Gears
I'm new to this discussion so if I sound ignorant, I may well be. I've watched the cold side gather more attention since the Turbojet hit its wall in the 50's. The idea is to turn blades efficiently and economically to produce the most thrust per wt. Fuel. Gears work, but the "load" originating aerodynamically ends up gnashing the teeth of the gearset. Petrol electrics have been used for 70 years in locomotives, but are heavy. Since N1 is just a big multiblade propellor anyway, an obvious thought would be varying the pitch of the vanes (blades). Another (Old) solution to isolating gear teeth from each other is Hydraulic drive. It's analogous to Generator to Motor drives, but substitute a Fluid pump for the generator and a driven turbine for the electric motor. The Hydraulic fluid absorbs the slam of the changing loads, the Hot Core can run at its most balanced power/fuel ratio continuously, the Pump changes out put to the Fan by directing fluid flow to separate vane incidence areas of the driven turbine, changing the RPM of the Fan.
There, I've wanted to put that out there for twenty years. Thanks for listening.