  Growth-fragmentation processes model the evolution of positive masses which
undergo binary divisions. The aim of this paper is twofold. First, we extend
the theory of growth-fragmentation processes to allow signed mass. Among
others, we introduce genealogical martingales and establish a spinal
decomposition for the associated cell system, following arXiv:1605.00581. Then,
we study a particular family of such self-similar signed growth-fragmentation
processes which arise when cutting half-planar excursions at horizontal levels.
When restricting this process to the positive masses, we recover part of the
family introduced by Bertoin, Budd, Curien and Kortchemski in arXiv:1605.00581.
