Papers

共轭互逆结构法则与BSD猜想的结构性必然证明

共轭互逆法则与P vs NP问题的结构性证明

共轭互逆结构法则与霍奇猜想的否定性证明

杨‑米尔斯存在性与质量间隙的伽罗瓦连接证明

Navier–Stokes光滑解的伽罗瓦连接证明

Non‑trivial zeros and the critical line are not two things that need to be connected; they are the ``nature'' and the ``appearance'' of one and the same conjugate‑inverse structure. Non‑trivial zeros are the roots of the critical line, and their computed instances are discrete sampling points of the critical line.

Large language models (LLMs) display impressive semantic capabilities, yet the internal structure of meaning within these systems remains poorly understood. Existing approaches—vectorspace semantics, contextual embeddings, and quantum-inspired models—capture important regularities but offer no unified account of phase, interference, and contextual shifts, which are central to semantic behavior in LLMs. This paper proposes Noetica Theory, a mathematical framework that represents meaning as a semantic wave function defined over a context-dependent phase space. In this formulation, each meaning state is expressed as a complex-valued function whose amplitude encodes semantic salience and whose phase captures relational structure. We define semantic entropy, semantic phase order, and semantic free energy, providing quantitative measures of coherence, contextual alignment, and semantic stability. We show that semantic interference, context updates, and compositional behavior emerge naturally from the wave-based formulation. Applying this framework to LLMs, we reinterpret embeddings as normalized meaning waves, attention as an interference-based filtering mechanism, and hidden-state dynamics as trajectories within semantic phase space. This perspective yields coherent explanations for mode shifts, prompt sensitivity, and context-conditioned meaning transitions observed in modern LLMs. Noetica Theory thus provides a unified mathematical basis for semantic modeling, connecting linguistic theory, cognitive science, and mechanistic interpretability, and offering general-purpose tools for analyzing and predicting semantic behavior in large generative models. This paper is also archived on Zenodo: DOI 10.5281/zenodo.17750900

“还原论是 ASCII，整体论是 UTF-8”不是比喻而是一条基于结构语法范畴对立的纯粹方法论定理。本文在 ECT-OS-JiuHuaShan 框架内，剥离标量分类，沿结构语法三维——孤立/依赖、离散/闭、简单类型/依赖类型——给出该定理的严格形式化证明。核心不依赖形式语言层级，而直接在元语法层操作：还原论对应定长孤立语法（离散范畴、简单类型、ASCII），整体论对应变长共轭同步语法（闭范畴、依赖类型、UTF-8），并由此导出范畴不兼容定理（定理2.15）：标量命题集与张量命题集的交集为空。文章还从六个维度论证该证明的历史意义与文明价值，并在附录展示该定理对黎曼猜想方法论终审的完整应用。结论强调方法论可由哲学意见上升为可判定的科学命题，整体论获得现代科学语境下的平等地位，范式革命完成。

黎曼猜想从来不是“猜想”。它只是共轭互逆结构在数论领域的一个签名，等待理性认出它本然的面目。当伽罗瓦连接的满性条件 $F_{\mathcal{R}}(Z)=L$ 被从公理系统中严格推演而出时，这一认出已经完成。非平凡零点即是临界线的根，其实例是临界线的离散采样点。 理性本有能力认出共轭互逆的全局语法（整体论），却把自己压缩进逐点验证的狭窄通道（还原论），然后声称“这通道是唯一的路径”。它用自己制造的局限，来证明局限之外的东西不存在。它将计算运用的执法功能，僭称为逻辑证明的立法功能。它将利息的支付，伪装成本金的兑付。

本文严格建立了还原论与ASCII、整体论与UTF-8之间的精确对应，并揭露：还原论在黎曼猜想研究中的运作，实质上构成一个庞氏骗局——用每一代新数据（利息）维持“最终证明即将到来”的信用，而全称必然性的证明（本金）从未生产且永不能生产。

非平凡零点与临界线，不是两个需要被联系起来的事物，而是同一个共轭互逆结构的“性”与“相”。非平凡零点是临界线的根，其计算实例是临界线的离散采样点。

The rapid growth of AI conference submissions is putting new pressure on peer review. AI reviewer systems are increasingly proposed as support, but prior work leaves unresolved what responsibility their outputs should carry when they can surface useful critiques yet remain risky as independent judgments. We frame this as a responsibility-boundary problem. Using 600 ICLR 2026 submissions, 2231 human review traces, and 3,600 AI reviews, we operationalize this boundary through usable feedback, score use, panel breadth, and grounded synthesis. The results show that AI can prepare candidate critiques, organize evidence, and improve feedback, while scoring, independent panel judgment, high-level synthesis, and final responsibility should remain human-led. Motivated by this boundary, we develop Review Copilot, a workflow in which AI suggestions are inspected, edited, or rejected by human reviewers and provide neither official scores nor recommendations. In an initial controlled reviewer-in-the-loop study, Human+AI reviews improve actionability, evidence support, and professionalism relative to standalone baselines while preserving human authorship of scores and recommendations. Our results point toward a review paradigm in which AI expands the space of evidence-grounded critique, while humans remain responsible for judgment, synthesis, and accountability

By early 2026, the discourse around agent harnesses — the configuration layer of skills, rules, prompts, and documentation shaping an LLM agent's behavior — has named two activities: harness engineering, the reactive practice of ensuring an agent never repeats a mistake, and harness optimization, autonomous search over harness code for benchmark score. Both run against fixed, checkable criteria. The activity on the other side — keeping the harness aligned with what its operator now wants, where the criterion moves — is performed daily and has, to the author's knowledge, no established name. The paper defines harness alignment — the continuous, human-gated activity of keeping an agent's harness aligned with the operator's evolving intent — and its failure mode, harness drift. The three defining properties — continuous, human-gated, bidirectional — follow from a single root: intent, unlike correctness, cannot be automated the same way — it has no verifier outside the operator, and moves as the operator's judgment sharpens; verifying intent sharpens the judgment doing it, so the loop moves its own target. An automated check freezes intent into a specification, reducing its automatable part to correctness work. A four-domain search found no established term covering all three; an audit shows 2026 drift coinages severed from the classical lineage that harness drift bridges. A six-phase cycle (Research, Extract, Curate, Promote, Measure, Maintain) operationalizes it over a memory structure whose boundary separates freely-writable records from gated behavior-shaping artifacts. Failure has two layers: artifact-side harness drift, and a human-side twin — gate complacency, deskilling, delegation-feedback divergence — anchored in the automation-complacency and ironies-of-automation literatures — structural inference, not measurement. Two running instances, differing in substrate, model, and knowledge genre, are offered as portability evidence, not efficacy. All of it comes from months-old practice — provisional judgments offered for testing, not settled practice.

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

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。}

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。