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Terminal Connectivity

Abstract

Terminal path arguments characterize connectivity for the remaining local pairing cases.

Theorem 1.1 (First terminal case).

Lean statement: D5/S3/Combinatorics/SemiMeanderSecondDiagonal/Stage4.connected_iff_A

Proof. Machine-checked in Lean as D5/S3/Combinatorics/SemiMeanderSecondDiagonal/Stage4.connected_iff_A (✓ std3). ∎

Source. Repository-derived.

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

Commentary.

The first admissible endpoint pattern is connected exactly under its stated rank condition.

Theorem 1.2 (Second terminal case).

Lean statement: D5/S3/Combinatorics/SemiMeanderSecondDiagonal/Stage4.connected_iff_C

Proof. Machine-checked in Lean as D5/S3/Combinatorics/SemiMeanderSecondDiagonal/Stage4.connected_iff_C (✓ std3). ∎

Source. Repository-derived.

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

Commentary.

The second terminal pattern has the corresponding necessary and sufficient connectivity condition.

References