Explain the Lean theorem `four_pi_in_interval` in module `IndisputableMonolith.Numerics.Interval.PiBounds`. Write for an educated reader who knows science and programming but may not know Lean. Cover: (1) what the declaration says in plain English, (2) why it matters in Recognition Science, (3) how to read the formal statement, (4) visible dependencies or certificates in the supplied source, and (5) what this declaration does not prove. Cite only declarations present in the supplied Recognition source.

The requested theorem four_pi_in_interval and its parent module IndisputableMonolith.Numerics.Interval.PiBounds are not present in the supplied slice of the Pith canon.

While the Recognition Science primer indicates that the framework establishes strict numerical bounds for derived constants (such as the fine-structure constant inverse $\alpha^{-1}$ falling strictly within the interval $(137.030, 137.039)$ without fitted parameters), the specific formal statement, dependencies, and proof of four_pi_in_interval cannot be analyzed without the corresponding Lean source code.

To explain how to read the formal statement, identify its visible dependencies, or detail what it does and does not prove, the module containing the declaration must be included in the context.