2 problems

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The canonical-weight criterion for the $\tau_B=\tau_R$ condition
Canonical-weight criterion conjecture. Up to $\operatorname{SL}(2,\mathbb{Z})$ , the condition
Conjectureopenbrane-tilings mahler-measure toric-diagramsarXiv posted 2 days ago
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The consistency and perfect-matching conjecture for brane tilings
Consistency and perfect-matching conjecture. A brane tiling is consistent if and only if the corresponding toric diagram has maximally tempered coefficients for its boundary points…
Conjectureopenbrane-tilings perfect-matchings toric-diagramsarXiv posted 2 days ago

The canonical-weight criterion for the τB=τR\tau_B=\tau_RτB​=τR​ condition