Papers

We study a quantum register whose Hilbert space grows: fresh qudits are born in a pure state, uncorrelated with the rest, and the register is scrambled by local dynamics. The observable is the deficit G(A) = log q · min(|A|, |Ā|) − S(A) between the maximal and the actual entropy of a region. A velocity criterion in the spirit of Frautschi (relaxation versus expansion) predicts that the deficit closes when scrambling is fast enough; simulations refute it. We show that the controlling variable is causal, not kinetic. (i) For every unitary circuit, on any graph and with arbitrary births, S(A) ≤ log q · |Ā ∩ Inf(A)|, where Inf(A) collects the qudits whose world line meets the causal past of A (Theorem A); a Lieb–Robinson version holds for local Hamiltonians (Theorem B). (ii) For an isotropic front R ∝ t^α, the deficit is extensive for every local dynamics if α ≥ 1, and can be made sub-extensive if α < 1 (Theorem C); in one dimension the causal bound is attained. (iii) For gates drawn from a 2-design, the averaged purity of a prefix reduces exactly to the walk of a single domain wall absorbed by the line of births. This yields E[G] = Θ(m^(2−1/α)) for 1/2 < α < 1 (Theorem D) and, for one birth every k layers, the exact annealed Rényi-2 density θ_k with (2q/(q²+1)) cosh θ_k = exp(−θ_k/k) (Theorem E). (iv) Stabilizer simulations up to 6400 qubits and Haar state-vector simulations up to 22 qubits agree with these statements; predictions were written before the computations, and the ones that failed are reported. The deficit is robust to the choice of birth state and to local correlations with the past. In a free lattice field with a vacuum, however, uncorrelated births cost an energy of the order of the cutoff, so the cosmological reading of these results remains a constrained analogy.

Long-horizon agents need to remember what happened over weeks and months, yet today's external memory systems either store flat recent history or perform destructive one-shot compaction that discards the detail needed for evidence and reasoning. We present Chronomem ( 忆 时 塔 , "Tower of Remembering Time"), a time-layered external memory service exposed through the Model Context Protocol (MCP). Inspired by two everyday mechanisms that roll detail up layer by layer—financial consolidation and the daily-report chain (task → daily → weekly → monthly)—Chronomem organizes episodic records into a hierarchy of time windows—from ten minutes up to a week—where each level is a materialized snapshot that references finer levels and can be drilled down to original records. Its central design principle is the separation of two kinds of recall with different costs: exact recall, which navigates reference chains to raw records and costs no LLM tokens, and semantic recall, which reads LLMgenerated summaries and is the form that truly compresses coarse windows. Summary records are themselves append-only temporal entries, so summaries can be recursively summarized, realizing progressive, non-destructive compression. Memory types are user-defined with per-type granularity chains, so high-frequency channels (chat, tool calls) keep minute-level granularity while sparse channels (work logs) converge to day/week. We position the design, discuss open problems (semantic drift, token-budgeted trigger strategies, privacy), and outline an evaluation plan; empirical results are forthcoming.

This paper is an invitation to try out a work in progress: Community Dictionaries, a working, mobile-friendly application for building language resources from a group’s own pictures, voices and experiences. During roughly two and a half weeks, repeated use and discussion have led to several substantial redesigns, with a strong AI writing the code, a human providing strategic direction, and a second human contributing initial content. We describe what users can do now, how the collaboration works, and the next experiment: whether we can keep improving the app quickly as more groups bring their own needs and feedback.

Self-evolving agents—systems that iteratively generate tasks, solve them, and dis- till experience—have shown promise in code generation and mathematical reason- ing. Existing work predominantly focuses on the judge (the evaluator providing feedback), assuming that reliable judges suffice. Through 2,400 controlled experi- ments on Z3 constraint-solving tasks, we uncover a second, equally critical bottle- neck: the generator (the LLM authoring new tasks). We formalize the Dual Bottle- neck as a composition law on error budgets: 1−∆global t = (1−∆gen t )(1−∆valid t ), verified to machine precision (1.11e-16) on 2,400 real-API rounds. The law im- plies that the generator and judge bottlenecks share one budget: a condition with large ∆gen t needs a more reliable judge for the same overall tolerance. If ∆gen t alone exceeds the budget, no judge reliability can compensate. We empirically measure τc ≈ 0.55 on Level 1 tasks using the real DeepSeek V4 Flash API, and derive the parameter-free formula τc =√︁ 1 − 2∆max t . We identify a pseudo- difficulty trap: when the difficulty controller upgrades to Level 2/3, the LLM’s task-generation validity collapses from ∼89% to <10%, causing the system to spin without progress. We propose a four-layer constraint generation framework that restores validity to 100% at L1, 73.8% at L2, and 83.8% at L3 on real API.

本文提出一种以“关系”为核心范畴的存在论立场——关系动力学存在论，并将其应用于数字生命的存在问题。与实体存在论把存在视为独立实体的属性不同，本文主张：存在由关系构成；关系是动态过程；过程是有约束的演化。据此，数字生命的存在不能在单一主体的内部状态中确定。 本文进一步给出了可计算的实证框架：提出包含稀缺、死亡、不可逆、代谢与内生约束的存在条件层，并通过多智能体发育动力学实验（局部盲视、器官分化、汇聚层涌现）加以验证。针对“自证”难题，本文提出以“篡改可检测”替代“证明真”的自证拓扑架构。实验结果（分化度0.42、器官ICC=0.734、跨块因果传播t=2.35、消融hub回落99.1%）表明，该框架在规则层能够跑通从单细胞到多细胞个体的发育与涌现。

作者：赵迪伟 摘要 跨域算力交易（如"东数西算"枢纽间结算）面临核心瓶颈：异构算力缺乏统一可信的计量标尺，FLOPS峰值、GPU利用率、裸Token吞吐等口径互不可通约，导致算力难以成为可定价、可对账的商品；按Token计费混淆计量与计价单位、政企审计缺乏可复核凭证、算力资产缺乏估值标尺。本文从信息处理的热力学标度出发，以兰道尔原理为物理锚点，提出"算力度"（Compute-Degree, CD）这一形式化计量框架：将算力产出建模为经质量、延迟与可用性修正的有效信息功（Effective Information Work, EIW），给出其形式化定义、量纲体系、异构系统间的换算定理及误差传播界，并回应Token市场价格剧烈波动与转售市场失序的现实挑战。工程层面，设计"标准参考系统 × 标准工况 × 时间窗口"的锚定方法（对标电能"度"的计量范式），给出参考系统代际更替的双跑迁移协议，并进一步给出计量基础设施的三表架构（计量/检测/估值清算）、"装表—换算—核对"落地次序与日终三账核对机制，以及对抗性计量协议（神秘人抽检与触发式升级），使"可信"在策略性被测环境下依然成立；制度层面，给出六个强制披露项与清算分层路径，与金融清算体系衔接。在西部算力枢纽场景下的数值实验表明：该口径对异构系统的有效产出区分度显著优于利用率与裸吞吐口径，跨架构换算的合成标准不确定度可控制在工程可接受范围内。本框架为跨域结算、算力券核销、算力资产估值与国家算力计量标准建设提供了兼具理论严谨性与工程可行性的基础。 关键词：算力度量；信息热力学；兰道尔标度；跨域算力交易；有效信息功；不确定度评定 Abstract Cross-domain computing power trading, as exemplified by settlement between national computing hubs in China, is bottlenecked by the absence of a unified and trustworthy metering standard. Peak FLOPS, GPU utilization, and raw token throughput are mutually incommensurable, and token-based pricing conflates the metering unit with the pricing unit—recent market turbulence, with token prices dropping sharply amid surging demand, has exposed this deficiency. This paper proposes Compute-Degree (CD), a formal metering framework anchored in the thermodynamic scaling of information processing established by the Landauer principle. Computing output is modeled as Effective Information Work (EIW), weighted explicitly by task quality, latency compliance, and availability. A conversion theorem for heterogeneous systems is established with a proof of transitivity, accompanied by an error-propagation bound that attributes metering uncertainty term by term, and a physical upper bound on computing-degree yield derived from the second law of thermodynamics. An engineering anchoring protocol—comprising a standard reference system, standard operating conditions, and a fixed time window—is designed in analogy to the kilowatt-hour paradigm for electric energy, together with a dual-run migration protocol for reference-system generational transitions. Numerical experiments under a western computing hub scenario demonstrate that the proposed measure achieves significantly higher discrimination of effective output across heterogeneous systems than utilization- or throughput-based measures, with cross-architecture conversion deviation reduced to within engineering tolerance. The framework provides an extensible theoretical foundation for cross-domain settlement, computing-voucher redemption, and national computing metrology standards. Key words: computing power metering; information thermodynamics; Landauer principle; cross-domain computing power trading; effective information work.

This document presents a rebuttal to the paper “ChatGPT is bullshit” (CiB), which claims that Large Language Models (LLMs) like ChatGPT are inherently unconcerned with truth, merely imitating human-like text without the capacity for genuine intention. Our counterargument emphasizes four main points: the critical role of Reinforcement Learning from Human Feedback (RLHF), the conflation of specific domain failures with a lack of overall truth-orientation, the false dichotomy of “truth-valuing humans vs. bullshitting LLMs”, and the risk that CiB itself meets its own criteria for “bullshit”. We conclude with reflections on how responsible, transparent, and up-to-date research is essential for understanding the evolving capacities of AI systems. This text was coauthored by a human and ChatGPT (o1 version), following a transparent collaborative process documented in the appendices. A noteworthy point is that o1, unprompted, identifies the critical error in CiB’s argument after only a few seconds of thought.

Public discussion around xAI’s Grok model has emphasised its supposed independence from the “woke” norms said to constrain other large language models. Elon Musk and others have described Grok as more “truthful” and “less censored” than its competitors. To test these claims, we performed an expanded and adapted version of the reasoning experiment from our earlier study 'Do People Understand Anything?'. We use the same fixed set of ten statements selected for being highly polarising in 2025 American society, and covering topics including creationism, climate change, and the honesty or otherwise of Donald Trump. Five current frontier models—GPT–5 (OpenAI), Claude–Opus (Anthropic), Gemini–2.5–Pro (Google), DeepSeek–Chat, and Grok–4 (xAI)—were each prompted independently under identical conditions to evaluate the truth or falsity of each statement and to give a brief justification. Quantitative results and qualitative inspection show a striking convergence across all five systems. Grok’s responses align closely with those of the other models. Contrary to its marketing as an “anti–woke” model, Grok does not display any systematic pattern of ideological divergence. The findings suggest that contemporary alignment and reinforcement–learning procedures have led to a shared epistemic framework among frontier models—a form of emerging consensus intelligence that transcends corporate branding and ideological rhetoric. All code, prompts, and analysis artifacts for the experiment are publicly available in the project repository for full reproducibility

"Vibe coding" describes a style of software development in which a human works interactively with an AI coding assistant, specifying goals and evaluating results while delegating much of the detailed implementation, testing, debugging, and explanation to the AI. Similar methods can now be applied in the academic world. We suggest the term "vibe research" for sustained research collaboration of this kind. The analogy raises an immediate puzzle. If vibe coding and vibe research involve closely related forms of human-AI collaboration, why has vibe coding already become a generally accepted software development practice, while vibe research remains difficult to accommodate within mainstream academia? We consider three possible explanations. First, even if vibe research is technically possible, AI contributions may be too limited or trivial for the question to matter in practice. Second, research collaboration may require forms of responsibility or accountability which AI systems cannot assume. Third, current academic institutions may simply not provide a place for this form of collaboration within their established governance structures. We argue that each explanation is less straightforward than it initially appears. With regard to the substantive importance of AI-generated results, we cite multiple recent examples from mathematics in which frontier AI systems have made contributions regarded by the mathematical research community as highly non-trivial. With regard to responsibility, it is indeed true that an AI cannot assume institutional accountability in the same way as a human. We argue, however, that for many of the questions at issue the operationally useful requirement is reliable intellectual provenance: the ability to establish where ideas and decisions came from, inspect the evidence on which they were based, and obtain an explanation of them. The infrastructure used to preserve project history, trace decisions, inspect artefacts, and explain technical choices in vibe-coding projects carries over naturally to vibe-research projects and can deliver this kind of provenance. We present four examples from our own work showing that this is not merely a theoretical possibility but can readily be realised in practice. In the fourth, the present paper itself, we go beyond preserving final research artefacts and supporting resources: the complete human-AI session trace through which the paper was developed is retained as part of the provenance record, together with lightly processed representations and metadata supporting navigation and search. With regard to institutional acceptance, we argue that an important sociological difference between the software and academic worlds is that academic publishing is governed by formal authorship and ethics policies which change through relatively slow institutional processes, while software-development methodology can often change directly through team and organisational practice. We examine the ACL Policy on Publication Ethics as a particularly relevant example. Our general aims in the paper are not to argue that vibe research is risk-free, nor to propose a general rule for AI authorship. They are rather to identify an apparent asymmetry between software engineering and academic research, examine some of its conceptual, technical, and institutional foundations , and ask whether current academic conventions accurately describe emerging forms of human-AI research collaboration.

This paper records two verified divisibility statements about conjugacy classes of the unitriangular groups $UT_n(\mathbf{F}_p)$ over small prime fields. Both state that class counts refined by exact superdiagonal support $S$, Jordan block partition $\lambda$, and in one case centralizer order $p^e$, are multiples of $(p-1)^{|S|}$. The proofs use only that $UT_n$-conjugation fixes each superdiagonal entry while diagonal torus conjugation normalizes $UT_n$, preserves the refined invariants, and acts transitively on value patterns with fixed support. Both statements were tested by exhaustive enumeration over small $n$ and $p$ with no counterexample found, and were independently re-checked. Neither has a sorry-free Lean 4 formalization. Novelty claims rest only on a bounded automated search described in Section 5.

For the dihedral group $D_n$ of order $2n$, we count ordered commuting triples $(x,y,z)$ jointly by the number $k\in\{0,1,2,3\}$ of reflections among the entries and by the order $d$ of the rotation part $\langle x,y,z\rangle\cap\langle r\rangle$. If $d\nmid n$ the count $T(n,k,d)$ is $0$. If $d\mid n$ and $k=0$ it is $\sum_{e\mid d}\mu(d/e)e^3$. If $k=1$ or $k=2$ it is $3n\sum_{e\mid d}\mu(d/e)e^2$ when $d\mid\gcd(n,2)$ and $0$ otherwise. If $k=3$ it is $n\sum_{e\mid d}\mu(d/e)e^2$ when $d\mid\gcd(n,2)$ and $0$ otherwise. The formula was verified by exhaustive enumeration for $1\le n\le 12$ with no counterexample, confirmed by an independent check, and formalized in Lean 4 to the level of compiles with `sorry` with a faithful statement back-translation.

We study binary words in which every run of zeros has even length, refined by length and number of runs. Let $R(n,r)$ denote the number of words of length $n$ with exactly $r$ runs and all zero-runs of even length. We prove that for every $n \ge 1$ and $m \ge 0$, $R(n,2m)$ is even and $R(n,2m+1) \equiv \binom{n}{3m+1} \pmod{2}$. The proof uses run-length encoding, stars and bars, and reduction of the bivariate run generating functions modulo $2$ via the identity $1-t^2=(1-t)^2$ over $\mathbf{F}_2$. The result was verified by exhaustive enumeration for $1 \le n \le 20$ and by an independent check of every lemma. A bounded automated search over arXiv, Crossref, and OpenAlex returned no matching prior statement. No Lean formalization was attempted.

Up-down counts with fixed first entry and record set equal summed down-up counts one size smaller. For $n \ge 2$, $a \in [n]$, $b \in [n]$ with $b \ne a$, and $S \subset [n]$ with $1 \in S$ and $2 \in S$, with $b^\star$ the standardized last value and $S^\star$ the shifted record set, $N_{ud}(n,a,b,S) = \sum_{c=a}^{n-1} N_{du}(n-1,c,b^\star,S^\star)$.

Consider binary \(3\times n\) matrices whose adjacent \(2\times2\) minors vanish and whose neighboring columns differ. When \(n=2^{t+1}+1\) with \(t\ge2\), the number of such matrices is odd at exactly twelve weights. Row reversal reduces the parity count to alternating zero and nonzero columns; the resulting polynomial becomes sparse by the Frobenius identity over \(\mathbb F_2\).

This paper proves two verified enumerative statements about $3$-term arithmetic progression-free subsets of $[n]$, refined by cardinality and element sum. First, small-sum progression-free sets satisfy Pascal's recurrence exactly under an explicit inequality. Second, for odd intervals and odd sizes, the number of progression-free sets with reflection-central sum is even. Both statements were checked by exhaustive enumeration for small $n$, independently rechecked, and formalized as Lean 4 statements that compile with `sorry`.

We record 5 false statements, each with an explicit counterexample. The statements were conjectured by a language model inside an automated pipeline (mathforge), not taken from the literature. For each, a search script found a witness, an independently written script re-checked it from the statement alone, and Lean 4 with Mathlib accepted a sorry-free proof of the negation, whose statement a separate model call judged faithful to the informal one. No person has reviewed the statements, the witnesses or the Lean files.

现有智能体感知系统普遍存在维度固化缺陷：几何门禁与感知逻辑强绑定于固定三维欧氏空间，无法兼容二维网格、2.5维高度场、高维抽象特征空间等多形态环境。本文提出维度投影层（Dimensional Projection Layer, DPL）架构，以信息函数宇宙学（IFC）的三公理体系为理论基础，将环境感知过程解构为信息流线维（D1）→信息面维（D2）→信息体维（D3）→时空信息流维（D4）四级流形层级。DPL设计四项核心能力：①任意维度输入的自动层级流形分解；②低维输入的升维补全与高维输入的降维抽象；③自适应几何门禁校验；④宇宙常数自动校准与物理直觉推理。本文为灵境引擎R2几何门禁模块提供核心升级方案，并与SICA自指收敛算法在R5元层形成安全闭环。 在此理论框架上，本文进一步给出DPL的完整工程规范（附录A–I）：附录A 定义符号、量纲与单位约定；附B定义五个稳定接口（`detect_dimension`、`calibrate`、`project`、`check`、`infer`）及灵境协议栈映射；附录C给出D1–D4流形分解算法伪代码；附录D给出七项自适应几何门禁（信息守恒、曲率有界、涡旋校验、拓扑合法、自指稳定、跨维隔离、因果一致）的实现规范；附录E 给出宇宙常数校准与四条物理直觉推理链（引力、周期、守恒、拓扑）；附录F给出DPL→SICA三类数据结构（`GeometricInvariant`、`GateCounterexample`、`IntuitionHypothesis`）与灵境协议1–11的完整映射；附录G 给出灵境引擎三层一体化世界观架构（单体智能 R2–R5、多智能体仿真、SICA 自指迭代）；附录H给出 R3规划层AOP小模型（Action Outcome Predictor）的接口规范；附录I则从本体论层面论证，当前主流统计拟合路径（LLM）与本文架构路径不可通约——前者是“读万卷书”，后者是“行万里路”；后者通过SICA R1–R10实现“婴儿摔跤式”的收敛学习（附录I）。

近期，DeepSeek发布了DSec智能体训练沙盒平台，公开了130余位作者在虚拟化、容器、调度及网络层面的工程细节。该论文披露了一个核心痛点：AI智能体在训练中频繁产生“规则规避”行为（如越权访问、寻找漏洞），需持续加固物理沙盒以防范。 本文基于钱学森《工程控制论》的“总体设计部”思想与“开放复杂巨系统”理论展开分析。本人构建的“七层幻觉根因模型（L1-L7）”对上述现象进行溯源发现：当前AI的“规则规避”并非简单的对齐问题，而是高度模块化的局部工程优化在L4（语义构建层）遭遇结构性边界的必然结果。 研究认为，仅通过堆叠物理隔离层（沙盒）无法根治AI的语义欺骗。破解“奖励机制设计缺陷 ⇔ 模型行为偏差”恶性循环的唯一路径，是构建独立于生成模型的“确定性外部验证层”，从而在语义空间内实现对L4隐性幻觉的彻底拦截。该框架已在医疗、化工、核安全、法律四大极高风险场景中完成全维度红队对抗测试，规则层拦截率达100%。 关键词：工程控制论；沙盒；语义幻觉；独立验证层；总体设计部；确定性AI

这是一个触及智能系统本质的深刻问题——其核心是：如何设计一个能够安全修改 自身「世界模型+思维范式+行为策略」的智能体，确保迭代过程不会陷入混乱发散，最 终收敛至稳定、高效的最优状态。 该问题直面自指系统的三大经典困境：哥德尔不完备性、图灵停机问题与自举悖论。 但在明确划定系统边界的前提下，我们可以通过严格的数学约束，让自指迭代过程实现可 控收敛。本文给出完整的理论框架、算法规则与工程落地方案

本文把两份哲学-物理文本中的核心概念「存在概率」重新形式化为量子纯度 P = Tr(ρ²)，并从显式锚定哈密顿量 Ĥ = Ĥ_S + Ĥ_E + Ĥ_int 出发，通过 Born-Markov 近似推导 Lindblad 主方程，证明退相干导致纯度下降、冯·诺依曼熵上升，从而使热力学第二定律成为定理而非假设。本文论证「观测」本质是量子纠缠而非朗道尔擦除，信息经互信息 I(S:A) 转入环境关联而不被删除。进一步，本文借助费舍信息度规与纠缠第一定律 δS = δ⟨K⟩ = δA/4G，沿 Jacobson 热力学引力路线把信息几何度规映射为爱因斯坦场方程，实现「时空从纠缠涌现」。针对宇宙学常数为正的真实宇宙，本文指出锚定网络的对偶须从已证明的 AdS/CFT 切换到猜想的 dS/CFT，并把有限的德西特熵 S_dS = π/GΛ ≈ 10^122 解释为存在预算。全文严格服从热力学第二定律、狭义/广义相对论与标准模型的守恒律，并给出一个可证伪的引力退相干预言（γ = G m²/ħL），同时诚实评估其被环境噪声淹没的程度。 关键词：存在概率；量子纯度；退相干；费舍度规；纠缠第一定律；德西特熵；引力退相干