7 problems

Ordered-or-defective twin conjecture. Ordered equilibria arise only from single-string tessellations, and stable equilibria are either ordered or have defects.

Bulk-energy delta-limit conjecture. The effects of the growing population of moderate-defect equilibria and the upper stability cutoff generate a self-similar distribution of inher…

Bulk self-similarity conjecture. The large-$N$ bulk distribution is independent of $\alpha$ and is self-similar in $N$ about the fixed energy $\bar{E}_*$.

Unbalanced-graph configuration conjecture. Apart from some trivial exceptions, this property is held only by balanced graphs. Equivalently, if $G$ is not balanced, then the minimum…

Cascade-of-local-events conjecture. Destabilization occurs by a cascade of local events: the destabilizing contribution acts independently on each pentamer and does not depend on i…

Small-world landscape conjecture. The small-world phenomenon might be a generic feature of landscapes with the structure-seeking palm tree' organisation.

A rigid cluster is a configuration of particles whose bond constraints leave no internal floppy motion. A floppy mode is a configuration with one or more internal degrees of freedo…