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The recent detections of the $\sim10$-s long $\gamma$-ray bursts (GRBs)211211A and 230307A followed by softer temporally extended emission (EE) andkilonovae, point to a new GRB class. Using state-of-the-art first-principlessimulations, we introduce a unifying theoretical framework that connects binaryneutron star (BNS) and black hole-NS (BH-NS) merger populations with thefundamental physics governing compact-binary GRBs (cbGRBs). For binaries withlarge total masses $M_{\rm tot}\gtrsim2.8\,M_\odot$, the compact remnantcreated by the merger promptly collapses into a BH, surrounded by an accretiondisk. The duration of the pre-magnetically arrested disk (MAD) phase sets theduration of the roughly constant power cbGRB and could be influenced by thedisk mass, $M_d$. We show that massive disks ($M_d\gtrsim0.1\,M_\odot$), whichform for large binary mass ratio $q\gtrsim1.2$ in BNS or $q\lesssim3$ in BH-NSmergers, inevitably produce 211211A-like long cbGRBs. Once the disk becomesMAD, the jet power drops with the mass accretion rate as $\dot{M}\sim t^{-2}$,naturally establishing the EE decay. Two scenarios are plausible for shortcbGRBs. They can be powered by BHs with less massive disks, which form forother $q$ values. Alternatively, for binaries with $M_{\rmtot}\lesssim2.8\,M_\odot$, mergers should go through a hypermassive NS (HMNS)phase, as inferred for GW170817. Magnetized outflows from such HMNSs, whichtypically live for $\lesssim1\,{\rm s}$, offer an alternative progenitor forshort cbGRBs. The first scenario is challenged by the bimodal GRB durationdistribution and the fact that the Galactic BNS population peaks atsufficiently low masses that most mergers should go through a HMNS phase.

A Unified Picture of Short and Long Gamma-ray Bursts from Compact Binary Mergers