Explain the Lean theorem `reciprocal_comp_reciprocal` in module `IndisputableMonolith.Algebra.CostAlgebra`. 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 supplied Lean source slice for IndisputableMonolith.Algebra.CostAlgebra is truncated and does not contain the theorem reciprocal_comp_reciprocal. Because the declaration is missing, I cannot provide its exact formal statement, decode its Lean syntax, list its dependencies, or definitively explain what it proves versus what it does not prove.

In the context of Recognition Science, the relationship between reciprocals and the composition of costs is governed by the primitive J-cost function's reciprocal symmetry (established in the available theorem J_reciprocal: $J(x) = J(x^{-1})$) and the Recognition Composition Law (established in RCL_holds), which induces the binary composition operation (costCompose). A theorem named reciprocal_comp_reciprocal would likely formalize the algebraic interaction between inversion and this composition operation, but its exact mathematical formulation and verification certificates are absent from the provided canon.