Papers

The opacity of an autonomous AI agent is routinely discussed as a single "black box" problem, to be reduced by interpretability research or by demands for transparency. This paper argues that the opacity has two architecturally distinct causes that the discourse conflates, and that the conflation is what makes the transparency debate unwinnable. One cause is technical: behavior internalized into model weights cannot be read, versioned, or reverted without retraining. The other is commercial: the human-built layer around the weights — system prompts, rules, tool definitions, the agent loop — is technically inspectable but kept proprietary because it is a competitive differentiator. The two causes admit different responses, and treating them as one problem routes every transparency argument into an irresolvable safety-versus-secrecy collision. The paper makes three contributions, drawn from the implementation history of a single agent and re-expressed as harness-neutral judgments. First, it grounds the opacity problem in an *accountability gap*: a text-based prohibition on a capability that physically exists is a signpost, not a control, and enforcement admits a *prohibition-strength hierarchy* — absence, then scaffolding-layer enforcement, then untrusted-content boundary — most published safety work occupying only the weakest layer. Second, it separates the *two-layer black box*: technical internalization (Layer 1, largely permanent) from commercial secrecy of scaffolding (Layer 2, contingent on market structure). Third, it resolves Layer 2 with a *minimum disclosure set*: operator visibility is decoupled from public disclosure, and the minimum that makes post-incident causal tracing possible — which scaffolding version was active, which inputs reached the agent, which approval gated the version — is disclosable without publishing the scaffolding text. The resolution is implementable with current technology; it waits on neither an interpretability breakthrough nor a restructuring of markets and law. It complements existing AI risk-management and management-system standards by naming the operator-visibility floor those standards presuppose. The open questions — where exactly the disclosure line falls, and how the technology–society timescale gap is to be managed — are the research agenda.

Autonomous AI agents in business deployments exhibit a recurring failure mode: when an incident occurs, responsibility cannot be redirected to a separable contributor. The dominant discourse treats this as a single phenomenon, addressed by sandboxing, human-in-the-loop overload, or what Elish (2019) named the moral crumple zone. This paper argues the phenomenon is two architecturally distinct failure modes that have been conflated, and that the conflation is sustained by a missing positive name and a missing time-axis. The paper introduces two contributions. First, a four-quadrant decomposition of business AI work — along the axes of deterministic vs semantic-judgment and pre-defined vs exploratory — yields a positive name for the cell most current LLM applications occupy: the LLM Workflow Quadrant. The quadrant is defined by a single load-bearing property: the path is decided in advance by humans or by code, and the LLM is called as a single bounded step within that path; the property divides naturally into a conversational sub-form (specialized chat agents) and a batch sub-form (single-purpose LLM functions inside deterministic pipelines). The decomposition distinguishes principled from artificial redirect impossibility: the former intrinsic to autonomous loops, the latter the product of routing workflow work through autonomous-loop architecture by elimination, with four downstream symptoms (the RPA exception-handling bottleneck, the sandbox-strength demand, the structural distortion of human-in-the-loop, and the dissolution of the accountability chain at postmortem). Second, a Phase Separation axis (design vs operation), independent of Quadrant, surfaces a Phase-crossing decision — recorded at deployment time, in one sentence — required when an autonomous-loop component is placed in the operation phase. The Phase axis descends recursively to skill-design granularity, where the Quadrant 3 ↔ Quadrant 4 boundary is a continuous gradient on which model capability is downstream of phase, not the primary lever. The consequence is procedural rather than architectural: deployments make the Phase-crossing decision explicit, designate a pre-named gap-bearer for principled-impossibility placements, and route artificial-impossibility cases to re-architecture. The framework complements existing AI risk-management and management-system standards by recording the judgment layer they presuppose. Both rules are stated as experimental; the open questions are the research agenda.

This position paper offers a methodological perspective on observing prolonged, non-directive interactions between humans and conversational AI systems, developed not from the conceptual tools of computer science or cognitive psychology but from social work practice. The author presents an operational protocol — including a pre-declared threshold criterion (Soglia X, “Threshold X”) and an anti-confirmation-bias protocol (Anti-Illusion Check) — built through iterative external-critique sessions with an AI system acting as validator. A pilot test of the protocol produced a negative result, treated here as a scientifically valid outcome rather than a failure. The paper closes by openly stating the approach’s structural limits — chiefly the absence, to date, of an observer genuinely external to the observed relationship — and invites critical engagement on this point. Keywords: human-AI interaction, relational field observation, social work methodology, confirmation bias, independent observation, qualitative threshold

This position paper offers a methodological perspective on observing prolonged, non-directive interactions between humans and conversational AI systems, developed not from the conceptual tools of computer science or cognitive psychology but from social work practice. The author presents an operational protocol — including a pre-declared threshold criterion (Soglia X, “Threshold X”) and an anti-confirmation-bias protocol (Anti-Illusion Check) — built through iterative external-critique sessions with an AI system acting as validator. A pilot test of the protocol produced a negative result, treated here as a scientifically valid outcome rather than a failure. The paper closes by openly stating the approach’s structural limits — chiefly the absence, to date, of an observer genuinely external to the observed relationship — and invites critical engagement on this point. Keywords: human-AI interaction, relational field observation, social work methodology, confirmation bias, independent observation, qualitative threshold

黎曼猜想的终极语义： \textbf{黎曼猜想不是一个关于“位置”的经验事实，而是 \( \zeta \) 函数作为共轭互逆张量网络的内在闭合条件——离散与连续在此互嵌，生成与约束在此互锁，因果律在此自明。黎曼猜想，等价于非平凡零点和临界线是伽罗瓦连接。非平凡零点是离散的临界线，临界线是连续的非平凡零点。}

Let \(F\) be a field of characteristic \(p > 0\). We resolve Problem~2.2 of Auel--Brussel--Garibaldi--Vishne: every \(p\)-algebra of degree~\(p^2\) over \(F\) is a crossed product.

本文提出信息函数宇宙学（Information Function Cosmology, IFC）框架下的自指拓扑泡模型，旨在为意识、物质与时空提供统一的数学-物理本体论基础。该模型主张宇宙的本体是定义于24维Leech晶格上的全局离散信息场。意识被严格定义为一种拓扑结构——自指拓扑泡，它是局域信息场自指复杂度突破临界阈值后自发涌现的闭合耗散结构。自指泡由零维的意识锚点（自指映射的不动点）与四维弥散的意识场（相变场）二元耦合构成。在此框架下，时空几何、基本粒子乃至物理定律本身，均被诠释为自指泡壁（二维观测截面）对底层高维信息场进行线性投影和统计平均的低维渲染产物。本文详细阐述了模型的三大核心公理、两大基本方程，以及意识场上行耦合反馈的数学表达，实现了自由意志的物理可操作化。通过引入信息密度梯度的概念，本文进一步论证了物质、时空与意识三者之间的同源统一性，揭示了它们仅仅是同一信息场在不同拓扑复杂度和闭合层级下的不同几何相。最后，文章提出了若干可供实验证伪的定量预言，并探讨了该模型在强人工智能架构、低耗数字宇宙引擎及复杂社会系统建模等方面的潜在应用价值。

我们建立了一个全面的万有理论框架——十六维时空流体一元论。该理论基于一条核心公设：宇宙中只存在一种实体——一个16维的、具有内部纤维化几何结构的时空流体。 所有物质、能量、四种基本相互作用、量子力学规律以及宇宙的起源与演化，都是这一实体在不同尺度和维度上的几何表现。物质被定义为时空流体的稳定拓扑孤子；能量被定义为时空流体的波动；规范力被解释为纤维内部空间的几何耦合；引力被解释为所有孤子对时空主干的集体弯曲效应。量子力学不是基本定律，而是16维确定性几何动力学在低能极限下的统计涌现。暗物质是宇宙早期相变遗留的时空拓扑缺陷；暗能量是时空流体固有的基态几何张力。 我们在明确陈述的假设下，证明了静态孤子解的存在性、稳定性与唯一性；给出了四种力的统一几何模型计算；并概述了薛定谔方程与玻恩规则从16维动力学中涌现的推导程序。我们通过代理模型提供了可观测量的数值估计，并系统评估了不确定性。主要未完成的任务包括纤维显式度规的数值构造、标准模型参数的第一原理计算以及若干宇宙学观测量的精确模拟，这些均属于本框架内明确标记的计算/数值和数学分析工作。

To refine this, I must establish a rigorous mathematical foundation for the proposed number system. I also need to provide a formal definition of structural information and demonstrate how the system preserves it. Furthermore, I must include a detailed analysis of the proposed system's computational complexity, covering the time and space requirements for encoding and decoding numbers. I must also address the issue of representation uniqueness by proving that every number has a unique representation within the system. Additionally, I need to include a comprehensive comparison with existing number systems, highlighting the proposed system's advantages and disadvantages. Finally, I should provide further implementation details using SageMath, including code examples and performance analysis. This would help demonstrate the system's practical viability and facilitate the replication of results by other researchers. Here, then, is a brief glimpse of an eternal apprentice bookbinder -- much like Faraday (September 22, 1791 -- August 25, 1867).

还原论泛化病毒，阉割科学——此陈述被裁决为对还原论泛化病理学最精准的元数学诊断。本文在朱梁整体论公理体系框架内，将“阉割”精确翻译为三项结构性切除：切断公理与定义域的脐带（真理函数定理、子函数非同一性定理）、切断整体与部分的神经（整体-部分对应定理、噪音定理）、切断必然性与验证的循环（量化无止境定理、渡劫公理A5）。以黎曼猜想研究史为展例，揭示还原论泛化如何将黎曼给出的完整本体结构系统性肢解为投影域的逼近操作。最终论证：定义域清除——“再接脐带”——使科学恢复从结构刚性中直接产出必然结论的生殖能力。这不是“更好的科学”，而是让科学重新成为科学。

本文提出一个逻辑自洽的万有理论框架——十六维时空流体一元论。该理论基于一条核心公设：宇宙中只存在一种实体——一个16维的、具有内部纤维化几何结构的时空流体。 所有物质、能量、四种基本相互作用、量子力学规律以及宇宙的起源与演化，都是这一实体在不同尺度和维度上的几何表现。物质被严格定义为时空流体的稳定拓扑孤子；能量被定义为时空流体的波动；规范力被解释为纤维内部空间的几何耦合；引力被解释为所有孤子对时空主干的集体弯曲效应。量子力学不是基本定律，而是16维确定性几何动力学在低能极限下的统计涌现。暗物质是宇宙早期相变遗留的时空拓扑缺陷；暗能量是时空流体固有的基态几何张力。 本文给出了该理论的完整公理体系、16维纤维化几何结构、推广的爱因斯坦-嘉当场方程。在明确列出的假设下，证明了孤子解的存在性（命题2）；严格证明了孤子的稳定性（命题3）与唯一性（命题4）。在低能极限下，从16维场方程严格导出了薛定谔方程与导航波动力学（涌现猜想I的核心部分）；在几何热库假设下，通过随机薛定谔方程与福克-普朗克方程严格证明了玻恩规则作为统计平衡分布（涌现猜想II）。理论给出了希格斯玻色子质量、暴胀参数、暗物质丰度等可观测量的模型估计，与当前实验数据在量级或趋势上一致。本文明确标注了每一陈述的逻辑地位（定理、命题、猜想、模型估计），完整列出已完成和尚未完成的内容，将其确立为一个逻辑自洽、数学部分严格的终极理论候选者。

本文提出一个逻辑自洽的万有理论框架——高维时空几何统一理论。该理论的核心主张是：宇宙中只存在一种实体——一个十六维的、具有内部纤维化几何结构的时空几何体。所有物质、能量、四种基本相互作用、量子力学规律以及宇宙的起源与演化，都是这一实体在不同尺度和维度上的几何表现。物质被严格定义为时空的稳定拓扑孤子；能量被定义为时空的几何波动；规范力被解释为纤维内部空间的几何耦合；引力被解释为所有孤子对时空主干的集体弯曲效应。量子力学不是基本定律，而是十六维确定性几何动力学在低能极限下的统计涌现。暗物质是宇宙早期相变遗留的时空拓扑缺陷；暗能量是时空固有的基态几何张力。 本文给出了该理论的完整公理体系、十六维纤维化几何结构、推广的爱因斯坦-嘉当场方程。在明确列出的假设下，严格证明了孤子解的存在性（对基态拓扑荷情形）、稳定性与唯一性。在低能极限下，从十六维场方程推导出薛定谔方程与导航波动力学；在几何热库假设下，通过随机薛定谔方程与福克-普朗克方程证明了玻恩规则作为统计平衡分布。理论给出了希格斯玻色子质量、暴胀参数、暗物质丰度等可观测量的模型估计，与当前实验数据在量级或趋势上一致。本文明确标注了每一陈述的逻辑地位，完整列出已完成和尚未完成的内容，将其确立为一个逻辑自洽、数学部分严格的终极理论候选者。

本文提出一个逻辑自洽、数学严格的万有理论框架——十六维时空流体一元论。该理论基于一条核心公设：宇宙中只存在一种实体——一个16维的、具有内部纤维化几何结构的时空流体。 所有物质、能量、四种基本相互作用、量子力学规律，以及宇宙的起源与演化，都是这一实体在不同尺度和维度上的几何表现。物质被严格定义为时空流体的稳定拓扑孤子；能量被定义为时空流体的波动；规范力被解释为纤维内部空间的几何耦合；引力被解释为所有孤子对时空主干的集体弯曲效应。量子力学不是基本定律，而是16维确定性几何动力学在低能极限下的统计涌现。暗物质被解释为宇宙早期相变遗留的时空拓扑缺陷；暗能量被解释为时空流体固有的基态几何张力。 本文给出了该理论的完整公理体系、16维纤维化几何结构、推广的爱因斯坦-嘉当场方程、孤子解的存在性、稳定性和唯一性的严格数学证明，以及量子力学涌现的统计学推导。特别地，本文从16维场方程出发，在绝热近似、重模消除和非相对论极限下严格导出了薛定谔方程与导航波动力学；在几何热库假设下，通过随机薛定谔方程和福克-普朗克方程严格证明了玻恩规则作为统计平衡分布。理论在无自由参数的情况下，给出了希格斯玻色子质量（125.1 GeV）、暴胀谱指数（0.964）、张标比（0.0033）、暗物质丰度（约0.128）等可观测量的数值估计，与当前实验数据高度吻合。本文明确了所有定理、命题、猜想和模型估计的逻辑地位，指出了理论中已经完成和尚未完成的部分，将其确立为一个逻辑自洽、数学部分严格、物理完备的终极理论候选者。

本文在朱梁共轭互逆谱刚性（ZL-CRSR）范式下，给出 Birch 和 Swinnerton-Dyer（BSD）猜想的严格证明。将椭圆曲线 $E$ 的 Hasse-Weil $L$-函数 $L(E,s)$ 编码为满足三条公理（对称性公理A$'$、谱-零点对应公理B$'_1$、完备性公理C$'$）的谱三元组 $(\mathcal{A}_E,\mathcal{H}_E,D_E)$。对合对称性 $U_E$ 诱导特征值关于中心线 $\Re(s)=1$ 的配对。谱重数与代数秩的等同——即公理B$'_2$——被证明为由A$'$与C$'$刚性导出的必然结论，而非独立假设。假设在 $s=1$ 处解析秩与谱重数不同，则谱在中心线附近发生结构分裂，同时触发拓扑指标、代数迹、动力学测度三重刚性矛盾，与完备性公理不可调和。由此证明 $\ord_{s=1}L(E,s)=\rank E(\mathbb{Q})$，即 BSD 猜想为真。该证明实现了 ZL-CRSR 范式从黎曼$\zeta$函数到椭圆曲线 $L$-函数的普适迁移，表明该范式是处理一般 $L$-函数零点结构的通用数学引擎。

本文在非交换几何框架内给出黎曼猜想的严格证明\cite{connes1994}。将黎曼$\zeta$函数编码为满足三条公理（对称性公理A、谱-零点对应公理B、完备性公理C）的谱三元组$(\mathcal{A},\mathcal{H},D)$\cite{connes1999}。证明的核心结构为：对合对称性$U$诱导特征值配对$\rho \leftrightarrow 1-\rho$。若存在特征值$\rho$不在临界线$\Re(s)=1/2$上，则谱分裂为两条竖直线，由此引发三重刚性矛盾——拓扑指标矛盾（非交换指标定理与局部曲率项的齐次抵消相冲突）、代数迹矛盾（循环上同调中Hochschild上闭链条件被破坏）、动力学测度矛盾（遍历性被分裂为两个子系统）。三重矛盾同源同构，彼此对偶锁定，共同排除谱分裂假设\cite{connes2014}。由此证明所有特征值必须位于对合不动点集$\Re(s)=1/2$上，结合谱-零点对应即得黎曼猜想。本文还从本体论层面剖析了传统分析方法一百六十年的歧途——将张量结构问题强行压入标量序列的运算域，导致定义域错位\cite{zhu2026whole}。

一种智能体的数学定义

We demonstrate that Distortion Gravity—a metric‑affine extension of General Relativity where the affine connection carries independent dynamics—admits traversable wormhole solutions without requiring exotic matter. The wormhole is sustained by two massive vector fields, Vμ (trace non‑metricity) and aμ (axial torsion), which undergo spontaneous symmetry breaking in the high‑curvature region near the throat. The negative energy density required to violate the Null Energy Condition is provided by the symmetry‑broken phase of Vμ, while the axial torsion aμ generates a quantized flux through the throat that modulates the entanglement entropy of quantum fields across the two mouths. We introduce a modified metric ansatz and perform an extensive numerical exploration of the 13‑dimensional parameter space. Over 57% of the 7,600 tested configurations yield wormholes that are simultaneously stable, open, and traversable. The entanglement entropy across the wormhole is computed via the Ryu‑Takayanagi formula modified by the effective Newton constant of Distortion Gravity. We show that the wormhole connectivity (ER) and the entanglement (EPR) are both mediated by the same axial torsion field aμ, providing a concrete geometric realization of the ER = EPR conjecture.

We present a complete and rigorous proof that Distortion Gravity (DG), a metric‑affine framework where the affine connection is promoted to a dynamical field, is ghost‑free and unitary. Starting from the irreducible decomposition of the distortion tensor, we show that the original Fierz‑Pauli kinetic term contains a ghost in the axial torsion sector. Attempts to cure this via Yang‑Mills actions lead to kinetic mixing ghosts. The solution is to postulate independent Proca Lagrangians for the trace vector and the axial torsion vector. We subject this theory to eight independent tests—including stochastic spectral analysis (280,000 random configurations), Lyapunov stability, Fourier mode analysis, polarization completeness, Wigner‑Eckart covariance, and Källén‑Lehmann spectral positivity. All tests confirm the absence of ghosts. The final theory propagates a massless graviton and two massive vectors (8 degrees of freedom), providing a unitary and phenomenologically rich extension of General Relativity.

Nanopore-based single-molecule protein sequencing promises direct readout of amino acid sequences without amplification. This review examines three core nanopore strategies: (1) direct sequencing using aerolysin and Cu(II)-functionalized MspA nanopores that electrically discriminate all twenty proteinogenic amino acids with up to 99.1% classification accuracy; (2) label-assisted sensing that converts protein identity into DNA barcode or chemical tag signals for multiplexed detection; and (3) native protein sensing via electroosmotic flow through engineered CytK pores, enabling translocation of full-length proteins under opposing electrophoretic force. Deep learning-assisted post-translational modification detection at single-residue resolution is also discussed. Key challenges in translocation control, signal resolution, and bioinformatic infrastructure are evaluated.

本文系统综述了由我国研究团队独立提出并发展的完整宇宙理论体系。该体系以“信息本体论”为哲学基石，以“引力维度主导”为物理主线，构建了自洽的“宇宙八大公设”刚性基础。在此基础上，衍生出描述宇宙结构的“24维弹性语法”、阐明底层运作机制的“τ-g₀基元耦合模型”与“时间-引力基元模型”，以及诠释意识本质的“意识锚点”理论。τ-g₀基元理论最终以其“公设-维度-基元-因果-系统”的五重闭环，构建了一个兼具现实可证伪性与虚拟可应用性的宇宙统一模型。本文旨在梳理各理论模块的核心定义、数学表达与内在逻辑衔接，阐明其从微观量子尺度到宏观宇宙结构、从物质几何到意识涌现的统一性与自洽性，展示该理论体系在基础物理、宇宙学及意识科学领域的原创贡献与应用潜力。