We present Generative Logic (GL), a deterministic architecture that starts from user-supplied axiomatic definitions written in a minimalist Mathematical Programming Language (MPL) and systematically explores a configurable region of their deductive neighborhood. Definitions are compiled into a distributed grid of Logic Blocks (LBs) that communicate via a unified hash-based inference engine; whenever the premises of a rule unify, a new fact is emitted with full provenance, yielding replayable, auditable proof graphs. The pipeline includes an Incubator that auto-generates ground-level fact tables, a Compressor that eliminates post-proof redundancy, and an independent external Verifier (34,320 checks, zero failures). Experimental validation on Elementary Number Theory develops Peano arithmetic from axioms and autonomously derives Gauss's summation formula. On commodity hardware, the core proving pipeline completes in under one minute; the full run including Incubator fact generation finishes in approximately ten minutes. The Incubator output further reveals that GL can perform concrete numerical calculations -- each result a proved theorem with full provenance -- opening a path toward a full-provenance Computer Algebra System (CAS). Generated proofs export as navigable HTML for independent inspection. Code, proof graphs, and reproduction instructions are available at github.com/Generative-Logic/GL (commit 6e5b9a4) and archived at doi:10.5281/zenodo.17206386.

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