Year: 2026
Type: preprint
Abstract: We give a new proof that 1-extension preserves generic local rigidity of bar-joint frameworks in all dimensions. The proof does not use a special position argument, which makes the approach potentially useful for X-replacement in 3-space. Instead, the balancing conditions recently introduced by the first author use directed paths in the line graph, and by modifying the end of these paths, we transfer a self-stress on the 1-extended graph back to the original. Treating the new vertex as variable allows us to extract the balancing condition of the smaller graph as one coefficient of a homogeneous quadratic. A Lean 4 formalization of the main results accompanies the paper.
Source: arXiv (Cornell University)
Authors: Heaton, Alexander, Winter, Martin
Language: English
Subfield: Civil and Structural Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223300257