Uniqueness and reconstruction of reciprocal constitutive generators from equilibrium response maps
Year: 2026
Type: preprint
Abstract: We recover a shared constitutive generator from equilibrium locations on weighted graphs. For an even $C^2$ log-coordinate potential with positive curvature, the complete two-site response map determines the generator up to positive scale. A sweep over all positive boundary values at one fixed, possibly unknown, unequal weight ratio gives global identification through a Schröder-Koenigs iteration. We extend this result to a three-vertex chain with two observed free vertices under a sweep condition. For variable-ratio control, we prove finite-target recovery, local Lipschitz stability, and noisy-bisection bounds. Fixed-ratio stability and nonparametric estimation under uncertain controls remain open. In the reciprocal family $J_p$, an exact Gaussian model-selection probability benchmarks synthetic experiments under observation noise and errors in variables. These are identifiability results under controls; no measured data or physical system is analyzed.
Source: arXiv (Cornell University)
Authors: Washburn, Jonathan, Simons, Megan
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223373920