).

Lean statement: D5/S3/Combinatorics/SemiMeanderSecondDiagonal/Stage2.crossing_eq_rankJoin

Proof. Machine-checked in Lean as D5/S3/Combinatorics/SemiMeanderSecondDiagonal/Stage2.crossing_eq_rankJoin (✓ std3). ∎

Source. Repository-derived.

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

Commentary.

The cross-half arches of an upper matching pair unmatched endpoints according to their ranks in the two midpoint cuts.

References

• Truth anchor: D5/S3/Combinatorics/SemiMeanderSecondDiagonal/Stage2.crossing_eq_rankJoin
• Dependency: D5/S3/Combinatorics/SemiMeanderSecondDiagonal/Stage1