从作者式数学到工作室式数学：大型语言模型之后的证明的生态生物形式
From Authorial Mathematics to Studio Mathematics:Ecobiontic Forms of Proof after Large Language Models
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中文总结 AI 辅助
本文探讨大型语言模型等技术催生的人机集合体（工作室生态生物）的认识合法性，提出需满足可追溯来源等治理条件，通过案例分析明确协作等维度的独立性，未声称其优于传统作者式数学实践。
中文摘要 AI 辅助
数学通常围绕作者式主体组织：一个人或一小群人通过语言、符号和判断构建证明。大型语言模型（Large Language Models）、证明助手（proof assistants）、形式库及存储库如今使另一种生产单元在技术上变得可信：人机集合体。本文将该单元称为工作室生态生物（studio ecobiont），并探讨其在认识上何时具有合法性。其治理论点为：只有当系统保留可追溯的来源、可重构的人类能力、质疑结果的能力、阻止或撤回结果的有效权限以及公共责任时，人类参与才是实质性的。这些条件区分了受治理的工作室与人类监督仅为仪式性的退化工作室。对Polymath、Liquid Tensor Experiment、Danus及Jacobian反例事件的比较表明，协作、形式化、技术编排和认识治理是相互独立的维度。所提出的理解审计和贡献权限追踪是治理设计，而非已验证的措施。本文未声称其相较于作者式实践具有因果优越性。
英文摘要
Mathematics has often been organized around an authorial subject: one person, or a small group, composing proofs through language, notation, and judgment. Large language models, proof assistants, formal libraries, and repositories now make another production unit technically credible: a human-machine assemblage. This article calls that unit a studio ecobiont and asks when it is epistemically legitimate. Its governance thesis is that human participation is substantive only when the system preserves traceable provenance, reconstructible human competence, capacity to challenge the result, effective authority to stop or withdraw it, and public responsibility. These conditions distinguish a governed studio from a degenerate studio whose human oversight is ceremonial. A comparison of Polymath, the Liquid Tensor Experiment, Danus, and the Jacobian counterexample episode shows that collaboration, formalization, technical orchestration, and epistemic governance are independent dimensions. The proposed understanding audit and contribution-authority trace are governance designs, not validated measures. No causal superiority over authorial practice is claimed.
