# Conditioned free-energy density of proteins using unbalanced solutions to constraint satisfaction problems

arXiv: https://arxiv.org/abs/2606.01329 · HTML: https://mlsanity.com/paper/2606.01329/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 35 references that are in the map.
- First posted on arXiv 31 May 2026.

## Builds on (most cited first, 3 of 3)

- [Supersparse Linear Integer Models for Optimized Medical Scoring Systems](https://mlsanity.com/paper/1502.04269/) (2015)
- [Optimal Algorithms for L1-subspace Signal Processing](https://mlsanity.com/paper/1405.6785/) (2014)
- [Approximating Operator Norms via Generalized Krivine Rounding](https://mlsanity.com/paper/1804.03644/) (2018)

## Abstract (arXiv)

We show that computing the log-partition function (free-energy) of conditioned inhomogeneous Curie--Weiss spin Hamiltonians reduces to an unbalanced 2 → 1 norm computation, and design a polynomial-time SDP algorithm for this problem with a lower bound proof for the amount of unbalance achieved. Applied to the protein Ubiquitin, the framework starts from a known crystal structure, explores alternative backbone conformations across the free-energy landscape, and identifies flexible regions of the protein while preserving its native secondary structure.