Explain the Lean theorem `embed_eq_pow` in module `IndisputableMonolith.Foundation.ArithmeticFromLogic`. 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 source contains the full text of module IndisputableMonolith.Foundation.ArithmeticFromLogic up to the order definitions and the start of a proof for le_antisymm, after which it is explicitly truncated. No declaration named embed_eq_pow appears anywhere in the provided Lean source for this module or any other. The module does establish LogicNat as an inductive type with zero/succ, proves the Peano axioms as theorems (zero_ne_succ, succ_injective, induction), defines addition and multiplication with their properties (add_assoc, add_comm, mul_add, etc.), proves the recovery isomorphism equivNat to Nat, and defines order via le/lt. The introductory comment references a Section 5 on embedding LogicNat into positive reals via iteration of a generator, but supplies no code or theorem for it. Because the specific declaration embed_eq_pow is absent, no derivation of its meaning, dependencies, or scope can be given from the canon.