This paper presents Generative Logic (GL), a deterministic architecture that systematically explores the inference domain based on user-provided axiomatic definitions, along with optional facts written in a minimal mathematical programming language (MPL). Definitions are compiled into a distributed grid of simple Logic Blocks (LBs) that exchange messages. Whenever an inference rule's premises are matched, a new fact is generated, including full provenance information, resulting in a reproducible and auditable proof graph. A prototype software implementation instantiates the workflow in first-order Peano arithmetic. Starting from the Peano axioms, GL enumerates conjectures, applies normalization, types, and CE filters, and automatically reconstructs machine-verifiable proofs of fundamental arithmetic laws, including the associative and commutative laws of addition, the associative and commutative laws of multiplication, and the distributive law.