  We examine the simplest realization of the linear seesaw mechanism within the
Standard Model gauge structure. Besides the standard scalar doublet, there are
two lepton-number-carrying scalars, a nearly inert SU2 doublet and a singlet.
Neutrino masses result from the spontaneous violation of lepton number,
implying the existence of a Nambu-Goldstone boson. Such "majoron" would be
copiously produced in stars, leading to stringent astrophysical constraints. We
study the profile of the Higgs bosons in this model, including their effective
couplings to the vector bosons and their invisible decay branching ratios. A
consistent electroweak symmetry breaking pattern emerges with a compressed
spectrum of scalars in which the "Standard Model" Higgs boson can have a
sizeable invisible decay into the invisible majorons.
