2 problems

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Periodic ABC arrangement conjecture for the ternary long-range Ising model
Consider a one-dimensional periodic cell containing $n$ balls of each type $A$ , $B$ , and $C$ , with positive radii parameters $\omega_i$ satisfying $\sum_i\omega_i=1$ , and let…
Conjectureopenlong-range-interactions one-dimensional-models ternary-systemsarXiv posted 2 days ago
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Conjecture on minimal-energy configurations for the one-dimensional zero-barrier model
Non-interacting intervals conjecture. The minimal energy is attained, or corresponds, to the energy of several non-interacting intervals.
Conjectureopencalculus-of-variations nonlocal-aggregation one-dimensional-modelsarXiv posted 2 days ago

Periodic ABC arrangement conjecture for the ternary long-range Ising model