This preprint introduces an observational model for the analysis of recursive exploration processes in formal systems executed on computational systems. The work focuses on the cumulative operational cost generated by recursive rule propagation and on the emergence of observable dissipative dynamics within the outcome space of the exploration. The proposed model describes how local transformations may remain operationally efficient while the global cumulative cost of exploration progressively degrades the overall efficiency of the system. The paper also discusses the emergence of observable basins associated with recursive trajectories and the influence of historical accumulation on the traversability of the exploratory space. This deposit is connected to the subsequent Zenodo record: Genesis of an invariant for the comparative measurement of formal systems https://zenodo.org/records/21345293 The subsequent document introduces the normalization of the observed transformative cost per slice and defines the abstract normalized unit named Pensore.