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.

翻译：本文提出生成式逻辑（Generative Logic，GL），这是一种确定性体系结构，它从用户提供的、以极简数学编程语言（Mathematical Programming Language，MPL）编写的公理化定义出发，系统性地探索其可配置的演绎邻域。该体系结构的一个定义性特征是其统一的基于哈希的推理引擎，该引擎同时执行代数操作和确定性逻辑变换。定义被编译成一个由简单逻辑块（Logic Blocks，LBs）组成的分布式网格，这些逻辑块交换消息；每当推理规则的前提被统一时，就会产生一个新的事实，并附带完整的来源追溯信息，从而生成可重放、可审计的证明图。实验验证在初等数论（Elementary Number Theory，ENT）上进行，采用了批处理执行策略。系统从基础公理和定义出发，首先发展出一阶皮亚诺算术，随后将其应用于自主推导并证明高斯求和公式作为主要结果。为了管理组合爆炸问题，GL通过算法枚举猜想，并应用规范化、类型约束和反例（counterexample，CE）过滤。在商用硬件上，一次端到端的运行在7分钟内完成。生成的证明可导出为可导航的HTML格式，使得每个推理步骤都可以被独立检查。我们概述了一条通向大规模并行实现的软硬件协同设计路径，并描述了未来与大型语言模型（large language models，LLMs）在自动形式化和猜想种子生成方面的集成。用于复现这些实验的Python、C++和MPL代码，以及HTML格式和机器可读文本格式的完整证明图，均可在项目的GitHub仓库（github.com/Generative-Logic/GL commit 1771330）获取，并已永久存档于doi:10.5281/zenodo.17206386。