Uniqueness and reconstruction of reciprocal constitutive generators from equilibrium response maps
Abstract
We recover a shared constitutive generator from equilibrium locations on weighted graphs. For an even C2 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 Jp, 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.
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BibTeX
@misc{washburn2026uniqueness,
title = {{Uniqueness and reconstruction of reciprocal constitutive generators from equilibrium response maps}},
author = {Jonathan Washburn and Megan Simons},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.30146},
eprint = {2610.30146},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.30146},
}
RIS
TY - UNPB
TI - Uniqueness and reconstruction of reciprocal constitutive generators from equilibrium response maps
AU - Jonathan Washburn
AU - Megan Simons
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.30146
UR - https://arxiv.org/abs/2610.30146
AB - 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.
ER -