Uniform marked-polygon estimates and sharp finite bridge moments
We prove a uniform bound for critical honeycomb polygons through two axial marks on a periodic staircase. The bound retains an explicit power of the ratio between the period and the marked separation. We also prove sharp finite strip estimates: bridge mass of order h −1/4 , first-length mass at most $Ch^{13/12}$, and mass at least $ch^{-1/4}$ on bridges with length at least $ch^{4/3}$.
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