My take on the core.... It's a "standard" core but there are two crystals that can be swapped in and out of the streams at will. It's a first-generation design... the next iteration will have two streams/two crystals operating at the same time to prevent "transition lag." The vessel has to switch propulsion mode from slip-stream to warp drive then to impulse to slow down and there can be a lag as the modes change from slip to warp-drive.
The pipe-and-rings are the injector constriction segments, the main conduit behind them is a sort of master coolant/control/feedback/regulator system. The pipes carry control signals, cooling fluids (hypersonic liquid metal pumped by a magnetic field) and control signals to the injector segments.
The central ring is the reaction chamber, with the crystals housed inside along with the special system for switching crystal modes.
As stated above future designs will run both crystals at the same time to prevent a possibly fatal transition lag. Future designs are postulated to do away with the dilithium crystal entirely.