| compatible boundary conditions | statement | lemma 3.3 | arxiv |
| interpolation between energy wells | statement | proposition 5.28 | arxiv |
| critical transition value of $\sigma$ | definition | definition 2.40 | arxiv |
| stability under $\bf m$-transform | definition | definition 2.26 | arxiv |
| convex-affine potentials as perturbations of truncated potentials | example | example 4.8 | arxiv |
| 3KEP3Z5EWZ | statement | proposition 6.4 | arxiv |
| effective strength of nearest-neighbour interaction | definition | definition 2.36 | arxiv |
| 3RJWV47GSN | example | example 3.16 | arxiv |
| trivial bounds for $\widehat Q_{\bf m}f$ | statement | proposition 2.11 | arxiv |
| incommensurability and non-trivial $\bf m$-stability | example | example 2.35 | arxiv |
| energy meta-wells | definition | definition 3.22 | arxiv |
| convexity of $g_N$ | statement | proposition 5.17 | arxiv |
| 55X1A1YJDQ | statement | proposition 2.32 | arxiv |
| projection of the quadratic part of the energies | statement | lemma 5.2 | arxiv |
| 628JHNV63N | statement | proposition 2.33 | arxiv |
| convexity of $\widehat Q_{\bf m}f$ | statement | proposition 3.4 | arxiv |
| characterization of $\widehat Q_\sigma f$ in terms of periodic arrangements | statement | proposition 5.14 | arxiv |
| shape of $\widehat Q_{\bf m}f$ and of the phase function $\theta$ | statement | theorem 4.1 | arxiv |
| 7TYP1KX6SW | statement | proposition 6.3 | arxiv |
| convex-affine potentials | example | example 3.19 | arxiv |
| 8F7NJBPH80 | statement | corollary 2.34 | arxiv |
| optimization over the phase fraction | statement | theorem 3.2 | arxiv |
| 960XDQSD98 | statement | proposition 3.10 | arxiv |
| 9QC4F3MDCC | statement | lemma A.2 | arxiv |
| double-well bi-quadratic potential | example | example 3.13 | arxiv |
| AJDN96DMKY | statement | proposition 3.18 | arxiv |
| differentiability with respect to $z$ | statement | proposition 3.25 | arxiv |
| optimality of $A(\theta)$ | statement | proposition 5.29 | arxiv |
| energy wells and locking states | statement | proposition 3.26 | arxiv |
| asymptotic equivalence | statement | theorem 5.6 | arxiv |
| locking states | definition | definition 3.5 | arxiv |
| truncated convex potentials | example | example 3.15 | arxiv |
| FHCVXDVM35 | statement | lemma A.1 | arxiv |
| interpolation between locking states | statement | lemma 4.4 | arxiv |
| convex nearest-neighbour interactions | statement | proposition 2.14 | arxiv |
| convexity properties with respect to $N$ with given parity | statement | proposition 5.20 | arxiv |
| convexity properties with respect to arbitrary $N$ | statement | corollary 5.21 | arxiv |
| J0KJ41637W | statement | lemma 5.9 | arxiv |
| $g^\sigma_N$ as an energy meta-well | statement | proposition 5.27 | arxiv |
| lower bound with nearest-neighbour energies | statement | proposition 5.5 | arxiv |
| locking states of $Q_\sigma f$ | statement | theorem 5.23 | arxiv |
| a lower bound for general $\bf m$ | statement | proposition 2.19 | arxiv |
| minimization of the quadratic part | statement | lemma 2.10 | arxiv |
| phase function | definition | definition 3.6 | arxiv |
| higher-dimensional equivalent formulation | statement | theorem 5.1 | arxiv |
| relaxation with concentrated kernel | statement | proposition 2.16 | arxiv |
| an algebraic lemma | statement | lemma 4.3 | arxiv |
| relaxation with kernel $\bf m$ | definition | definition 2.3 | arxiv |
| equivalence with the Novak-Truskinovsky model | statement | theorem 6.5 | arxiv |
| SPMZ57MVFW | statement | corollary 2.12 | arxiv |
| a characterization of the convex envelope | statement | proposition 2.1 | arxiv |
| existence of positive critical transition values | example | example 2.41 | arxiv |
| $\bf m$-stability and convexity | statement | proposition 2.28 | arxiv |
| convexity of $\widehat Q_{\bf m}f$ | statement | proposition 2.7 | arxiv |
| periodic spin characterization of $\widehat Q_{\bf m} f(\theta,z)$ | statement | proposition 3.21 | arxiv |
| Non differentiability at the energy wells | conjecture | conjecture 3.27 | arxiv |
| X84ECRWMSQ | statement | proposition 2.20 | arxiv |
| XNSBB9FVS7 | statement | proposition 2.38 | arxiv |
| concentrated kernels | definition | definition 2.15 | arxiv |
| $\mathbf m$-transform of $f$ | definition | definition 2.22 | arxiv |
