In the research domain of cellular automata algorithmics, the firing squad synchronization problem is a famous problem that has been solved in many ways. However, very few of these solutions have a detailed formal proof suitable for proof assistant and for human understanding. The reason is that the correctness of those solutions is more easily seen from a high level point of view and from the way the solution has been constructed than from the actual formal description of the constructed solution. The field-based approach consists in giving a formal description of a new high-level and modular description and the reduction process down to the final low-level solution. The decomposition in modules are natural from a design point of view and is a precise counterpart of the previous informal high-level description. This research report aims to present an understandable proof of correctness of the high-level field-based solution suitable for an implementation in Coq.