Extreme Energy Cosmic Rays "Treasure Maps": a new methodology to unveil the nature of cosmic accelerators

Extreme Energy Cosmic Rays, EECRs -- cosmic rays with energies beyond the GZK cutoff (i.e. greater than 100 EeV) are scarce. Only a few of such events have been detected by air shower experiments and the nature of the primary particles are still unknown. Individual EECRs sources become more prominent, relative to the background, as the horizon diminishes. We show that an event-by-event, composition-dependent observatory would allow us to limit the character of the sources and learn about the intervening magnetic fields, as the deflections in the intervening Galactic and extragalactic magnetic fields depend on the nature of the particle. A major goal here is to provide a methodology to distinguish between steady and transient sources.