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.

翻译：我们提出生成逻辑（Generative Logic, GL），这是一种确定性架构。它从用户以极简数学编程语言（MPL）提供的公理化定义出发，并系统性地探索其演绎邻域内的可配置区域。这些定义被编译成由逻辑块（Logic Blocks, LBs）构成的分布式网格，这些逻辑块通过统一的基于哈希的推理引擎进行通信；一旦某个规则的前提条件得到满足，就会发出一个带有完整来源的新事实，从而生成可重放、可审计的证明图。该流程包括一个自动生成基础事实表的孵化器（Incubator）、一个消除证明后冗余的压缩器（Compressor），以及一个独立的外部验证器（共34,320次检查，零失败）。在初等数论上的实验性验证从公理出发发展了皮亚诺算术，并自主推导出高斯求和公式。在普通硬件上，核心证明流程在不到一分钟内完成；包括孵化器事实生成的完整运行大约需要十分钟。孵化器的输出进一步揭示，GL能够执行具体的数值计算——每个结果都是一个带有完全来源的已证明定理——这为通向完全来源的计算机代数系统（CAS）开辟了道路。生成的证明可以导出为可导航的HTML格式以供独立检查。代码、证明图和复现说明可在 github.com/Generative-Logic/GL（提交号：6e5b9a4）获取，并归档于 doi:10.5281/zenodo.17206386。