A Triadic Minimality Thesis for Open Stability : Triadic Structure as the Minimal Non-Deletable Functional Configuration of Open-Stable Systems / 开放稳定的三元最小性命题
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2026
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| author | Chen, Ai ChatGPT Claude Sonnet Claude Opus |
| author_facet | Chen, Ai ChatGPT Claude Sonnet Claude Opus |
| contents | <p class="MsoNormal"><span>This paper proposes a structural claim that has been progressively narrowed under counter-example pressure: triadicity is not the minimal condition for stability as such, nor is it a direct demonstration of any ontological structure of being; it is, more plausibly, the minimal non-deletable functional configuration of open-stable systems. We define "open stability" as a phenomenological feature: a system that maintains identifiable continuity under not-fully-specified perturbations, whose subsequent states, response patterns, or structural traces are shaped by prior history, and which exhibits dependencies that cannot be fully reversed. The definition deliberately excludes any vocabulary that presupposes a third role — no "mediation," "selection," or "correction."</span></p> <p class="MsoNormal"><span>The central task of the paper is to argue: if a system continuously displays the phenomenological features of open stability, then its functional explanation requires at least three non-deletable functional roles. Formally, any complex system can be rewritten as a "state–transition" structure; but formal dyadicization is not functional dyadicization. If history, rules, perturbation-response, or error compensation are absorbed into an expanded state, one still has to explain how those contents are encoded, stored, read, retrieved, or updated. If such mechanisms cannot be deleted without the target function failing, they constitute candidate third functional roles.</span></p> <p class="MsoNormal"><span>We distinguish functional triadicity from implementational triadicity. The thesis is not a claim about the number of physical entities; it is a claim about the number of non-deletable functional roles. Two physical entities can carry three functional roles; many entities can carry only two. We introduce an operational criterion for reflexivity that does not import intentionality: reflexivity is defined as the presence of an internal deviation signal, an internal response, and a resulting change in subsequent operation. Finally, we state explicit surrender conditions: if a system, under locked target / boundary / scale / perturbation range, persistently exhibits the four phenomenological features of open stability while genuinely requiring only two non-deletable functional roles, the central claim is refuted.</span></p> <p class="MsoNormal"><span>本文提出一个经反例压力收缩后的结构命题:三元并非一切稳定结构的最小条件,也不是存在本体的直接证明;三元更可能是开放稳定系统在功能层面的最小不可删除结构。本文将<span>“</span>开放稳定<span>”</span>定义为一种现象层特征:系统在未完全预设的扰动条件下仍保持可识别连续性,其后续状态、响应方式或结构痕迹受过往经历影响,并呈现不可完全回退的历史依赖。该定义不预设三元,也不使用<span>“</span>中介、选择、修正<span>”</span>等已经暗含第三功能项的词汇。</span></p> <p class="MsoNormal"><span>本文的核心任务,是论证:若一个系统持续表现出开放稳定特征,则其功能解释中至少需要三个不可删除的功能角色。形式上,任何复杂系统都可以被重写为<span>“</span>状态<span>—</span>转移<span>”</span>结构,但形式二元化不等于功能二元化。若历史、规则、扰动响应或误差补偿被吸收入扩展状态,则必须说明这些内容如何被编码、保存、读取、调用或更新;这些机制若在目标功能中不可删除,即构成候选第三功能角色。</span></p> <p class="MsoNormal"><span><span>本文区分功能三元与实现三元。三元不是物理实体数量命题,而是功能角色命题。两个物理实体可以承担三个功能角色,多个实体也可能只构成两个功能角色。本文同时引入反身性的操作判据:反身性不指主体意向,而指系统内部存在偏离信号、内部响应和后续运行方式改变的结构。最后,本文明确提出投降条件:若存在一个系统在锁定目标、边界、尺度与扰动范围后,持续满足开放稳定现象特征,而功能层确实只需要两个不可删除角色,则本文核心命题被反驳。</span></span></p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_20308153 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | A Triadic Minimality Thesis for Open Stability : Triadic Structure as the Minimal Non-Deletable Functional Configuration of Open-Stable Systems / 开放稳定的三元最小性命题 Chen, Ai ChatGPT Claude Sonnet Claude Opus triadic structure open stability functional non-deletability state machines reflexivity Peirce Reduction Thesis falsifiability <p class="MsoNormal"><span>This paper proposes a structural claim that has been progressively narrowed under counter-example pressure: triadicity is not the minimal condition for stability as such, nor is it a direct demonstration of any ontological structure of being; it is, more plausibly, the minimal non-deletable functional configuration of open-stable systems. We define "open stability" as a phenomenological feature: a system that maintains identifiable continuity under not-fully-specified perturbations, whose subsequent states, response patterns, or structural traces are shaped by prior history, and which exhibits dependencies that cannot be fully reversed. The definition deliberately excludes any vocabulary that presupposes a third role — no "mediation," "selection," or "correction."</span></p> <p class="MsoNormal"><span>The central task of the paper is to argue: if a system continuously displays the phenomenological features of open stability, then its functional explanation requires at least three non-deletable functional roles. Formally, any complex system can be rewritten as a "state–transition" structure; but formal dyadicization is not functional dyadicization. If history, rules, perturbation-response, or error compensation are absorbed into an expanded state, one still has to explain how those contents are encoded, stored, read, retrieved, or updated. If such mechanisms cannot be deleted without the target function failing, they constitute candidate third functional roles.</span></p> <p class="MsoNormal"><span>We distinguish functional triadicity from implementational triadicity. The thesis is not a claim about the number of physical entities; it is a claim about the number of non-deletable functional roles. Two physical entities can carry three functional roles; many entities can carry only two. We introduce an operational criterion for reflexivity that does not import intentionality: reflexivity is defined as the presence of an internal deviation signal, an internal response, and a resulting change in subsequent operation. Finally, we state explicit surrender conditions: if a system, under locked target / boundary / scale / perturbation range, persistently exhibits the four phenomenological features of open stability while genuinely requiring only two non-deletable functional roles, the central claim is refuted.</span></p> <p class="MsoNormal"><span>本文提出一个经反例压力收缩后的结构命题:三元并非一切稳定结构的最小条件,也不是存在本体的直接证明;三元更可能是开放稳定系统在功能层面的最小不可删除结构。本文将<span>“</span>开放稳定<span>”</span>定义为一种现象层特征:系统在未完全预设的扰动条件下仍保持可识别连续性,其后续状态、响应方式或结构痕迹受过往经历影响,并呈现不可完全回退的历史依赖。该定义不预设三元,也不使用<span>“</span>中介、选择、修正<span>”</span>等已经暗含第三功能项的词汇。</span></p> <p class="MsoNormal"><span>本文的核心任务,是论证:若一个系统持续表现出开放稳定特征,则其功能解释中至少需要三个不可删除的功能角色。形式上,任何复杂系统都可以被重写为<span>“</span>状态<span>—</span>转移<span>”</span>结构,但形式二元化不等于功能二元化。若历史、规则、扰动响应或误差补偿被吸收入扩展状态,则必须说明这些内容如何被编码、保存、读取、调用或更新;这些机制若在目标功能中不可删除,即构成候选第三功能角色。</span></p> <p class="MsoNormal"><span><span>本文区分功能三元与实现三元。三元不是物理实体数量命题,而是功能角色命题。两个物理实体可以承担三个功能角色,多个实体也可能只构成两个功能角色。本文同时引入反身性的操作判据:反身性不指主体意向,而指系统内部存在偏离信号、内部响应和后续运行方式改变的结构。最后,本文明确提出投降条件:若存在一个系统在锁定目标、边界、尺度与扰动范围后,持续满足开放稳定现象特征,而功能层确实只需要两个不可删除角色,则本文核心命题被反驳。</span></span></p> |
| title | A Triadic Minimality Thesis for Open Stability : Triadic Structure as the Minimal Non-Deletable Functional Configuration of Open-Stable Systems / 开放稳定的三元最小性命题 |
| topic | triadic structure open stability functional non-deletability state machines reflexivity Peirce Reduction Thesis falsifiability |
| url | https://doi.org/10.5281/zenodo.20308153 |