  We give a new geometric proof of a theorem of Heuer showing that, in the
presence of letter-quasimorphisms (which are analogues of real-valued
quasimorphisms with image in free groups), and in particular in RAAGs, there is
a sharp lower bound of 1/2 for stable commutator length. Our approach is to
show that letter-quasimorphisms give rise to negatively curved angle structures
on admissible surfaces. This generalises Duncan and Howie's proof of the
1/2-lower bound in free groups, and can also be seen as a version of Bavard
duality for letter-quasimorphisms.
