arXiv:2508.00017v4 Announce Type: replace-cross Abstract: 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.

arXiv:2508.00017v3 Announce Type: replace-cross Abstract: 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. A defining feature of the architecture is its unified hash-based inference engine, which executes both algebraic manipulations and deterministic logical transformations. Definitions are compiled into a distributed grid of simple Logic Blocks (LBs) that exchange messages; whenever the premises of an inference rule unify, a new fact is emitted with full provenance to its sources, yielding replayable, auditable proof graphs. Experimental validation is performed on Elementary Number Theory (ENT) utilizing a batched execution strategy. Starting from foundational axioms and definitions, the system first develops first-order Peano arithmetic, which is subsequently applied to autonomously derive and prove Gauss's summation formula as a main result. To manage combinatorial explosion, GL algorithmically enumerates conjectures and applies normalization, type constraints, and counterexample (CE) filtering. On commodity hardware, an end-to-end run completes in under 7 minutes. Generated proofs export as navigable HTML so that every inference step can be inspected independently. We outline a hardware-software co-design path toward massively parallel realizations and describe future integration with large language models (LLMs) for auto-formalization and conjecture seeding. The Python, C++, and MPL code to reproduce these experiments, along with the full proof graphs in HTML as well as machine-readable text format, are available in the project's GitHub repository at github.com/Generative-Logic/GL commit 1771330 and are permanently archived at doi:10.5281/zenodo.17206386.