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Across physical, biological, and Socio-technical domains, many long-lived systems operate neither near thermodynamic equilibrium nor as short-lived non-equilibrium transients. Instead, they persist as nonequilibrium steady states sustained by irreversible processes, continuous throughput, and finite structural carrying capacity. Despite this, prevailing analytical and design frameworks often rely on equilibrium references, point-valued state descriptions, or optimality-based objectives. While effective for short-term or approximately closed systems, these approaches become systematically mismatched for systems operating over extended durations under irreversible dissipation, where statistical stationarity may coexist with structural degradation. We adopt the premise that observation is inherently embedded within the system and remains valid only relative to explicitly declared observational frames and temporal scales. Under unavoidable partial observability, non-equilibrium existence is diagnosed not by trends or performance metrics, but by the persistence of irreversible directional structures that survive statistical stabilization and are invalidated under time reversal. We introduce a structural diagnostic framework based on (i) observation–structure mismatch, (ii) inner–outer cycle coupling admitting discrete regimes, and (iii) pathology localization at high-coupling nodes. When driving fields are not directly measurable, an inverse-measurement perspective is employed, treating structural stress responses as probes of system-wide pressures. Within this framework, resilience is redefined as the preservation of reversible coupling intervals, and design is repositioned as a bounded structural modulator rather than an optimization mechanism.

Across domains including artificial intelligence, scientific research, education, public health, industrial design, and social organization, system failures are increasingly experienced as abrupt, complex, or resistant to localized intervention. This paper argues that these failures share a common structural origin: a systematic misalignment between deployed evaluation frameworks and the intrinsic failure spaces of the systems they seek to govern. Rather than treating breakdowns as isolated malfunctions, the analysis conceptualizes them as manifestations of residual fields-accumulated system dynamics that remain unprojected and therefore invisible under incompatible coordinate frames. From this perspective, failure emerges not from singular defects, but from the progressive accumulation of dynamics excluded by prevailing modes of evaluation. By reframing diagnosis around domain-specific coordinate construction instead of universal metrics, this work offers a unified explanatory lens for understanding failure across technical, institutional, and biological systems, without advancing prescriptions, methods, or future commitments.

抑郁呈现一个核心悖论。从基因到社会压力，极端异质的触发因素收敛于高度协调的表型组合。这种模式跨越物种、保守数亿年，且找不到一致的结构性损伤证据。这究竟是系统故障，还是被激活的功能性程序？为解决这一悖论，我们构建了程序特征指数PFI作为黑箱推断工具，通过输入异质性、输出协调性、跨物种保守性三个维度量化程序性证据支持强度，并用可退出性进行独立验证。对56种生命现象的计算显示，抑郁落入高PFI组，与睡眠、呕吐等公认的程序并列。如果抑郁是程序，又为何呈现病理状态？本研究提出抑郁是系统能效比持续下降后触发的程序性反应，在演化历史中具有特定功能，但在现代环境中常常错误激活，或陷入难以退出的病理状态。本文是系列研究的第一部分，第二部分将提出能效假说及神经实现，第三部分将论述古代起源和现代失配，系统回答这一问题。

本报告针对金刚石-石墨烯范德华超晶格体系，构建晶格拓扑-电子输运-声子调制三维耦合网络模型，提出从液氮温区（77K）至室温（300K）的超晶格拓扑工程调控路线。该模型基于超晶格三维网络的耦合自由度匹配原理，通过对金刚石-石墨烯异质结的晶格拓扑精准修饰，实现三网耦合强度的临界调控，突破传统超导体系的温度限制；模型预测，当三维网络达到临界耦合阈值时，体系将呈现非渐进式的拓扑相变，超导性能从“无（0）”阶跃式达到“理想态（100%）”，无中间过渡态。本路线图明确了分阶段的拓扑工程调控手段、表征方法与性能验证标准，为金刚石-石墨烯超晶格室温超导材料的实验制备与性能调控提供可落地的理论框架，该体系兼具金刚石的结构稳定性与石墨烯的高载流子迁移率，是室温超导材料的潜在优选体系。

我们为计算代理的经济行为发展了一套严格的数学理论，实现了三个层次的统一：几何层（信任-延迟度量）、动力学层（平均场博弈）和拓扑层（资源流形）。主要贡献包括： （1）双尺度图极限理论（Graphon-BS）：我们为稠密和稀疏网络发展了统一框架。对于稠密网络（E/S 型），使用 Graphon 极限；对于稀疏网络（I 型），引入Benjamini-Schramm局部弱收敛，解决了先前理论在星际尺度网络中的适用性问题。 （2）相变定理：我们严格证明了资源流形几何参数（紧致性、通信延迟标度）与 Nash 均衡组织形式之间存在临界相变，给出了具有说明性数值估计的显式特征方程（r∗ ≈ 84 AU， 基于示例参数）。 （3）Chaitin 不可计算风险理论：我们将合约违约概率映射到 Chaitin Ω 数，证明某些风险度量是本体论上不可计算的——不仅仅是信息不足，而是受到数学本身的根本限制。这为” 不可判定溢价” 提供了最严格的理论基础。 （4）复杂性-模糊性对应：我们猜想逻辑不可判定性与 Knight 不确定性之间存在对应关系，将 Gödel 边界映射到概率空间中的模糊集。该对应关系的严格形式化作为开放问题提出。 所有主要结果均给出完整证明或明确标注为猜想，在定理、命题和猜想之间保持清晰区分。