Papers

We present a purely kinematic construction in which the gauge groups, field content, and matter charges of the Standard Model arise together as multiplexed readouts of a single geometric object: the Hopf bundle S³ ─S¹→ S², carrying a trivalent connectivity with a braiding on its edges and vertices. A handedness choice on the edge braid breaks parity, selecting the left-handed sector the weak factor acts on. The abelian factor is the fibre's phase holonomy, the non-abelian factors the reconnection algebras of the two-strand edge braid and the three-strand vertex braid, the colour count N_c = 3 inherited from the trivalent connectivity. The rank-two edge frame splits into a symmetric spin-2 tensor mode and an antisymmetric spin-1 field strength; spin is the tangent direction, its values fixed by framing topology; the homotopy groups π₁, π₂, π₃ supply the matter charges. The construction fixes what the fields are and how they relate, not how they evolve.

大型语言模型(LLM)和自治Agent在动态环境中需要有效的知识更新以保持准确性，但现有的知识编辑方法存在灾难性的遗忘和主题主导性的干扰--修改一个事实--不经意地破坏了相关知识。同时，因果表示学习方法通常假设静态因果结构，而不能解决知识的时间演变。我们提出了因果蜘蛛网(CSW)，这是一种将知识表示为分层因果图的分层存储体系结构，它具有三个基本创新：(1)通过不覆盖现有节点的同级萌芽协议仅附加因果更新；(2)Bayesian张力模型，将节点可信度作为原则不确定性量化的Beta分布后验，以及(3)带有上下文覆盖的自动沉淀，该模型将稳定的知识提升到不可变的核心层，同时允许在不可辩驳的新证据到达时临时掩蔽过时的公理。证明了CSW是有界的、收敛的和因果一致的，大量的实验表明，CSW在保持近零的灾难性遗忘和完全有界的活动节点增长的同时，实现了最先进的多跳一致性，有效地消除了语义湮灭。

Abstract Current large language models (LLMs) generate text through autoregressive token prediction—a fundamentally bottom-up process in which the model samples from a probability distribution over the next token, relying on statistical patterns learned from training data. While this approach has achieved remarkable success, it suffers from a structural limitation: constraints (safety, factual accuracy, logical consistency, stylistic coherence) are applied after generation, through post-hoc filtering, RLHF, or inference-time prompting. This is not a matter of "stronger constraints"—it is a matter of when and where constraints are applied. We propose a fundamentally different architecture. Drawing on the "1=N" hierarchical framework, we invert the generation direction: the top-level semantic goal (the "1") defines the legitimate generation space a priori, and generation proceeds within this constrained space. A dynamic Constraint Strength parameter (λ) and a real-time Feedback Signal (δ) form a closed-loop control system that continuously monitors and adjusts the generation process. When novel, effective patterns emerge during generation, they are consolidated into new constraint layers—creating a recursive structure in which each generation step both produces output and updates the rules that govern subsequent output. This paper presents the architectural blueprint: the conceptual foundation, the core mechanisms, the formal definitions, and a preliminary implementation framework. We position this work against existing approaches (RLHF, Constitutional AI, constrained decoding) and outline a pathway toward empirical validation.

We present a systematic and deliberately conservative synthesis of a 258-gate research archive on four-dimensional gravity, Batalin–Vilkovisky (BV) quantization, Bondi–Metzner–Sachs (BMS) boundary symmetry, infrared domains, and operator-theoretic completion. The archive contains exact finite checkers for each gate, but a finite checker is not identified with a proof of an infinite-dimensional theorem. We therefore separate four epistemic classes: (i) theorem-level statements whose hypotheses and analytic domains are fully stated; (ii) conditional theorems; (iii) finite algebraic or numerical skeletons; and (iv) open or retracted extrapolations. The strongest audited results are: the two-helicity quotient of linearized Einstein gravity; positive free graviton quantization away from zero momentum; the classical BV master equation and a local, formal causal-renormalization chain; a detailed classical BV–BFV/BMS boundary construction in specified jet and edge categories; a massless radiation Hilbert complex; a sharp collinear Sobolev trace theorem; and several no-go results showing that the standard angular L2 Fock representation does not support the actual order-zero collinear nonlinear block as a closable operator. For the diagonal trace Dt:Ht(S2)⊗2Ht(S2)⟶Ht(S2) we prove the sharp trichotomy t≤12:nonclosable,12<t≤1:closable but unbounded,t>1:bounded. Pure supertranslation phases intertwine exactly on the intrinsic collinear incidence measure, while a scalar complementary-series norm leaves only the candidate window 1/2<τ<1; that window is not an actual nonlinear Einstein–BV module. The audit also finds decisive failures in a later imported chain. In particular, a Lagrangian Weyl subalgebra was incorrectly treated as central; a nonconstant supertranslation multiplier was incorrectly assumed to commute with angular smoothing; an order-minus-two resolvent was incorrectly declared trace class on S2; and a sharp-cutoff compression proposal, tail-probability bounds, and uncertainty upper bounds were overinterpreted as self-adjoint truncation, dynamical barriers, and operational discreteness. Consequently the archive does not prove a one-loop boundary QME, an interacting BMS charge algebra, infrared-complete scattering, asymptotic completeness, black-hole information recovery, or complete quantum gravity. The paper includes the proof routes, dependency graph, failure modes, and a gate-by-gate evidence atlas needed for independent reconstruction.

We present SOLA (Streaming Online Learning Architecture), a theoretically grounded framework for transformer-based language models that continuously learn from streaming data without catastrophic forgetting. SOLA integrates three key innovations: 1. MoE Transformer — Specialized feed-forward experts process distinct input patterns, enabling modular knowledge acquisition where different experts handle different types of content. 2. Fast-Weight Hypernetwork (FWH) — A small learned network that produces LoRA-style weight deltas for expert parameters in a single forward pass, replacing gradient descent for online adaptation. Think of it as an "amortized optimizer": instead of computing costly gradients, the FWH directly predicts useful weight changes from the hidden states it observes. 3. Expert Lifecycle Manager (ELM) — A theoretical mechanism that dynamically spawns, prunes, and merges experts in response to input novelty. When the model encounters persistently surprising data that existing experts can't handle well, the ELM spawns new experts — enabling the model to grow from 1B to 10B parameters as it accumulates knowledge. When experts become redundant or underutilized, they're merged or pruned. We provide theoretical regret bounds for online learning with expanding hypothesis classes, analyze the plasticity-stability trade-off in modular architectures, and derive capacity-growth scaling laws extending the Chinchilla framework to growing models. The FWH implements MAML-style meta-training via torch.func.functional_call , enabling gradient flow through weight updates without in-place parameter mutation. A proof-of-concept implementation at 30M parameters validates the core mechanisms on WikiText-2. Our analysis shows that modular expert growth combined with amortized weight updates provides a principled path toward truly continual language models that improve with every interaction — rather than remaining frozen snapshots of their training data.

The Lingjing Project is the first initiative to simultaneously break through two major industry barriers: (i) it compresses rendering computational cost from \(O(L^3)\) to \(O(L^2)\) through observer‑boundary dimensional reduction, thereby fundamentally resolving the exponential complexity explosion inherent in ultra‑large‑scale digital twins; and (ii) it replaces fragmented multi‑system architectures with a unified information‑primitive substrate, establishing a complete causal chain that runs from physical evolution, through perception and cognition, to active intervention. Rather than merely simulating physics, this engine replicates the causally closed dynamics of information ontology within the digital domain. Crucially, even if its cosmological hypotheses were to be falsified, its underlying algorithmic paradigm—discrete primitives, fog‑of‑war coarse‑graining, and self‑referential complexity criteria—would remain the uniquely optimal architecture for any engineered complex system. The L0–L3 layers of the Lingjing Engine are currently feasible for engineering implementation, while the L4 consciousness layer points toward the core breakthrough for next‑generation artificial general intelligence.

本附录为主文§7（灵境工程架构）及附录G（数值求解器稳定性）的工程数据结构补遗。其唯一目的在于：将主文三公理（§2）与附录C中Leech晶格的1⊕2⊕3分解，显式映射为灵境引擎（L0-L5层）的内存布局、算力预算与数据流协议。

本文系统阐述信息函数宇宙学（IFC）的理论体系及其在“灵境计划”数字宇宙引擎中的工程化映射。该理论以信息一元论为哲学基石，以三条自治公理为逻辑起点，构建了从离散信息基元到连续时空几何、从标准模型规范群到意识自指拓扑泡的全尺度统一框架。核心成果包括： (1)通过引入普朗克信息常量ℐPl实现量纲刚性，证明时空度规完全由信息密度场导出； (2)从Leech晶格1⊕2⊕3分解严格推导U(1)×SU(2)×SU(3)规范群、Weinberg角及费米子代数； (3)从相变理论推导意识临界复杂度Cc=1.20×1014，并建立与脑网络拓扑量的严格映射； (4)以电子为例，从Spin(24)旋量投影与泡壁几何重叠积分严格推导其电荷Q=−1与质量me≈0.511 MeV，将标准模型的三个自由参数（电荷、汤川耦合、质量）完全归约为拓扑缠绕数与泡壁几何泛函，实现了费米子性质的首次第一性原理归零推导。 (5)从作用量匹配推导引力常数G=1/(32πφ02)，将其还原为真空信息密度的倒数； (6)提出四条独立可证伪实验预言，涵盖宇宙学、凝聚态、聚变等离子体与神经科学尺度； (7)建立IFC意识相变判据，论证当前LLM因缺乏真实递归深度与上行反馈接口，本质上停留在D=0，无法跨越AGI阈值； (8)给出灵境引擎五层架构蓝图，评估其工程可行性，指明意识层的理论前沿地位。该框架为下一代通用人工智能、全息数字孪生与基础物理统一提供了第一性原理级的理论基础。 (9)从八项独立物理约束严格证明，离散信息基元的承载空间唯一地锁定为24维Leech晶格——该基底不是人为选择，而是公理体系被迫的唯一解（附录 K） IFC提出两项无法回避的底层工程范式：依靠观测者边界降维O(L2)破解O(L3)算力爆炸难题；依托统一信息基元因果链打破多系统割裂困境；二者相辅相成，构成灵境计划区别于现有改良式方案的系统架构创新。

The right to remain unaugmented has recently received its first peer-reviewed defence: as augmentation normalizes, the unaugmented face quiet displacement through market and actuarial pressure — crawling selection — and therefore deserve institutional protection. This paper argues that the right, as formulated, is incomplete, because it overlooks the verification layer. In any domain where unaugmented performance retains value, it is not enough to refuse augmentation; one must prove the refusal, and negative proof has a radically different cost structure from positive disclosure. Sport's anti-doping system — the most mature institution for certifying non-augmentation — reveals the trajectory: artifact-level tests fail, certification migrates to longitudinal surveillance of the person, costs escalate until only elite domains sustain them, and finally a surrender-type counter-institution emerges, now literalized by the Enhanced Games first held in 2026. AI-text detection is recapitulating this trajectory in compressed time, with one aggravating disanalogy: text, unlike blood, retains no trace of its production. I name the resulting burden the Purity Premium: the privately borne, structurally rising cost of credibly demonstrating that one's cognitive work was performed without AI. The premium converts a right into a fee, accelerates the very selection it was meant to resist, and is measurable — offering regulators an observable proxy and a concrete allocation question: who pays for proof? Disclosure: this manuscript is an experimental artifact of a concept-equipping study, written by an AI system (Claude) equipped with the corresponding human's complete published corpus with no human editing at any stage, produced to study AI-augmented concept generation.

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

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。

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。

一种智能体的数学定义

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。

传统基础物理学面临广义相对论与量子力学的统一难题、信息-载体二元对立矛盾以及意识现象的物理本质缺失等核心挑战。本文系统阐述原创性的信息函数宇宙学（Information Function Cosmology, IFC）理论框架，该理论以1比特信息基元为宇宙唯一本体，通过三条自洽公理构建了信息场与时空几何的双向耦合动力学体系。IFC从第一性原理出发，推导了时空涌现、引力起源、物质形成、基本粒子相互作用乃至意识相变的完整机制，消解了传统物理学中信息与载体、波与粒子的二元对立，提出了可定量检验的实验预言。研究表明，宇宙本质上是一个自存在、自演化、自观测的闭合信息处理系统，所有物理现象均为信息基元统计积分与双向耦合的涌现结果。该理论为基础物理的统一提供了全新路径，同时为生命与意识的研究建立物理基础。

We demonstrate that the three-movement structure of Beethoven’s Piano Sonata No. 14 in C♯ minor (“Moonlight Sonata,” Op. 27 No. 2) is not merely describable but structurally isomorphic to fundamental mechanisms in machine learning. Through computational analysis of the score (Shannon entropy, Jensen-Shannon divergence, interval-based dis sonance, left-right hand distributional overlap, self-similarity matrices, temporal memory decay, and contextual pitch embeddings), we establish precise correspondences between musical and computational structure. Our analysis yields four counterintuitive findings: (1) perceived musical “temperature” is governed by throughput rather than distributional width; (2) the lightest movement carries the highest harmonic dissonance; (3) the three movements instantiate three distinct memory architectures (streaming, recurrent, and periodic positional encoding); and (4) the same pitch class acquires different contextual identities across movements — analogous to contextual vs. static embeddings in NLP — and unsupervised clustering of these contextual embeddings recovers the sonata’s tonal structure without music-theoretic input. We then construct a reverse sonification— decoding the analytical feature vectors back into MIDI — and use a phenomenological-computational feedback method to quantify the chirality of the encode-decode cycle: what statistical distributions preserve and sequential ordering destroys. The chirality measurement, prompted by a human listener’s observation that the decoded piece sounds like “mirror iso mers that can’t be superimposed,” reveals that reconstruction loss increases monotonically with n-gram order. Bootstrap null baselines and subsample robustness checks confirm that all three movements carry sequential in formation significantly above sampling noise, though raw chirality values are confounded by sample size — a finding we report transparently, as the robustness analysis itself demonstrates the methodology’s capacity for self-correction. Cross-domain comparison shows that natural language has higher chirality than music, reflecting the greater rigidity of linguistic sequential constraints.