Unit edges survive deletion

Abstract

Finite signed contraction on the actual rectangular height grid.

Definition 1.1 (The actual signed slope).

Citation. Chakshu Gupta (2026). One construction for the Miura-ori flip-graph degree sequence. DOI: 10.48550/arXiv.2607.05567. URL: https://arxiv.org/abs/2607.05567v3.

Commentary.

The slope is the row-zero height difference between the frozen column and its left neighbour.

Theorem 1.2 (Slope transport to every row).

Citation. Chakshu Gupta (2026). One construction for the Miura-ori flip-graph degree sequence. DOI: 10.48550/arXiv.2607.05567. URL: https://arxiv.org/abs/2607.05567v3.

Commentary.

For a unit-edge height function, this same signed slope equals that horizontal difference in every row.

Theorem 1.3 (The slope is a unit sign).

Citation. Chakshu Gupta (2026). One construction for the Miura-ori flip-graph degree sequence. DOI: 10.48550/arXiv.2607.05567. URL: https://arxiv.org/abs/2607.05567v3.

Commentary.

The actual frozen slope is either one or negative one.

Definition 1.4 (Signed deletion).

Citation. Chakshu Gupta (2026). One construction for the Miura-ori flip-graph degree sequence. DOI: 10.48550/arXiv.2607.05567. URL: https://arxiv.org/abs/2607.05567v3.

Commentary.

Delete one internal frozen column and subtract its uniform signed slope from every column to its right.

Theorem 1.5 (Unit edges survive deletion).

Citation. Chakshu Gupta (2026). One construction for the Miura-ori flip-graph degree sequence. DOI: 10.48550/arXiv.2607.05567. URL: https://arxiv.org/abs/2607.05567v3.

Commentary.

For every pair of adjacent surviving grid cells, the contracted height difference has absolute value one, including the new seam.