Seam differences preserve signs

Abstract

Finite signed contraction on the actual rectangular height grid.

Definition 1.1 (The surviving-cell injection).

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 map embeds the smaller physical rectangle in the original rectangle by skipping exactly the deleted internal column.

Theorem 1.2 (No surviving cells are identified).

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 surviving-cell map is injective on the actual rectangular cell type.

Theorem 1.3 (Every surviving cell is represented).

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.

Every original cell outside the deleted column is the image of one cell of the smaller rectangle.

Theorem 1.4 (The origin stays normalized).

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.

A normalized unit-edge height function remains normalized after signed deletion because the origin lies strictly before the removed internal column.

Theorem 1.5 (Seam differences preserve signs).

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.

Across the new seam the contracted height difference equals the corresponding original incident difference, using the uniform frozen slope.