## 1 Introduction  
The cosmic ray energy spectrum extends from below \(\sim\)100 MeV [1] up to \(\sim\)10\({}^{20}\) eV [2]. The spectrum and composition of cosmic rays for energies up to the \"knee\" is compatible with diffusive shock acceleration mechanisms [3]. The maximum energy achievable in this shock acceleration process is at about PeV region [4; 5]. The types of objects in the Universe that are able to accelerate particles at even higher energies are limited in number. In the case of ultra high-energy cosmic rays, it seems that there are few places capable of accelerating particles above 10\({}^{20}\) eV: large scale shocks surrounding galaxy clusters, internal or external shocks of starburst-superwinds, Active Galactic Nuclei (AGN) or Gamma-Ray Bursts, AGN flares, jets, magnetars, lobes of giant radio galaxies, see [6] for a review of these. Some of the exotic models can be verified by searching for new, rather unexpected behavior of cosmic rays at the highest energies. One of them is a focus of the Cosmic-Ray Extremely Distributed Observatory (CREDO) Collaboration. This global approach allows the testing of hypothesized events of ultra-high energy cosmic ray 'bunches' observed as simultaneous Extensive Air Showers (EAS) over the entire exposed surface of the Earth: so-called Cosmic Ray Ensembles (CRE) [7; 8; 9]. Such a phenomenon has never been seen, but there are several models under which such an event is a possibility. To observe such events, a system operating on that global scale is required. Due to the extreme geographical scale of the data acquisition, the CREDO Collaboration makes use of non-expert science enthusiasts. They participate in research with their own mobile devices equipped with the CREDO Detector application [10] which enables detection of ionizing radiation using the CMOS sensors. (with their own smartphones). The idea of using an array of smartphones as cosmic ray/muon detectors is a quite recent possibility--as the density of smartphones per squared km is a significant feasibility parameter [11]. This was realized, to some extent, by the DECO [12; 13] and CRAYFIS [14] projects, and even in muon flux determination measurements [15], but at the same time the quality of individual data as well as the idea itself was criticized [16; 17]. The possibility of registering an EAS by detectors of such small active area requires a large number of smartphones concentrated in a relatively limited footprint. The typical EAS array of contemporary cosmic ray experiments consists of hundreds of detectors exceeding several square meters in size (e.g., KASCADE in Karlsruhe [18]; MAS at Mount Chacaltaya [19], or GRAPES at Ooty [20]). To effectively study cosmic ray physics at energies of \(10^{19}\) (\(10^{20}\)) eV, the density of smartphones (constantly working taking \"dark\" frames) should be 5000 (1000) per km\({}^{2}\)[17] or as few as 400 [11], which remains a challenging scale of detectors. To have an EAS smartphone array comparable to the large experiments like Pierre Auger Observatory or Telescope Array, we would require millions of phone cameras across an area of thousands of square kilometers, all permanently 'on'. The goal of registering every EAS from each CRE at close to 100% effectiveness, and measuring its characteristics (total number of particles, their distribution with respect to shower core, and incoming direction) is simply unfeasible. However, it may be possible to detect some signal from any CRE using a coincidence across very distant sets of detectors (smartphones). Another noted challenge is the contamination of smartphone camera signals by sources other than cosmic ray. In principle, this includes the housing of the camera itself, as a smartphone is not made to be \"low radiation background\". It typically contains many radioactive nuclei of isotopic composition similar to the Earth's crust, which constantly decay to give signals in the semiconductor camera matrix elements.