Cap-selected amplitudes and triangle chords for honeycomb walks

At the critical honeycomb fugacity, self-avoiding port-to-port chords in an equilateral lattice triangle of side R, summed over both boundary endpoints and restricted to diameter at least $R/100$, have partition sum comparable to R${}^{3/4}$ and mean length $R^{4/3+o(1)}$. We also determine the amplitude selected by two vacuum caps on a cylinder of circumference N and prove that it grows as $N^{1/6+o(1)}$.