  A previous result about the decategorified bordered (sutured) Heegaard Floer
invariants of surfaces glued together along intervals, generalizing the
decategorified content of Rouquier and the author's higher-tensor-product-based
gluing theorem in cornered Heegaard Floer homology, was proved only over
$\mathbb{F}_2$ and without gradings. In this paper we add signs and prove a
graded version of the interval gluing theorem over $\mathbb{Z}$, enabling a
more detailed comparison of these aspects of decategorified Heegaard Floer
theory with modern work on non-semisimple 3d TQFTs in mathematics and physics.

Geometric Topology;Quantum Algebra;Representation Theory