Nuclear g-factors are of the most accurate probes in modern nuclear physics investigations. Sensitive to the precise structure of the nuclear states, single-particle or collective nature is accessed directly by their measurement. At the border of nuclear existence, key regions of nuclei around 208Pb, 132Sn, 100Sn, and 78Ni are highly appealing for such studies. Shell structure, magicity, new shell gaps, nucleon-nucleon interaction, collectivity, deformation, and shapes are among the burning questions about these regions of exotic species scientifically addressed. With the new gSPEC project, we aim to perform such challenging g-factor investigations at the GSI/FAIR facility and to scan isomeric states of nuclei along the entire nuclear chart. The starting phase gSPEC-0, which is already running with a well-defined program, requires the design and construction of a new and specific experimental apparatus, part of which is a new gDEGAS type of HpGe detectors, operating in a magnetic field and able to perform fast timing experiments together with excellent energy resolution. The newly proposed DEGAS detector reformatting and R&D, together with mechanical cryostats and electronics preamplifier developments, are specifically addressed in this proposal. Furthermore, the ancillary detector set is expanded by a new fast-timing gVeto detector, operating in magnetic field for light particle rejection and as a regulator of the beam implantation. Provided successful phase-0 at the FRS beamline at GSI, new scientific goals on nuclear moments can be achieved with gSPEC-0. Moreover, gDEGAS is a fundamental ingredient of the next gSPEC-1 phase for the first Early Science experiments at NUSTAR. An important role is played also by the ancillary gVeto, whose R&D also aims best particle-gamma tagging performance with FAIR beams. In this proposal, together with the fundamental scientific goals, we address the new R&D and the technical defy.