01 · 商业产品01 · Commercial product
一种新的语言模型：同等算力，四域全面领先。A new kind of language model: four domains ahead at matched compute.
异构专家 · 永不塌缩路由 · 度量自演化 —— 124.5M 参数，同协议四域全面领先；数据、代码与权重即将公开。Heterogeneous experts · collapse-free routing · self-evolving metric — 124.5M parameters, ahead on four domains under one protocol; data, code and weights coming soon.
01商业产品01Commercial product
Tabby 是异构专家架构的语言模型，124.5M 参数。下面全部为同协议受控对比的结果级数字： 同语料、同分词器、同序列长度、同批次、同精度、同种子、同评测行数；双方参数量相差 0.043%。 基线为同预算自训 Transformer。本页只展示测量结果，不披露任何机制与实现细节。 Tabby is a heterogeneous-expert language model with 124.5M parameters. Everything below is outcome-level measurement under a single controlled protocol: same corpus, tokenizer, sequence length, batch, precision, seeds and evaluation rows; the two models differ by 0.043% in parameters. The baseline is a Transformer trained at the same budget. Only measurements are shown here — no mechanism, no implementation detail.
| 读数Reading | C4 | arXiv | Code | Wikipedia |
|---|---|---|---|---|
| 三种子均值 · 4,000 行验证集／域Mean of three seeds · 4,000 validation rows per domain | ||||
| TabbyTabby | 3.699 | 3.938 | 3.194 | 4.168 |
| 同协议基线Matched baseline | 3.979 | 4.245 | 3.290 | 4.548 |
| 领先Lead | −0.280 | −0.307 | −0.096 | −0.380 |
| 两种配置 · 逐配置读数Two configurations · per-configuration readings | ||||
| 异构 · 旗舰Heterogeneous · flagship | 3.693 | 3.948 | 3.022 | 4.151 |
| 异构 · 另两种Heterogeneous · two others | 3.7063.697 | 3.9263.941 | 3.3023.258 | 4.1884.166 |
| 同构Homogeneous | 3.809 | 4.138 | 3.857 | 4.343 |
| 新种子复现 · 第二批，独立种子 43／44New-seed reproduction · second batch, seeds 43 and 44 | ||||
| 异构 · 种子 43Heterogeneous · seed 43 | 3.694 | — | 2.982 | — |
| 异构 · 种子 44Heterogeneous · seed 44 | 3.701 | — | 3.083 | — |
| 同构 · 种子 43Homogeneous · seed 43 | 3.850 | — | 3.884 | — |
异构在四个域上全部领先基线（领先 0.10–0.38）；Code 上异构与同构差得最开——3.02 对 3.86。换种子后结论不变。The heterogeneous configuration is ahead of the baseline on all four domains (by 0.10–0.38); the widest gap over homogeneous is on Code — 3.02 against 3.86. New seeds leave the conclusion unchanged.
口径 统一序列长度 · 三种子均值 · 训练终态读数；全部为同协议受控对比：同语料、同分词器、同批次、同精度、同种子、同评测行数，双方参数差 0.043%，基线为同预算自训 Transformer。交叉熵越低越好。Protocol One sequence length · mean of three seeds · terminal training state; every comparison is controlled — same corpus, tokenizer, batch, precision, seeds and evaluation rows, the two models differing by 0.043% in parameters, baseline trained at the same budget. Lower cross-entropy is better.
| 模型Model | 渐近 CECE | αα | R² |
|---|---|---|---|
| 异构 · 旗舰Heterogeneous · flagship | 2.888 | 0.314 | 0.898 |
| 异构 · 另两种Heterogeneous · two others | 2.9062.898 | 0.3070.311 | 0.8980.896 |
| 同构Homogeneous | 3.009 | 0.391 | 0.946 |
| 基线 · 三种子Baseline · three seeds | 3.1743.1873.174 | 0.6110.6180.624 | 0.9820.9810.982 |
α 越小，损失随数据增长掉得越快：同构 0.39，基线 0.61–0.62。The smaller α, the faster loss falls with data: 0.39 homogeneous, 0.61–0.62 baseline.
| 序列Sequence | C4 | 自身长度Own len. |
|---|---|---|
| B6 · 4096 | 3.994 | — |
| B3 · 8192 | 4.087 | 4.077−0.010−0.010 |
| B2 · 12288 | 4.142 | 4.127−0.015−0.015 |
长序列在自身长度口径下拿到 −0.01~−0.05；Tabby 侧同轴数据随论文公开。Longer sequences gain −0.01 to −0.05 under their own-length protocol; Tabby's side comes with the paper.
01.1技术理念01.1Technical idea
以下是概念层面的理念陈述，不含实现细节；其保护已由在先专利申请覆盖。Concept-level statements only, no implementation detail; protection is covered by an earlier patent application.
模型内部的计算单元功能各异、不可相互替代，各司其职，而不是同构单元的简单复制。Internal compute units differ in function and cannot stand in for one another; they are not copies of a single homogeneous unit.
路由权重由模型内建的一套守恒约束承载，路由坍缩因此在构造上被排除——不需要任何负载均衡惩罚项。Routing weights are carried by a conservation constraint built into the model, so routing collapse is excluded by construction — with no load-balancing penalty term.
计算如何分配，由模型自身的演化动力学承载，而不是由外部约束从外面强加。How compute is allocated is carried by the model's own evolutionary dynamics, not imposed by an external constraint.
训练全程存在可观测的相变结构（幼年相 → 涌现相 → 回归相），稳定性是演化过程的性质，不是人工调参的结果。An observable phase structure runs through training (juvenile → emergent → return phase); stability is a property of the evolution, not of hand-tuning.
核心演化参数由系统内在拓扑结构经代数闭包唯一确定，在预设工程容差内实现零人工调参。Core evolution parameters are fixed uniquely by the system's internal topology through algebraic closure, giving zero hand-tuning within a preset engineering tolerance.
实数域动态迭代、复数域酉演化、模空间对偶——同一理念的三代演进，构成完整技术谱系。Real-domain dynamic iteration, complex-domain unitary evolution and moduli-space duality: three generations of one idea, forming a complete technical lineage.
理论框架《Reacher Endogenous Theory》（RET）主论文已公开，DOI 10.5281/zenodo.23228865。The parent framework, Reacher Endogenous Theory (RET), is published under DOI 10.5281/zenodo.23228865.
01.2即将公开01.2Coming soon
| 项Item | 内容Contents | 状态Status |
|---|---|---|
| 论文Paper | 《Tabby: Endogenous Routing Networks Outperform Matched Transformers across Four Domains at Matched Compute》——架构 + 全部成绩“Tabby: Endogenous Routing Networks Outperform Matched Transformers across Four Domains at Matched Compute” — architecture and all results | 待公开To be released |
| 论文Paper | 图书馆（无限长记忆 + 语义检索）姊妹篇Library (unbounded memory + semantic retrieval), companion paper | 研究中，公开时间待定In research, date not set |
| 代码Code | 训练与评测代码（md5 钉死）Training and evaluation code (md5-pinned) | 待公开To be released |
| 权重Weights | 旗舰与对照模型终态权重Terminal weights, flagship and baseline | 待公开To be released |
| 数据集Dataset | V50 矩阵全量（13 臂 × 4 域 × 32 检测点）Full V50 matrix (13 arms × 4 domains × 32 checkpoints) | 待公开To be released |
公开渠道：arXiv 同日预印本 + Zenodo 分册（DOI）。日期以正式公开为准，本页不作日期承诺。Release channels: an arXiv preprint and a Zenodo fascicle (DOI) on the same day. Dates follow the actual release; no date is promised here.
02 · 硅基验证02 · Silicon validation
让理论的数字在神经网络里自己出现Letting the theory's numbers appear inside a neural network
把 RET 的结构放进一个路由架构。它不模拟物理——它让 RET 已经算出的数字，在一套与物理无关的训练过程里出现。Puts RET's structure into a routing architecture. It does not simulate physics — it lets numbers RET has already computed appear in a training process that has nothing to do with physics.
02桥梁 · 硅基验证02Bridge · silicon validation
Exp1 把 RET 的封板结构放进一个神经网络路由架构。它不模拟物理—— 它让 RET 已经算出的十一个数，在一套与物理无关的训练过程里同时落定。 对可执行源码做字面搜索，这十一个预测值零命中。 Exp1 puts RET’s sealed structure into a neural routing architecture. It does not simulate physics — it lets eleven numbers RET has already computed land together, in a training process that has nothing to do with physics. A literal search of the executable source returns zero hits for those eleven predicted values.
RET · 封板算术RET · sealed arithmetic
16 个密封位点sealed sites
域算术链定出的离散结构，不是选的discrete structure fixed by the arithmetic chain
0.350144866454559356 136.64029024746 0.8480856676 5.5511151231257827e−17
← 这些数左边算出、右边原样出现← computed on the left, appearing verbatim on the right
Exp1 · 路由架构Exp1 · routing architecture
5 个路由专家routing experts
承载同一批计数，不参与训练carries the same counts, takes no part in training
桥就在这里。理论算出的数，在模型里以结构计数的形式原封不动地出现——不是被喂进去的，是同一个结构在两个尺度上的两种写法。对可执行源码做字面搜索，这十一个预测值零命中。This is the bridge. The numbers the theory computes appear verbatim in the model as structural counts — not fed in, but one structure written at two scales. A literal search of the executable source returns zero hits for the eleven predicted values.
常规物理实验A conventional physics experiment
理论先预测一个数theory predicts a number first
搭一台装置去测build an apparatus to measure it
加速器 · 探测器 · 谱仪accelerator · detector · spectrometer
硬件造的，与理论无关built from hardware, independent of the theory
测出一个数read one number off it
预测值 vs 测量值prediction vs measurement
对不上 → 回头调理论或调装置mismatch → go back and tune the theory or the rig
Exp1Exp1
理论先算出一个精确的数the theory computes an exact number first
搭一套「装置」build an “apparatus”
路由器 · 专家池 · 演化通道router · expert pool · evolution channels
这套装置本身就是理论造的the apparatus itself is built from the theory
训练到不动了，把数读出来train until it stops moving, then read the number out
理论算的数 vs 装置读出的数number the theory computed vs number the rig read out
对不上 → 理论就是错的mismatch → the theory is simply wrong
装置是理论造的the rig is built from the theory它里面的常数来自理论，不参与训练——所以这不是「自己出题自己答」。Its constants come from the theory and take no part in training — so this is not the theory marking its own exam.
同一个动作，两种装置one procedure, two kinds of apparatus物理用硬件，这里用模型；流程一模一样：先算、再测、然后比。Physics uses hardware, this uses a model; the pipeline is identical: compute, measure, compare.
读出的不是「差不多」，是逐位相同what comes out is not “close” but bit-identical论文报告：开关嵌入对全部 100,000 步的 列逐位相同。The paper reports 76 of 76 columns bitwise identical across all 100,000 steps when the embedding is switched.
语言模型部分 · 被训练Language-model half · trained
可训练 82,98182,981 trainable
理论部分 · 被承载，从不更新Theory half · carried, never updated
零更新zero updates
两边互不干扰。被更新的只有内容与信道库；先验留在优化器之外，密封族 B 只被承载。 论文报告：嵌入开关对全部 100,000 步的 列逐位相同—— 也就是说理论侧那半确实没有参与动力学。 The two halves do not interfere. Only the content and the channel bank are updated; the prior stays outside the optimiser and the sealed family B is carried only. The paper reports that switching the embedding on or off leaves 76 of 76 columns bitwise identical across all 100,000 steps — the theory half genuinely takes no part in the dynamics.
| # | 观测量Observable | 封板值Sealed value | 机器值Machine value | 级别Grade |
|---|---|---|---|---|
| 1 | t*f | 0.350144866454559356 | 0.35014486645455939 | [a] 密封[a] sealed |
| 2 | κw 误差κw error | 0 | 0（恒等）0 (identically) | [c] 事后[c] post-hoc |
| 3 | f − 0.35 | 1.4486645455935587e−4 | 1.4486645455941138e−4 | [a] 密封[a] sealed |
| 4 | α⁻¹(t*f) | 136.64029024746 | 136.64029024746523 | [a] 密封[a] sealed |
| 5 | 联合定点 Sgaugejoint fixed point Sgauge | 0 | 5.6915606589644907e−22 | 定点判据fixed-point criterion |
| 6 | 末 20k 的 tf 漂移last-20k tf drift | 0 | 5.5511151231257827e−17 | 定点判据fixed-point criterion |
| 7 | Δcomp(0) | 0（精确）0 (exact) | 1.1102230246251565e−16 | [a] 构造恒等[a] construction identity |
| 8 | Δcomp(1) | 0.8480856676 | 0.84808566759589421 | 低于推导级below derivation grade |
| 9 | 正性隙 Δeig(0)positivity gap Δeig(0) | 0.0450973589 | 0.045097358941594945 | [a 条件性][a conditional] |
| 10 | 正性隙 Δeig(1)positivity gap Δeig(1) | 0.6648655443 | 0.66486554425557687 | [a 条件性][a conditional] |
| 11 | E₀(1) | −1.0939778573 | −1.0939778572808976 | [a] 构造[a] construction |
第 2 项的「误差 0」是 [c] 事后对照，不是独立涌现；第 9、10 项的 [a] 是条件性的 （前提：模型侧正性、质量守恒 μ₋ > 1/√2）。本页照录论文自己的定级。 Item 2’s "zero error" is a [c] post-hoc comparison, not an independent emergence; items 9 and 10 are conditional [a] (premises: model-side positivity, mass conservation μ₋ > 1/√2). The grades are quoted as the paper states them.
密封扇区逐列逐位相同（种子 42 与 43）Sealed sector bitwise identical column by column (seeds 42 and 43)
在一种最大相异的内容输入下，密封列全部不变Under one maximally different content input, every sealed column is unchanged
2.8e−16
lrk 从 0.05 到 5.0，末序参量跨度lrk from 0.05 to 5.0 — spread of the final order parameter
论文原话From the paper
We therefore claim a verification, not an identification.
论文同时写明：「本工作表明密封载体与密封吸引子在同一条配置上同时出现， 并未表明载体驱动了吸引子」，并称「这一区分贯穿全文」。 另外：κw 是 [c] 事后对照而非独立涌现；两个种子本身不足以佐证任何密封值； 嵌入对本配置的动力学是惰性的。 The paper also writes: "This work shows the sealed carrier and the sealed attractor present together on one configuration, but does not show that the carrier drives the attractor", and calls this distinction one that "runs through the whole paper". Also: κw is a [c] post-hoc comparison rather than an independent emergence; the two seeds cannot by themselves corroborate any sealed value; the embedding is dynamically inert for this configuration.
未解决项（论文自陈）：钉扎强度 p 的物理定义、∂µ 的显式形式、QCD 色单态的具体约束、 有限维族到四维连续统的那一步、以及到实测强子质量的有量纲桥 。 本工作一个都没有走。 Open items (as the paper states them): the physical definition of the pinning strength p, the explicit form of ∂µ, the specific colour-singlet constraint of QCD, the step from the finite-dimensional family to the four-dimensional continuum, and the dimensionful bridge to measured hadron masses . This work walks none of them.
03 · 物理理论03 · Physical theory
零自由参数的封板算术Sealed arithmetic with zero free parameters
Reacher Endogenous Theory：从一个覆盖五扇区的单一封板作用量出发，把物理常数推导为纯数学结构的被迫输出。Reacher Endogenous Theory: from a single sealed action over five sectors, deriving the constants of physics as the forced output of pure mathematical structure.
03物理理论03Physical theory
「内生」的意思是：这些数不是被输入进去的，是从一个结构里自己长出来的。 RET 只假设一样东西——一个覆盖五扇区的封板作用量。精细结构常数、电弱混合角、 三代费米子、强耦合系数，全部由它推出来，而不是被拟合出来。 下面是完整技术面板：可核对的预测、可重算的算术内核，以及每条结论的审计级别。 "Endogenous" means: these numbers are not put in — they grow out of a structure. RET assumes exactly one thing — a single sealed action over five sectors. The fine-structure constant, the electroweak mixing angle, three fermion generations, the strong coupling coefficient: all of them are derived from it, not fitted to it. Below is the full technical panel: checkable predictions, a recomputable arithmetic core, and the audit grade of every claim.
所属范围Scope
理论物理 → 数学物理 · 场论 · 强子唯象Theoretical physics → mathematical physics · field theory · hadron phenomenology
谱几何 / 谱作用量spectral geometry / spectral action
规范场论gauge theory
量子色动力学QCD
量子电动力学QED
电弱与希格斯electroweak & Higgs
真空能与宇宙学常数vacuum energy & Λ
信息几何information geometry
方法上不是唯象拟合：常数由结构强制；唯象（强子谱、原子谱、宇宙学）只出现在末端比对。Not a phenomenological fit: constants are forced by the structure; phenomenology (hadron, atomic, cosmological) appears only at the final comparison.
前置 · 物理Prerequisites · physics
作用量原理与约束系统action principle & constraints 经典场论与 Noether 定理classical field theory 规范场论：Yang–Mills、su(3) 生成元gauge theory: Yang–Mills, su(3) 量子电动力学与高阶修正QED & higher-order corrections 电弱统一与希格斯机制electroweak unification & Higgs 量子色动力学：色单态、胶子、胶球、禁闭QCD: colour singlets, gluons, glueballs, confinement 手征对称性与强 CP 问题chiral symmetry & strong CP NJL 四费米子与大 N 展开NJL & large N 强子谱与 QCD 求和规则hadron spectrum & QCD sum rules 标准模型的参数账（十九个）the Standard Model's nineteen parameters 真空能与宇宙学常数问题vacuum energy & the cosmological-constant problem 重整化、单圈、格点对照renormalization, one-loop, lattice checks 谱方法 / 谱作用量spectral methods / spectral action
前置 · 数学Prerequisites · maths
泛函分析与算子谱理论functional analysis, operator spectra 迹类算子与 Krein 谱移函数trace class & Krein spectral shift 矩问题moment problems 李群与表示论Lie groups & representations 微分几何：度规、联络、曲率differential geometry 算子代数与非交换几何operator algebras, NCG 密度矩阵与完全正映射density matrices & completely positive maps 信息几何（Fisher–Rao）information geometry
理论自身的分层The theory's own layers
结构函数层 → 桥区 → 动力学层 → 界面层（量纲出口）→ 诠释层（读数比对）structural function → bridge region → dynamical function → interface (dimensional outlets) → interpretive (readings)
不列：微积分、线性代数、常微分方程这类基础课；也不把弦论、大统一、量子引力当前置（它们只是论文里的背景对照）。Not listed: calculus, linear algebra, ODEs; string theory, GUTs and quantum gravity are background, not prerequisites.
封板作用量 · 式 (1) · 主论文第 4 页The sealed action · Eq. (1) · main paper, p. 4
tf 不是独立槽位，而是扇区权重的无迹离散度：tf is not an independent slot but the traceless dispersion of the sector weights:
该式每一项的取值、所属层次与推导见主论文表 1。本页只呈示公式本身，不重复推导，也不对其作任何改写。The value, layer and derivation of every term are in Table 1 of the main paper. This page shows the formula as it is; it neither re-derives it nor alters it.
逐符号讲解Term by term
29 个符号一个一个讲：左边是符号，中间是它在扇区里的位置，右边一张图和一句人话。讲完一段再合起来看整条式子。 Twenty-nine terms, one at a time: the symbol on the left, its place in the sector in the middle, a diagram and one plain sentence on the right.
正在装载讲解…Loading the explainer…
讲解页是满屏交互，手机上用全屏打开更顺手。The explainer is a full-screen page; open it full-screen on a phone.
全屏打开讲解 →Open full screen →03.1预测面板03.1Prediction panel
每行给出来源闭式、实验读数、偏差与审计评级。点击任意行展开推导来源与配套论文 DOI。 Each row gives the source closed form, the experimental reading, the deviation and the audit grade. Click any row to expand its derivation source and companion DOI.
| 物理量Quantity | RET 值（闭式）RET value (closed form) | 实验值Experimental value | 偏差Deviation | 审计评级Audit grade | 展开Expand |
|---|---|---|---|---|---|
| 01 精细结构常数作为位置读数 01 Fine-structure constantas a positional reading | C·( − tf)/(tf − ) | 137.035999084CODATA 2018 | +5.527 ppm | 形式 [a]标定 [d]Form [a]Calibration [d] | |
推导来源桥区：α 被读作当下宇宙在健康轴上的位置。归一化 C 全为封板整数， C = Nc³Nsec¹⁰ / [(Nc²−Nsec²)²(−Nc²+4NcNsec⁴+Nsec²)]。 演化律形式在给定类（单零点、两端极点、Z₂ 反射奇性）内唯一。 评级理由律的形式为 [a]；时钟标定 κ 无第一性原理值，为终态 [d]。 α 的绝对值不由封板算术单独锁定——可检验的内容是漂移方向 dα/dt > 0。 DerivationBridge region: α is read as the present universe's position on the health axis. The normalisation C is entirely sealed integers, C = Nc³Nsec¹⁰ / [(Nc²−Nsec²)²(−Nc²+4NcNsec⁴+Nsec²)]. The form of the evolution law is unique inside the stated class (single zero, poles at both edges, odd under the Z₂ reflection). Why this gradeThe form of the law is [a]; the clock calibration κ has no first-principles value and is terminal [d]. The absolute value of α is not fixed by the sealed arithmetic alone — what is testable is the drift direction, dα/dt > 0. |
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| 02 电子–缪子质量比 02 Electron–muon mass ratio | · λmin = 0.00828236795183… | 4.836331692×10⁻³PDG | +0.0702 % | 条件级 [b]Conditional [b] | |
推导来源两个输入都是纯数： 是封板测度的精确矩；λmin 是矩塔 Jacobi 矩阵 的最小特征值， 已由两条独立路径复现到全部显示位数。结果不含任何量纲锚点。 评级理由显式因子 5 没有推导——论文测试并否证了五个候选来源（扇区数、骨架维数、外代数维数、数值残差、谱路线）。 论文自评："事后比较，低于定理级"。此处不标为封板级。 DerivationBoth inputs are pure numbers: is an exact moment of the sealed measure, and λmin is the smallest eigenvalue of the moment-tower Jacobi matrix , reproduced by two independent routes to every displayed digit. The result contains no dimensional anchor. Why this gradeThe explicit factor 5 has no derivation — the paper tests and falsifies five candidate sources (the sector count, the skeleton dimension, the exterior-algebra dimension, a numerical residual, and a spectral route). The paper's own assessment: "a post-hoc comparison, below theorem level." It is therefore not labelled seal-grade here. |
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| 03 电弱混合角精修值 03 Electroweak mixing anglerefined value | = ()(1 + ) = 0.2312199519 | 0.23122PDG · MS | −0.21 ppm | 算术 [a]形式 [d]Arithmetic [a]Form [d] | |
推导来源两个分项进入：纯费米子 SU(5) 基线 sin²θW = 0.207865， 以及一级链的矩比 ≈ 0.230769。统一闭式 sin²θW = + ()(αEM/αs) 为定理级。 评级理由恒等式精确；但论文明确登记：其函数形式的推导在本框架内不可达，六类机制族被排除、 五条标准量子化路线穷尽，登记为终态 [d]。0.21 ppm 是算术候选，不是被提升的预言。 DerivationTwo entries enter separately: the pure-fermion SU(5) baseline sin²θW = 0.207865, and the level-one moment ratio ≈ 0.230769. The unified closed form sin²θW = + ()(αEM/αs) is theorem-level. Why this gradeThe identity is exact; but the paper registers explicitly that the derivation of its functional form is unreachable within this framework — six mechanism families are excluded and the five standard quantisation routes are exhausted, so it is registered terminal [d]. The 0.21 ppm is an arithmetic candidate, not a promoted prediction. |
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| 04 真空能比值 04 Vacuum-energy ratio | , = = 1.8591353781… | 2.5532 / 2.5152 / 2.9721 ×10⁻⁴⁷ GeV⁴ · Planck-2018 ×2 · SH0ES | −1.80 % −3.26 % +14.31 % | 恒等式 [a]机制 [c]Identity [a]Mechanism [c] | |
推导来源ρeff = ΛCM⁴·e−S*， S* = 150 ln 2 = 103.9720770840， ρvac = ρeff/G₁ = 2.599951×10⁻⁴⁷ GeV⁴。 G₁ 的三个分量都是独立结构计数：45 = 10⊗5̄ 的分量数，24 = 伴随维数，x = 封板乘子期望值。 评级理由恒等式精确到末位（[a]）。但"G₁ 是这个位置的机制，还是恰好落在观测带内的精确算术恒等式" 仍未决，登记为候选 [c]。预注册的谱分层检验路线已执行并关闭， 三条预注册标准全不满足——该路线不再是可用的提升路径。 Derivationρeff = ΛCM⁴·e−S*, S* = 150 ln 2 = 103.9720770840, ρvac = ρeff/G₁ = 2.599951×10⁻⁴⁷ GeV⁴. The three components of G₁ are independent structural counts: 45 = the component count of 10⊗5̄, 24 = the adjoint dimension, x = the sealed multiplier expectation value. Why this gradeThe identity is exact to the last digit ([a]). But whether G₁ is the mechanism of this placement or an exact arithmetic identity that happens to sit inside the observed band remains undecided, and is registered as a candidate [c]. The pre-registered spectral-layering test route has been executed and closed, with all three pre-registered criteria unmet — it is no longer an available upgrade path. |
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| 05 三代费米子结构 05 Three fermion generations | Ngen = 12/(Nc+1) = 3 一代 = Λeven(C⁵) = 1 ⊕ 10 ⊕ 5̄，维数 16 One generation = Λeven(C⁵) = 1 ⊕ 10 ⊕ 5̄, dimension 16 | 3观测Observed | 0 | 计数 [a]强涌现 [d]Count [a]Strong emergence [d] | |
推导来源一代的表示内容与超荷零和由结构给出；给定 SU(5) 嵌入，Yukawa 单态唯一（Hom 空间一维、零自由指标）， 故生成结构在表示论意义上唯一。计数恒等式与色数挂钩，从独立方向佐证同一内容。 评级理由计数与表示内容为 [a]；"为何机制恰好给出三、而不是别的数"的强涌现未决，登记为 [d]。 五个候选复制机制（含最自然的置换对称路线）被逐一写下并否证。 DerivationThe representation content of one generation and the vanishing hypercharge sum follow from structure; given the SU(5) embedding the Yukawa singlet is unique (one-dimensional Hom space, zero free indices), so the generation structure is representation-theoretically unique. A counting identity tied to the colour number corroborates the same content from an independent direction. Why this gradeThe count and the representation content are [a]; why the mechanism yields exactly three and not another number is undecided, registered [d]. Five candidate replication mechanisms — including the most natural permutation-symmetric route — are written down and falsified one at a time. Companion papersS02 · Three fermion generations from one five-dimensional sector |
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| 06 强 CP 角消失 06 Vanishing strong-CP angle | 质量矩阵实、对称、正定 Mass matrix real, symmetric, positive definite | < 10⁻¹⁰实验上限Experimental bound | — | 恒等 [a]Identity [a] | |
推导来源θ̄ 恒等地为零，因为本理论的质量矩阵是实对称正定的——零是精确结果，不是拟合。 评级理由恒等为 [a]。需注意：这与实验上限一致，但本框架未就此作超出理论层级的声称 （未对中子电偶极矩作数值预言）。 Derivationθ̄ vanishes identically because the mass matrix of this theory is real symmetric and positive definite — zero is an exact result, not a fit. Why this gradeThe identity is [a]. Note that this is consistent with the experimental bound, but the framework makes no claim here beyond the theory level (it makes no numerical prediction for the neutron electric dipole moment). Companion papers |
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| 07精细结构常数M-5 读数07Fine-structure constantM-5 reading | 1/αEM = 137.0359990828137.0359990828 | 137.035999084CODATA 2018 | −1.20×10⁻⁹ | 恒等 [a]Identity [a] | |
推导来源M-5 读数由谱算术链给出，与自对偶值是不同的两条链：自对偶值 137.036756482 高 5.5 ppm，M-5 读数则落在 CODATA 的末位上。 评级理由条目 #181、#182 记于套件。两个数不是同一个数，不能混用。 DerivationThe M-5 reading comes from the spectral-arithmetic chain, a different chain from the self-dual value: the self-dual value 137.036756482 is high by 5.5 ppm, whereas the M-5 reading lands on CODATA's last digit. Why this gradeEntries #181 and #182 are recorded in the suite. The two numbers are not the same number and must not be conflated. Companion papersS04 · Electroweak mixing angle and fine-structure registration | |||||
| 08真空能密度与观测带对照08Vacuum-energy densityagainst the observed band | ρeff = ΛCM⁴·e−S*, S* = 150 ln 2ρvac = 2.599951×10⁻⁴⁷ GeV⁴ | −1.80% / −3.26% / +14.31%Planck-2018 / SH0ES | 见左see left | 恒等 [a]机制 [c]Identity [a]Mechanism [c] | |
推导来源恒等式精确到末位；「G₁ 是机制还是恰好落在带内的恒等式」仍未决，登记 [c]。预先登记的谱分层检验路线已执行并关闭——三条标准全不满足。 评级理由跨约 120 个数量级的宇宙学常数问题。三个数据集的偏差分别按框架值为分母。 DerivationThe identity is exact to the last digit; whether G₁ is a mechanism or an identity that merely happens to fall inside the band remains undecided, registered [c]. The pre-registered spectral-tiering test route has been executed and closed — none of its three criteria is met. Why this gradeThe cosmological-constant problem across some 120 orders of magnitude. For each of the three datasets the deviation takes the framework value as its denominator. | |||||
| 09重子不对称精确有理数09Baryon asymmetryexact rational | ηB = 6/Cat(17,26)，Cat = 97946895066.1257685×10⁻¹⁰ | Planck 测定PlanckPlanck determinationPlanck | 1σ 内within 1σ | [a] 精确有理数[a] exact rational | |
推导来源分子 6 = NB = Nc!；分母是同一 Cat 数（= 1/det Mq），与 α 的归一化同源。 评级理由条目 #134 记「≈6.1258e−10（0.065%）」。P6 表列其为精确有理数。 配套论文DerivationThe numerator 6 = NB = Nc!; the denominator is the same Catalan number (= 1/det Mq), of the same origin as the normalisation of α. Why this gradeEntry #134 records "≈6.1258e−10 (0.065%)". P6 tables it as an exact rational. Companion papers | |||||
| 10宇宙学密度分数平坦性钉住10Cosmological density fractionpinned by flatness | ，0.690983005625 | 0.6889 ± 0.0056Planck-2018 | −0.301% | [d] 升级条件[d] upgrade condition | |
推导来源这一条的级别是 [d]，不是封板值。P6 逐列标注「升级条件，由平坦性钉住」「不在档案内」。和与比恒为 1 与 √5，形式极简——一个条件而非两个。 评级理由Ωm 对 0.3153 ± 0.0073 差 +2.033%，两者都落在 1σ 内。 DerivationThis entry is graded [d], not a seal value. P6 labels it column by column: "an upgrade condition, pinned by flatness", "not in the archive". The sum and the ratio are always 1 and √5; the form is minimal — one condition rather than two. Why this gradeΩm differs from 0.3153 ± 0.0073 by +2.033%, and both fall within 1σ. | |||||
| 11夸克质量比md/ms11Quark mass ratiomd/ms | ，31 = 2NcNsec+10.0533246 | 0.0500PDG | −6.235% | [a] 定理[a] theorem | |
DerivationP1 Table 5 labels it [a] row by row. The deviation from the lattice average 0.0514(8) is −3.609%. Why this gradeThe deviation takes the framework value as its denominator. Companion papers | |||||
| 12π 尺度量候选量12π-scale quantitycandidate | fπ = ΛCM·130.1587 MeV | 130.2(1.2) MeVPDG 汇编130.2(1.2) MeVPDG compilation | +0.032% | [c] 候选[c] candidate | |
DerivationThe anti-coincidence significance is 1.59σ, below the framework's own 2σ promotion line, so it is not promoted. This is a case of "registered but not promoted". Why this gradeP1 Table 5 records it as a candidate. Companion papers | |||||
| 13冻结弦张力禁闭开启点13Frozen string tensionwhere confinement opens | σ = ΛCM²/2π = 1681/(12800π) GeV²0.041803 GeV² | σlat ≈ 0.19 GeV²格点σlat ≈ 0.19 GeV²Lattice | 比值 4.55–4.63ratio 4.55–4.63 | 定理级算术归一化 [d]Theorem-level arithmeticNormalisation [d] | |
推导来源σ 是 ΛCM 的定理级推论；但定义里的归一化因子 2π 是借用的、不是内生的。κσ 的第一性原理值记入终局开放 [d]。 评级理由与格点的商 4.55–4.63 是外部读法的单位换算，不是框架预言。 配套论文Derivationσ is a theorem-level corollary of ΛCM; but the normalisation factor 2π in the definition is borrowed, not endogenous. The first-principles value of κσ is recorded as terminal and open [d]. Why this gradeThe quotient 4.55–4.63 against the lattice is a unit conversion of an external reading, not a framework prediction. Companion papers | |||||
| 14封板槽位强耦合四个封板整数之比14Sealed-slot strong couplinga ratio of four sealed integers | 1/αg = RK|K₂|/(NcNα) = 0.1171875 | —— | — | [a] 零自由参数[a] zero free parameters | |
DerivationA ratio of four sealed integers, with zero free parameters. It must not be read as "this value holds at every energy scale". Why this gradeEntry #193 records "a convention tension of 0.16%". Companion papersS08 · The one-loop coefficient from a projected colour sector | |||||
所有预测结构均零自由参数。所有边界、候选与未解项均按四态协议公开登记。 Every predicted structure carries zero free parameters. All boundaries, candidates and open items are registered openly under the four-state protocol.
03.2重大推论03.2Major corollaries
每一条都是封板算术的直接后果。点击任意行展开：给出闭式、推导要点、来源论文与审计级别。 级别为空的条目，表示该论文自评尚未定级——我们留空，不替它升格。 Each one is a direct consequence of the sealed arithmetic. Click any row to expand: the closed form, the derivation in brief, the source paper and its audit grade. Where a grade is empty, the paper has not yet graded itself — we leave it blank rather than upgrade it on its behalf.
| 推论Corollary | 闭式Closed form | 来源Source | 级别Grade | 展开Expand |
|---|---|---|---|---|
| 01四大力是同一结构的投影01Four interactions as projections of one structure | 四种相互作用 ← 一个结构的不同投影Four interactions ← projections of one structure | S14 | 结构 [b]Structural [b] | |
推导要点四种相互作用被表述为同一结构在不同扇区上的投影，而不是四套彼此独立、各自带耦合常数的相互作用。 这是本页主线"五扇区 ↔ 五专家"那条桥的理论出处。 为什么标 [b]投影关系是结构性的、可写的；但从结构到各耦合常数的数值要经过逐层的接口约定—— 每一层的前提都写在论文里。结构成立，数值依赖已声明的公设链。 DerivationThe four interactions are stated as projections of one structure onto different sectors, rather than four independent interactions each carrying its own coupling constant. This is where the page's spine — five sectors ↔ five experts — comes from. Why [b]The projection relation is structural and can be written down; but going from the structure to the numerical value of each coupling passes through layer-by-layer interface conventions, each with its premises stated in the paper. The structure holds; the numbers depend on a declared postulate chain. |
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| 02谱算术在整数处闭合02Spectral arithmetic closes on integers | ζ | S01 | 恒等 [a]Identity [a] | |
闭式ζJ(1) = N(N+11)/2，对每一个截断 N = 2…16 都成立。 N = 16 时给出 ； ； 。 为什么它是 [a]倒数幂和落到整数上，且不只是某一个尺寸的巧合——它在 15 个不同的截断上全部闭合。 若闭合只是尺寸的假象，不会在每一个尺寸上都成立。 Closed formζJ(1) = N(N+11)/2, holding at every truncation N = 2…16. At N = 16 it gives ; ; . Why it is [a]The reciprocal-power sums land on integers, and not as an accident of one size — the closure holds at fifteen different truncations. A closure that were an artefact of the size would not hold at every size. |
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| 03电弱混合角03Electroweak mixing angle | sin²θW = | S04 | 算术 [a]形式 [d]Arithmetic [a]Form [d] | |
闭式sin²θW = = ()(1 + ) = 0.2312199519。 两个分项进入：纯费米子 SU(5) 基线 0.207865，一级链矩比 。 统一闭式 sin²θW = + ()(αEM/αs) 为定理级。 为什么是 [a]/[d]恒等式精确（与 PDG 差 −0.21 ppm）。但论文明确登记： 其函数形式的推导在本框架内不可达——六类机制族被排除、五条标准量子化路线穷尽。 所以恒等式是 [a]，而形式的来源是终态 [d]。0.21 ppm 是算术候选，不是被提升的预言。 Closed formsin²θW = = ()(1 + ) = 0.2312199519. Two entries enter separately: the pure-fermion SU(5) baseline 0.207865, and the level-one moment ratio . The unified closed form sin²θW = + ()(αEM/αs) is theorem-level. Why [a]/[d]The identity is exact (−0.21 ppm against PDG). But the paper registers explicitly that the derivation of its functional form is unreachable within this framework — six mechanism families excluded, the five standard quantisation routes exhausted. So the identity is [a], and the origin of the form is terminal [d]. The 0.21 ppm is an arithmetic candidate, not a promoted prediction. |
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| 04电子–缪子质量比04Electron–muon mass ratio | S12 | 条件级 [b]Conditional [b] | ||
闭式me/mμ = = 4.839729981×10⁻³。 两个输入都是纯数： 是封板测度的精确矩； λmin = 0.008282367951834317806477564456700357807405 是 的最小特征值，已由两条独立路径复现到全部 42 位有效数字。 为什么只到 [b]与 PDG 差 +0.0702%。但显式因子 5 没有推导——论文测试并否证了五个候选来源 （扇区数、骨架维数、外代数维数、数值残差、谱路线）。 论文自评："事后比较，低于定理级"。所以这里不标封板级。 Closed formme/mμ = = 4.839729981×10⁻³. Both inputs are pure numbers: is an exact moment of the sealed measure, and λmin = 0.008282367951834317806477564456700357807405 is the smallest eigenvalue of , reproduced by two independent routes to all 42 significant digits. Why only [b]+0.0702% against PDG. But the explicit factor 5 has no derivation — the paper tests and falsifies five candidate sources (sector count, skeleton dimension, exterior-algebra dimension, numerical residual, spectral route). The paper's own assessment: "a post-hoc comparison, below theorem level." So it is not labelled seal-grade here. |
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| 05真空能比值落在观测带内05Vacuum-energy ratio inside the observed band | S11 | 恒等式 [a]机制 [c]Identity [a]Mechanism [c] | ||
闭式，， 即 = 1.8591353781…。 ρeff = ΛCM⁴·e−S*， S* = 150 ln 2 = 103.9720770840， 得 ρvac = 2.599951×10⁻⁴⁷ GeV⁴。 为什么是 [a]/[c]恒等式精确到末位，落点偏离三个观测值 −1.80% / −3.26% / +14.31%。 但"G₁ 是这个位置的机制，还是恰好落在带内的精确恒等式"仍未决，登记为候选 [c]。 预注册的谱分层检验路线已执行并关闭——三条标准全不满足，那不是可用的提升路径。 Closed form, , that is = 1.8591353781…. ρeff = ΛCM⁴·e−S*, S* = 150 ln 2 = 103.9720770840, giving ρvac = 2.599951×10⁻⁴⁷ GeV⁴. Why [a]/[c]The identity is exact to the last digit and lands −1.80% / −3.26% / +14.31% away from the three observed values. But whether G₁ is the mechanism of this placement or an exact identity that happens to fall inside the band remains undecided, registered as candidate [c]. The pre-registered spectral-layering route has been executed and closed — all three criteria unmet, so it is not an available upgrade path. |
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| 06强耦合系数06Strong coupling coefficient | c² | S08 | 恒等 [a]巧合 [d]Identity [a]Coincidence [d] | |
闭式c²，从投影色扇区得出。 色数 Nc = 3 由结构给出，不是输入。 同篇记录了一个被否证的巧合论文标题里就写着 and a falsified coincidence—— 一条曾看起来成立的数值巧合被检验并否证，如实留在论文里。 这是本框架审计纪律的样本：否证结果不删除。 Closed formc², obtained from the projected colour sector. The colour number Nc = 3 comes from structure, not from input. The same paper records a falsified coincidenceThe title itself reads and a falsified coincidence — a numerical coincidence that once looked like it held was tested and falsified, and is kept in the paper as written. It is a sample of this framework's audit discipline: negative results are not deleted. |
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| 07三代费米子07Three fermion generations | Ngen = 12/(Nc+1) = 3 | S02 | 计数 [a]强涌现 [d]Count [a]Strong emergence [d] | |
闭式Ngen = 12/(Nc+1) = 3。 一代的表示内容 Λeven(C⁵) = 1 ⊕ 10 ⊕ 5̄，维数 16。 给定 SU(5) 嵌入，Yukawa 单态唯一（Hom 空间一维、零自由指标）。 为什么是 [a]/[d]计数与表示内容为 [a]；"为何机制恰好给出三、而不是别的数"的强涌现未决，登记 [d]。 五个候选复制机制（含最自然的置换对称路线）被逐一写下并否证。 Closed formNgen = 12/(Nc+1) = 3. One generation is Λeven(C⁵) = 1 ⊕ 10 ⊕ 5̄, dimension 16. Given the SU(5) embedding, the Yukawa singlet is unique (one-dimensional Hom space, zero free indices). Why [a]/[d]The count and the representation content are [a]; why the mechanism yields exactly three and not another number is undecided, registered [d]. Five candidate replication mechanisms — including the most natural permutation-symmetric route — are written down and falsified one at a time. |
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| 08强 CP 角恒等消失08Strong-CP angle vanishes identically | 主论文 §2.5Main paper §2.5 | 恒等 [a]Identity [a] | ||
闭式，恒等成立。实验上限 < 10⁻¹⁰。 推导要点本理论的质量矩阵是实、对称、正定的，于是 θ̄ 恒等为零—— 零是精确结果，不是拟合、也不是被调小的参数。 这是"结构强制结果"最干净的一个例子。 Closed form, identically. The experimental bound is < 10⁻¹⁰. DerivationThe mass matrix of this theory is real, symmetric and positive definite, so θ̄ vanishes identically — zero is an exact result, not a fit and not a parameter tuned down. This is the cleanest instance of "structure forcing a result". |
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| 09正性间隙定理09Positivity gap theorem | 最低激发分离 > 0lowest excitation separation > 0 | S07 | 条件定理Conditional theorem | |
核心陈述间隙不是数值观察，而是族算术内的定理；若质量守恒界 μ₋ > 1/√2 不成立，陈述退化为条件定理。与全态定理、手征性定理共同构成动力学功能层十二个对象中的第 5、6、7 项。 推导要点级别标为 [a 条件性]，两个前提显式写出：模型侧正性 Δ > 0、质量守恒 μ₋ > 1/√2（负模数 Nc²−1 = 8）。论文自陈「它是证明链里的一步，不是招牌值」。 级别与来源主论文 §4；S07 · 有限谱族内的禁闭定理 StatementThe gap is not a numerical observation but a theorem inside the family arithmetic; if the mass-conservation bound μ₋ > 1/√2 fails, the statement degrades to a conditional theorem. Together with the all-state theorem and the chirality theorem it forms items 5, 6 and 7 of the twelve objects in the dynamical-function layer. Derivation in briefThe grade is marked [a conditional], with its two premises written out explicitly: positivity on the model side, Δ > 0, and mass conservation, μ₋ > 1/√2 (negative mode number Nc²−1 = 8). The paper says of itself that "it is one step in a proof chain, not a headline value". Grade and sourceMain paper §4; S07 · Confinement theorems inside a finite spectral family | ||||
| 10全态定理10All-state theorem | Δ∞th = 0.8480856676 | S07 | [a][b] | |
核心陈述闭式 Δ∞ = √(p∞(1+q∞²))(1−δ∞)·0.8480856676，δ∞ = 2.94×10⁻⁸，p∞ = 1 以复制动力学的赢者通吃定理为条件。 推导要点取 q∞ = 0 求值 0.8480856551，低于主值 δ∞ 修正 1.25×10⁻⁸。机制由约束驱动：完全正性禁止带色荷通量逃逸。 级别与来源级别两说并存，本页照录不调和：恒等式 #221 与 P1 记「无条件全态值 / [a]」，P5 记「定理级但条件闭，判定等级为 [b]」。主论文 §4 式(13)；S07 StatementClosed form Δ∞ = √(p∞(1+q∞²))(1−δ∞)·0.8480856676, with δ∞ = 2.94×10⁻⁸ and p∞ = 1, conditional on the winner-take-all theorem of the replication dynamics. Derivation in briefEvaluating at q∞ = 0 gives 0.8480856551, below the main value by the δ∞ correction of 1.25×10⁻⁸. The mechanism is constraint-driven: complete positivity forbids the escape of flux carrying colour charge. Grade and sourceTwo accounts of the grade coexist, and this page records both without reconciling them: identity #221 and P1 record "unconditional all-state value / [a]", while P5 records "theorem-level but conditionally closed, judged grade [b]". Main paper §4, Eq. (13); S07 | ||||
| 11右手征中微子是保迹信道的零模11The right-handed neutrino is the zero mode of the trace-preserving channel | 零模zero mode | S17 | [a] | |
核心陈述右手征中微子被表述为保迹信道的零模——不是被额外引入的粒子。 推导要点配套的有量纲锚 MR = vcond²/mν = 1.212×10¹⁵ GeV；论文注明这属于协议条目，不是内部推导的主张。 级别与来源S17 指出该能标被中微子振荡数据钉在 1.21×10¹⁵ GeV 的 1.167 倍以内。在协议层级不主张任何中微子质量数值。S17 · 右手征中微子作为保迹信道的零模 StatementThe right-handed neutrino is formulated as the zero mode of the trace-preserving channel — not a particle introduced in addition. Derivation in briefThe companion dimensional anchor MR = vcond²/mν = 1.212×10¹⁵ GeV; the paper notes that this belongs to the protocol register, not to a claim of internal derivation. Grade and sourceS17 notes that this scale is pinned by neutrino-oscillation data to within a factor of 1.167 of 1.21×10¹⁵ GeV. No neutrino mass value is claimed at the protocol level. S17 · The right-handed neutrino as the zero mode of the trace-preserving channel | ||||
| 12π 的来源：连续统是一个输入12The origin of π: the continuum is an input | π-ENDOGEN 判据π-ENDOGEN criterion | S19 | [a] | |
核心陈述框架中每一处 π 都可追溯到一项被采用的连续测度或度规；框架唯一的内生超越量是 S* = 150 ln 2。 推导要点两方向验证：π 只能被迁移、不能被消除；且指定该对象不需要 π——各阶矩是有理数、有支集有界使矩问题确定。 级别与来源这是一个否定性的、精确的结论：不是「还没找到 π 的来源」，而是「这个模型不含 π 的自由度」。S19 · π 的起源：连续统是一个输入 StatementIn the framework every occurrence of π can be traced back to a continuous measure or metric that has been adopted; the framework's only endogenous transcendental quantity is S* = 150 ln 2. Derivation in briefVerification in both directions: π can only be relocated, never eliminated; and specifying this object requires no π — the moments at every order are rational, and bounded support makes the moment problem determinate. Grade and sourceThis is a negative and exact conclusion: not "the origin of π has not been found yet" but "this model contains no degree of freedom for π". S19 · The origin of π: the continuum is an input | ||||
| 13宇宙学密度分数被平坦性钉住13The cosmological density fraction is pinned by flatness | 和恒为 1，比恒为 √5sum always 1, ratio always √5 | P6 | [d] | |
核心陈述= 0.690983005625…， = 0.309016994375…；二者之和恒为 1、之比恒为 √5。 推导要点判据是「平坦性把分数唯一钉住」。对照 0.6889 ± 0.0056 差 −0.301%，对照 0.3153 ± 0.0073 差 +2.033%，都在 1σ 内。 级别与来源⚠️ 级别是 [d]：P6 明列「升级条件，由平坦性钉住」「不在档案内」——不是封板值。本页据此标注，不与 [a] 级条目并列。P6 · 宇宙学谱 Statement= 0.690983005625…, = 0.309016994375…; their sum is always 1 and their ratio always √5. Derivation in briefThe criterion is that "flatness pins the fractions uniquely". Against 0.6889 ± 0.0056 the difference is −0.301%; against 0.3153 ± 0.0073 it is +2.033% — both within 1σ. Grade and source⚠️ The grade is [d]: P6 states explicitly "an upgrade condition, pinned by flatness" and "not in the archive" — this is not a seal value. This page marks it accordingly and does not list it alongside [a]-grade entries. P6 · The cosmology spectrum | ||||
| 14胶球色单态的精确计数14An exact count of colour singlets for glueballs | Nn 三条独立路线互校Nn cross-checked by three independent routes | P2 | 结构性计数Structural count | |
核心陈述n 个胶子构成的独立色单态数：n = 0…10 为 1, 0, 1, 2, 8, 32, 145, 702, 3598, 19280, 107160；。三条互相独立的路线逐项互校到 n ≤ 11。 推导要点计数由封板算术在比较之前定死，不带可调参数；通道分配与奇特态（1⁻⁺ 在 1/2/3 胶子都不可得）逐条给出。 级别与来源同篇明文：「封板算术不给出任何胶球质量」，并与格点 1.754 GeV 并列给出比值 3.13 / 4.31，声明「这一并置不构成触达断言」。可证伪条件逐条列在表 13。P2 · 胶球谱中的色单态 StatementThe number of independent colour singlets formed by n gluons: for n = 0…10 it is 1, 0, 1, 2, 8, 32, 145, 702, 3598, 19280, 107160; . Three mutually independent routes cross-check term by term up to n ≤ 11. Derivation in briefThe count is fixed by the sealed arithmetic before any comparison, with no adjustable parameters; channel assignments and exotic states (1⁻⁺ unavailable at 1/2/3 gluons) are each given explicitly. Grade and sourceThe same paper states in plain terms: "the sealed arithmetic gives no glueball mass", and it sets the ratios 3.13 / 4.31 alongside the lattice value 1.754 GeV while declaring that "this juxtaposition does not constitute a claim of contact". The falsification conditions are listed one by one in Table 13. P2 · Colour singlets in the glueball spectrum | ||||
本节持续补充。级别为空的条目表示论文自评尚未定级——我们留空，不替它升格。 This section grows over time. An empty grade means the paper has not yet graded itself — we leave it blank rather than upgrade it.
03.3算术内核03.3Arithmetic core
链的起点是一个结构数字：谱度 dsp = 16。谱闭合强制判别式 17，判别式–域双射唯一选出 Q(√17)，该域的算术给出不变量对 ， 两个锁定约束把 Beta 参数逼到唯一解 (2, 10)。下面三幅图全部由该闭式重算绘制。 The chain starts from one structural number: the spectral degree dsp = 16. Spectral closure forces the discriminant 17; the discriminant–field bijection then selects Q(√17) uniquely; and the arithmetic of that field supplies the invariant pair , while two locked constraints drive the Beta parameters to the unique solution (2, 10).All three figures below are drawn from a recomputation of that closed form.
，而闭合要求 32——机制特异于此域。这一判别力是与"拟合"的分界。 Q(√5) yields |K₂| = 4 where closure would require 32 — the mechanism is specific to this field. That discriminating power is the line between a chain and a fit.
倒数幂和落到整数上，且对每一个截断 N = 2…16 都闭合为多项式 ζJ(1) = N(N+11)/2。 闭合若只是尺寸的假象，不会在每一个尺寸上都成立。 The reciprocal-power sums land on integers, and close to a polynomial ζJ(1) = N(N+11)/2 at every truncation N = 2…16. A closure that were merely an artefact of the size would not hold at every size.
宇宙位于窗内自对偶点上方 处，正朝全弧吸引子爬升。 α⁻¹ 沿该方向下降至 136.640——观测到 α 反向漂移将否证这一图像。 The universe sits above the self-dual point inside the window, climbing toward the full-arc attractor. Along that direction α⁻¹ falls to 136.640 — an observed drift of α the other way would falsify this picture.
03.4方法03.4Method
一个理论最容易作弊的地方，是在知道答案之后回头调参数。 下面三条纪律就是为了让这件事做不到——它们是可核对的，不是声明。 The easiest place for a theory to cheat is to look at the answer and tune a parameter back into place. The three rules below exist to make that impossible — and they can be checked, not merely asserted.
01
任何测量值都不作为输入进入推导，只在事后作为对照出现。 每一个比较都显式写出它的参照基（例如电弱混合角相对 PDG 中心值 0.23122）。No measured value enters a derivation as input; measurements appear only afterwards, as comparisons. Every comparison states its reference basis explicitly (for instance the electroweak mixing angle against the PDG central value 0.23122).
主论文 Methods M5；S13 · 审计纪律Main paper Methods M5; S13 · audit discipline
02
关键输入由两条互不使用的路径各自得出。例如 Jacobi 对 (α, β) = (1, 9)： 它既作为封板输入进入公理清单，又由域算术路径在不使用该条目的前提下独立重新导出。Key inputs are obtained by two routes that do not use each other. The Jacobi pair (α, β) = (1, 9), for example, enters the axiom list as a sealed input, and is independently re-derived by the field-arithmetic route without using that entry.
主论文 Methods M7；S03 · 域算术链Main paper Methods M7; S03 · field-arithmetic chain
03
203 条闭式恒等式全部通过独立符号计算核验，0 失败。 核验套件由四个脚本组成、经单一入口执行，任何一项失败即以非零退出码返回—— 这是公开的复现入口。All 203 closed-form identities pass independent symbolic verification, with 0 failures. The suite is four scripts behind a single entry point, and any failure returns a non-zero exit code — it is the public reproduction entry point.
主论文 Methods M7；S13Main paper Methods M7; S13
还有两条更硬的纪律：2σ 提升线（数值候选的统计显著性低于 2σ 就登记但不晋级， 例如 1.59σ 的 π 尺度候选）与四要素同时满足（机制、唯一性、统计显著性、先推导后比较） 才能升到定理级。早期启发材料与封板结果分开记档，十五处早期更正作为勘误记录归档。 Two harder rules sit behind those: the 2σ promotion line (a numerical candidate below 2σ significance is registered but not promoted — the 1.59σ pion-scale candidate is the example) and four conditions satisfied together (mechanism, uniqueness, statistical significance, derive-before-compare) before anything reaches theorem grade. Early exploratory material is filed separately from the sealed results, and fifteen documented corrections are archived as an erratum record.
05论文库与技术背书Paper library and technical backing
FluxRuta 是大项目，RET 是它的核心理论与核心主论文。 核心主线 28 篇已全部公开并分配 DOI，哲学组 5 篇同样已发表，合计 33 篇；其余四组已完成注册准备。 FluxRuta is the project; RET is its core theory and core main paper. The 28 core papers are all public with DOIs assigned, the 5 philosophy papers are published as well — 33 in total; the four remaining groups are ready for registration.
全部推导受一套显式审计协议约束：四态分级、2σ 提升线、 提升到定理级需机制／唯一性／统计显著性／比较前先推导四项同时成立。 三条常设规则：未知不得当作已知；未导出不得比较；等值不蕴含同源。 15 条更正记录保留前后文而非删除。 Every derivation is governed by an explicit audit protocol: four-state grading, a 2σ promotion line, and promotion to theorem level requiring mechanism, uniqueness, statistical significance and derivation-before-comparison — all four at once. Three standing rules: the unknown is never treated as known; nothing is compared before it is derived; equal values do not imply common origins. Fifteen documented corrections are kept with their before-and-after statements rather than erased.
S13 · An audit discipline for a theory's own derivations
10.5281/zenodo.23241035
框架的六个未决项与十项边界登记在主论文 §7，逐条给出级别、已尝试的路线与闭合所需条件。 The framework's six open items and ten boundary registrations are listed in §7 of the main paper, each with its grade, the routes already attempted, and what closing it would require.
主论文 §7 · Open items and framework boundaries
10.5281/zenodo.23228865
Main paper §7 · Open items and framework boundaries
10.5281/zenodo.23228865
03.5一般问题答疑03.5General questions answered
下面八条是从外部视角最常被提出的质疑。每一条都分两栏：左栏是大白话，右栏是论文自己的说法—— 数字、级别与措辞均照录，未作调和。 Eight objections most often raised from outside. Each is laid out in two columns: plain language on the left, the paper’s own account on the right — numbers, grades and wording quoted as written.
质询Objection 01为什么偏偏是 ℚ(√17)、为什么是五维、为什么 Kraus 秩是 16？这不就是数秘术式的后验选择吗？Why ℚ(√17), why five dimensions, why Kraus rank 16 — isn't this numerology chosen after the fact?
有人说，这套理论里的数字——五维、16、√17——看着就像先知道答案、再回头凑出来的。这种怀疑很正常。但论文里的顺序是反的：先把起点钉死，然后证明从这一步往下走，每一步都没有别的选择。一步接一步，最后剩下的答案只有一个。People suspect the numbers in this theory — five dimensions, 16, √17 — were chosen after seeing the answer. That suspicion is fair. But the order in the paper runs backwards: pin the starting point first, then show that from there, every step has no alternative. Step after step, and only one answer is left standing.
论文自评级别：论文把「为什么是五维」——等价地「为什么是这个谱次数、从而为什么在所有实二次域中是这一个域」——登记为该理论的公理边界；扇区计数与五维结构的等同级别为 [b]，Kraus 秩 16（N_sp = 16）是表 S1 的封板输入，其三条等价表述（16 = dim = 10 ⊕ 5̄ ⊕ 1）在档内记为同一对象的恒等式。The paper's own grade: The paper registers “why five dimensions” — equivalently why this spectral degree and hence this field among all real quadratic fields — as the axiom boundary of the theory; the identification of the sector count with the five-dimensional structure is graded [b], and the Kraus rank 16 (N_sp = 16) is a sealed input of Table S1 whose three equivalent statements (16 = dim = 10 ⊕ 5̄ ⊕ 1) are recorded in the archive as identities of one object.
主论文 §1 输入边界、§2.6、Methods M3/M7；S03 摘要与 §4/§5/§7(ii)（10.5281/zenodo.23240982）；恒等式 #1、#30–#32Main paper §1 input boundary §2.6 Methods M3/M7 ; S03 abstract and §4/§5/§7(ii) (10.5281/zenodo.23240982); identity #1 #30–#32
质询Objection 02一套谱算术怎么过渡到连续时空里的局域量子场论？它有没有传统 QFT 的微扰与非微扰动力学支撑？How does a spectral arithmetic reach local quantum field theory in continuous spacetime — does it carry the perturbative and non-perturbative dynamical support of conventional QFT?
有人问：一堆矩阵和数字，凭什么算物理理论？论文自己先划了一条线：它做的是「骨架」，不是「血肉」。骨架指的是量子场论的基本框架——有哪些自由度、信息怎么流动、怎么组合起来。至于具体的动力学数字，论文明确说那不在它的产出之内。The question is why a stack of matrices and numbers should count as physics. The paper draws the line itself: it builds the skeleton, not the flesh. The skeleton is the basic frame of quantum field theory — what the degrees of freedom are, how information flows, how things compose. The dynamical numbers on top of that frame are explicitly declared not to be its output.
论文自评级别：色扇区＝封板规范结构的颜色块（八个生成元以零新参数复现 su(3) 结构常数、块在乘法下封闭）为 [a] 定理级，单圈 _c² 为扇区内推导；到局域 su(3) Yang–Mills 的限制映射与「与 QCD 特定色单态约束的等同」登记为开放边界（§7(x)）；量子场论运动学骨架的重建登记为前设层级的框架自描述，级别低于定理级。The paper's own grade: The colour sector as the colour block of the sealed gauge structure (eight generators reproducing the su(3) structure constants with zero new parameters, the block closed under multiplication) is theorem-level [a], and the one-loop _c² is derived inside the sector; the restriction map to local su(3) Yang–Mills and the identification with QCD's specific colour-singlet constraint are registered as open boundaries (§7(x)); the reconstruction of the kinematic skeleton of QFT is a registered framework self-description at premise level, below theorem level.
主论文 §4(EN p.19)、§7(x)(xi)(EN p.25–26)；S07 10.5281/zenodo.23240995；S08 10.5281/zenodo.23240998；S09 10.5281/zenodo.23241002Main paper §4 (EN p.19) §7(x)(xi) (EN p.25–26); S07 10.5281/zenodo.23240995; S08 10.5281/zenodo.23240998; S09 10.5281/zenodo.23241002
质询Objection 03唯一的有量纲入口 是靠注入 1 GeV 得到的，这不是人工锚定吗？The unique dimensionful entrance comes from injecting 1 GeV — isn't that a hand-made anchor?
理论算出来的都是纯数字，没有单位。可现实里的物理量是有单位的——最后总得有人把「1 GeV」放进去。论文没有绕开这一步，而是把它完整摊在桌面上：这个出口只开一次，写在明面上， = + + ，三项各有各的来历。这是记账，不是事后调数。What the theory produces are pure numbers with no units. Real physical quantities do have units, so someone eventually has to put “1 GeV” in. The paper does not dodge this; it lays the step out in full: the exit is opened once, in the open, as = + + , each term with its own origin. That is bookkeeping, not tuning.
论文自评级别：Λ_CM 本身登记为接口赋值（interface assignment），而非谱输出； 与 在封板算术中精确， = 1/N_sec 承载扇区计数、是本框架的一项设定而非推导，且在 R_KRAUS = 16 为封板输入的前提下三项组成部分同处设定层级；其来历按两个时间切片记录：封板之前由弦张力拟合反演而得，封板之时被冻结为一个定义，封板之后它是定义而非拟合；该接口赋值陈述的强度为条件式（若出现第二个独立量纲出口则降格）。The paper's own grade: Λ_CM itself is registered as an interface assignment rather than a spectral output; and are exact in the sealed arithmetic, while = 1/N_sec carries the sector count and is a setting of the framework rather than a derivation, and with RKRAUS = 16 a sealed input all three components stand at the same setting level; its provenance is recorded in two time slices — before sealing it was obtained by inverting the string-tension fit, at sealing it was frozen as a definition, after sealing it is a definition rather than a fit; the strength of the interface-assignment statement is conditional (it would be downgraded if a second independent dimensionful outlet appeared).
主论文 §5 接口层(EN p.19–20)、§1、§7(iv)(v)(EN p.24)；S05 §2（10.5281/zenodo.23240988）；恒等式 #81、#82、#153Main paper §5 interface layer (EN p.19–20) §1 §7(iv)(v) (EN p.24); S05 §2 (10.5281/zenodo.23240988); identity #81 #82 #153
质询Objection 04为什么不直接用实验值反推常数？你们怎么保证不是先知道答案再回头凑推导？Why not simply read constants back off experiment — how do you guarantee the derivations were not reverse-engineered from known answers?
数字和实验对上了，会不会是先看了实验值、再倒推公式？这是最容易作弊的地方，所以论文直接把规则写死了：测量值不参与推导，只在事后当对照。而且每一次对照，都要写明是拿哪个数比的。If the numbers agree with experiment, were the formulas reverse-engineered from the measured values? That is the easiest place to cheat, so the paper fixes the rule outright: measured values take no part in a derivation — they appear only afterwards, as comparisons. And every comparison has to say which value it was measured against.
论文自评级别：比较纪律登记在方法层（主论文 M5；S13 的 M1–M4，不引入也不提升任何级别）；此外论文把 α 的「位置读法」如实登记为对测量值的反解——t_obs = 0.3500002763 的零残差是自动的，因为位置正是通过反演测量值来定义的——并把登记表谱读法 登记为已定位的边界（反向转录而非独立推导）。The paper's own grade: The comparison discipline is registered at the methods layer (main paper M5; S13's M1–M4, which introduce and promote no grades); in addition the paper records α's position reading as an inversion of the measured value — the zero residual of t_obs = 0.3500002763 is automatic because the position is defined by inverting the measured value — and registers the registry-table spectral reading as a located boundary (a reverse transcription rather than an independent derivation).
主论文 Methods M5/M6(EN p.34)、§3(EN p.12)、附录第 7 条(EN p.52)；S13 摘要与 Methods M1；S04 §6；恒等式 #78、#79、#180Main paper Methods M5/M6 (EN p.34) §3 (EN p.12) appendix item 7 (EN p.52); S13 abstract and Methods M1 ; S04 §6 ; identity #78 #79 #180
质询Objection 05数字对上了，怎么排除只是算术巧合？The numbers line up — how do you rule out mere arithmetic coincidence?
这么多数字，怎么知道不是碰巧？论文把这件事做成了能查的程序，不是靠嘴说。它设了一条硬线（2σ）：够得着才能往上升，够不着的就只登记、不升格。被推翻的巧合也照样留在论文里——第 8 篇的标题里就带着 and a falsified coincidence。With this many numbers, how do you know they are not luck? The paper turns that into a procedure you can check, rather than an assertion. It sets a hard line (2σ): clear it and a candidate can be promoted; miss it and it is merely registered. Coincidences that were refuted stay in the papers too — the title of paper 8 literally carries and a falsified coincidence.
论文自评级别：反巧合判据与 2σ 提升线写在主论文 Methods M5 与 S13 §3；未达阈值的候选按其登记级别留在 [c]（位于提升线之下的观测层面候选），该审计纪律本身为方法学层级、不引入也不提升任何级别。The paper's own grade: The anti-coincidence criterion and the 2σ promotion line are written down in main paper Methods M5 and S13 §3; candidates below the threshold stay at their registered grade [c] (an observation-level candidate below the promotion line), and the audit discipline itself is at methods level, introducing and promoting no grades.
主论文 Methods M5/M6、§7(iii)(EN p.23)；S13 摘要与 §3 巧合审查（10.5281/zenodo.23241035）；S08 §3 与 §7(ii)（10.5281/zenodo.23240998）；恒等式 #128、#193、#214Main paper Methods M5/M6 §7(iii) (EN p.23); S13 abstract and §3 coincidence review (10.5281/zenodo.23241035); S08 §3 and §7(ii) (10.5281/zenodo.23240998); identity #128 #193 #214
质询Objection 06它和标准模型、QCD、引力、大统一或弦理论是什么关系？是要取代它们，还是复现它们的结构？How does it relate to the Standard Model, QCD, gravity, grand unification or string theory — does it replace them or reproduce their structure?
它是要取代标准模型吗？不是。论文说的是：强、弱、电磁、引力四种相互作用，是同一个结构的四个侧面。而且在别人已经算好的地方，它能用零个新参数把结构重新算出来。Is it meant to replace the Standard Model? No. What the paper says is that the four interactions — strong, weak, electromagnetic, gravitational — are four faces of one structure. And where others have already done the calculation, it reproduces the structure with zero new parameters.
论文自评级别：四力作为同一骨架的块与射影为结构性陈述 [a]；色扇区＝封板规范结构的颜色块为 [a]； 为扇区内推导（条件性 [a]）；引力系数 被登记为结构上确立的不可推导性（一条边界定理，而非一处缺失的推导）；与 QCD 特定色单态约束的等同为开放边界，跨域等同仍停留在 [b]；明确不主张统一能标、荒漠与质子衰变。The paper's own grade: The four interactions as blocks and projections of one skeleton is a structural statement [a]; the colour sector as the colour block of the sealed gauge structure is [a]; is derived inside the sector (conditional [a]); the gravitational coefficient is registered as a structurally established non-derivability (a boundary theorem rather than a missing derivation); the identification with QCD's specific colour-singlet constraint is an open boundary and the cross-domain identification remains at [b]; no unification scale, desert or proton decay is claimed.
主论文 §2.0 表 2、§4 式(14)、§7(x)(xi)、§3 弦张力、讨论；S14 10.5281/zenodo.23241039；S08 10.5281/zenodo.23240998；S05 10.5281/zenodo.23240988；P1 10.5281/zenodo.23241060Main paper §2.0 Table 2 §4 Eq.(14) §7(x)(xi) §3 string tension discussion; S14 10.5281/zenodo.23241039; S08 10.5281/zenodo.23240998; S05 10.5281/zenodo.23240988; P1 10.5281/zenodo.23241060
质询Objection 07论文用 AI 做了什么？结果怎么保证？What was AI used for — and how are the results checked?
论文用 AI 做了什么？排版和数值复核。真正的内容是一条能查的流程：每个结论在使用之前先贴上标签（哪些是算出来的、哪些还带条件、哪些只是候选、哪些是边界），然后任何人拿到脚本都能重跑一遍。What was AI used for? Typesetting and numerical checking. The substance is a process anyone can inspect: every claim is labelled before it is used (which are derived, which are conditional, which are only candidates, which are boundaries) — and then anyone can re-run the scripts.
论文自评级别：审计纪律本身处于方法学层级：主论文附录写明「此处引用的级别就是正文中给出的级别；本附录不引入任何级别，也不提升任何级别」；工具声明见 Exp1——AI 工具（OpenCode、DeepSeek）用于排版与数值复核。The paper's own grade: The audit discipline itself sits at methods level: the main paper's appendix states that “the grades cited here are exactly the grades given in the body; this appendix introduces no grade and promotes no grade”; the tool statement appears in Exp1 — AI tools (OpenCode, DeepSeek) were used for typesetting and numerical checkingl.
S13 10.5281/zenodo.23241035（摘要、Methods M1、§2、§3）；主论文 Methods M6、§2.7、附录(EN p.53)；Exp1 funding/tool statement；恒等式 #15、#79、#199、#200；S18 10.5281/zenodo.23241053S13 10.5281/zenodo.23241035 (abstract, Methods M1 §2 §3); Main paper Methods M6 §2.7 appendix (EN p.53); Exp1 funding/tool statement; identity #15 #79 #199 #200; S18 10.5281/zenodo.23241053
质询Objection 08凭什么说它「零自由参数」？On what grounds is it called “zero free parameters”?
因为论文把「允许事先输入的东西」列成了一张清单。清单上只有七个数，而且其中四个是代数数论里早就有的定理——不是它自己挑的。清单以外的一切，都得靠推。Because the paper lists everything it is allowed to assume up front. There are seven numbers on that list, and four of them are pre-existing theorems of algebraic number theory — not choices of its own. Everything outside the list has to be derived.
论文自评级别：输入清单被逐项列出（表 S1 的七项数论输入 + 单位定义 + 等权分离公设 + 扇区设定），其中 N_sp = 16、A = 1、B = 9 三项为封板输入、其余域算术条目为代数数论定理；各条量化叙述按其登记级别分别定级（如 α_g 为封板槽位值，不得读作「在任意能标上都取该值」；扇区设定与单位定义同为公设，「为什么是五维」登记为公理边界）。The paper's own grade: The input list is itemised (the seven number-theoretic inputs of Table S1 plus the definitions of units, the equal-weight separation postulate and the sector setting), of which N_sp = 16, A = 1 and B = 9 are sealed inputs and the remaining field-arithmetic entries are theorems of algebraic number theory; each quantitative statement carries its own registered grade (e.g. α_g is a sealed-slot value and must not be read as ‘this value at every energy scale’; the sector setting and the unit definitions are likewise postulates, and ‘why five dimensions’ is registered as the axiom boundary).
主论文 §1(EN p.5)、Methods M5/M7 与表 S1(EN p.34–35)、§3、§5；恒等式 #1、#6、#92、#188、#189Main paper §1 (EN p.5) Methods M5/M7 andTable S1 (EN p.34–35) §3 §5 ; identity #1 #6 #92 #188 #189
03.6恒等式套件03.6Identity suite
封板算术的闭式恒等式在论文里自带分组——四个已验证套件加一组封板级结果， 其下再分 24 个主题小组。这里照录论文的分组结构，便于按主题查阅。 The closed-form identities of the sealed arithmetic come with their own grouping in the papers — four verified suites plus one group of seal-grade results, subdivided further into 24 thematic subgroups. The grouping structure is reproduced here as written, for reference by theme.
封板常数链sealed constant chain 1–13 · 13
α 完全内生闭式fully endogenous closed form for α 14–15 · 2
矩塔moment tower 16–37 · 22
类数簇 Q(√17)class-number cluster Q(√17) 38–72 · 35
健康窗口与 tfhealth window and tf 73–80 · 8
界面量interface quantities 81–97 · 17
真空能链vacuum-energy chain 98–101 · 4
乘子约化multiplier reduction 102–104 · 3
演化系数evolution coefficients 105–110 · 6
Beta–Fermat 族Beta–Fermat family 111–122 · 12
混合与宇宙学读数mixing and cosmological readings 123–136 · 14
电弱锚点electroweak anchors 137–141 · 5
α 读数（1.859）α reading (1.859) 142–149 · 8
18.4 基线（θW, σflux, γF）18.4 baseline (θW, σflux, γF) 150–156 · 7
谱–组合族spectral–combinatorial family 157–169 · 13
137 读数137 reading 170–174 · 5
M-5 读数M-5 reading 175–183 · 9
质量比mass ratios 184–187 · 4
αg 与弦数据αg and string data 188–193 · 6
数值汇合numerical convergences 194–198 · 5
深核常数 C3-Kdeep-core constant C3-K 199–200 · 2
偏斜与 σTskewness and σT 201–206 · 6
反馈反转与最终真空能有理数feedback reversal and final vacuum-energy rational 207–211 · 5
封板级结果sealed-level results 212–221 · 10
03.7论文群03.7Paper groups
主论文群 28 篇已全部发表，哲学组 5 篇同样已发表，合计 33 篇在 Zenodo 可解析。 化学组、数学组与扩展组共 99 篇已有 reserved DOI 但尚未发布——本页照实标注， 并把每篇的登记名与 DOI 一并列出。 The 28 papers of the main paper group are all published, the 5 philosophy papers as well — 33 in total, with resolvable DOIs on Zenodo. The chemistry, mathematics and extension groups — 99 papers in all — have reserved DOIs but are not yet released; this page marks that honestly and lists each paper's registered title together with its DOI.
这篇讲的是 RET 这套理论整体：物理定律被当作纯数学结构的必然输出，推导中不放任何测量值，全部内容架在一条「密封」作用量上。真空能量由一串密封算术给出，落在观测区间内；三代费米子和色荷数目是被算出来的。作者只把落位机制登记为候选，并说健康轴的绝对定标是框架内推不出来的边界。This is the RET framework: physical law is treated as the forced output of pure mathematical structure, no measured value enters any derivation, and everything rests on one sealed action. The vacuum energy comes out as a closed chain of sealed arithmetic inside the observed band, and three fermion generations and the colour number are computed rather than assumed. The author registers the placement mechanism as a candidate only, and calls the health-axis calibration a boundary the framework cannot reach.
zenodo.23228865这篇搭了一个实验平台，用来检验那些「输出精确数字」的理论：这种数字没法被拟合，只能对上或对不上。平台的常数全部来自理论内部而不是拟合，主体是一个用大模型同类组件搭出来的保正路由系统。在零输入、载体嵌入和三轴不变性这三条原则下，十一个由理论算术定住的观测量在同一次配置中同时成立，而任何被预言的数值都没有以可执行形式进入平台。The paper builds an experimental platform for theories whose predictions are exact numbers: such a number cannot be fitted, it either agrees or it does not. Every constant on the platform comes from inside the theory rather than from a fit, and the platform itself is a completely-positive routing system assembled from the same components that carry large language models. Under a zero-input constitution, a carrier embedding and three-axis invariance, eleven observables fixed by the theory's arithmetic held at once, with no predicted value entering in executable form.
zenodo.23241085这篇讲的是一个测度如何把普通的谱问题变成算术问题。二次域的算术把单位区间上的密度逼成 Beta(2,10) 形式，矩序列随即塌缩成精确递推，谱不变量也全是闭形式，其中两个是整数。作者强调这种收拢属于测度本身、与维数无关；结论依赖给出该测度的姊妹论文，最小特征值只是按显示精度引用，而非严格界。The point is that one measure turns an ordinary spectral problem into an arithmetic one. The arithmetic of a quadratic field forces the density on the unit interval into the Beta(2,10) form, the moment tower collapses to an exact recursion, and the spectral invariants become closed forms, two of them integers. That closure belongs to the measure rather than the dimension, yet stays conditional on the companion paper supplying it.
zenodo.23240933这篇讲的是费米子为什么正好有三代。标准模型把「有几代」当作输入，这里它由结构推出，而且靠排除法而不是断言：先写下五种可能的复制机制，再把它们逐个否证，其中也包括那个最自然的对称置换方案，这一轮排除才是结论的分量所在。作者同时标明，嵌入本身仍是公设，「正好三代」被登记为一个有具体位置的边界，而 μ 子那一层的数值还依赖两个尚未完成的环节。This asks why there are exactly three fermion generations. The Standard Model takes the count as an input; here it follows from structure, and it is established by elimination rather than assertion: five candidate replication mechanisms are written down and falsified one at a time, including the permutation-symmetric route that would be the natural first guess. The author states plainly that the embedding remains a postulate, that the strong emergence of exactly three generations is registered as a located boundary, and that the muon-sector numerical layer waits on two named closures.
zenodo.23240978这篇把一条链从头走到尾，中间没有拟合，链的前一半是纯算术。谱闭合逼出判别式 17，判别式与域的对应又唯一选出二次域 Q(17)，这个域的算术再给出不变量对，从而把谱测度唯一钉成 110x(1−x)^9 的形式。作者另用 Q(5) 做对照说明这条链有区分力：换成那个域，同样的步骤就对不上。五维扇区设定仍是登记在案的公设，推导中没有放入任何测量值。This walks one chain end to end with no fitted step; its first half is pure arithmetic. Spectral closure forces the discriminant 17, the discriminant-field correspondence then selects the quadratic field Q(17) uniquely, and the arithmetic of that field supplies the invariant pair that pins the spectral measure to 110x(1-x)^9. A control case, Q(5), shows the chain has discriminating power rather than merely fitting. The five-dimensional sector setting remains a registered postulate, and no measured number enters any step.
zenodo.23240982这篇讲的是电弱混合角在这套理论里同时存在好几种说法，必须先按认识地位分开：哪个值来自恒等式、哪个值来自定理、哪个还只是候选，这三者不是一回事。基线 是谱梯的矩比恒等式，它是不跑动的常数；统一公式是定理级的；而候选修正把基线的偏差压到极小。作者逐条给出等级，并说明候选的函数形式在本框架内够不着，属于终点级判断。This is about the electroweak mixing angle, which carries several statements at once that must be separated by epistemic status: a value from an identity, a value from a theorem and a value from a candidate are not the same kind of thing. The baseline is a moment-ratio identity and a constant rather than a running quantity; the unified formula is theorem-level; and the exact correction candidate carries the baseline to a very small agreement with measurement. Each statement is graded where it stands, and the candidate's functional form is graded terminal.
zenodo.23240986这篇讲的是禁闭（夸克不能单独存在这件事）在这套理论里不是从头到尾都在，而是在某一点才「打开」，而打开点上的弦张力是算出来的、不是拟合的。这个点由序参量形式摆在健康窗口的下沿，那里三样结构正好重合：窗口边界本身、演化律的点燃点、以及手征对称破缺的标度。作者说明冻结核验值属于定理级算术，与格点结果的对照按既定程序进行而不是宣称一致，而把禁闭读成健康轴上的一个相仍是候选。This says confinement, the fact that quarks cannot exist on their own, does not hold throughout the framework: it switches on at a point, and the string tension there is arithmetic rather than fitted. That point sits at the lower edge of the health window, where three structures coincide: the window boundary, the ignition point of the evolution law and the chiral-symmetry-breaking scale. The frozen value is theorem-level arithmetic, the lattice comparison follows a stated protocol rather than claiming agreement, and reading confinement as a phase of the health axis remains a framework candidate.
zenodo.23240988这篇讲的是宇宙在一条一维健康轴上的位置，遵循一条不是被选出来、而是被逼出来的规律。在给定条件下——单零点、两端极点、在窗口反射下取奇——最低阶可容许的规律是唯一的，逼近边缘的指数也是固定的，而不是可调参数。作者也说明哪些部分没有推导出来：那个孤立的定标值会从所有无量纲预言中约掉，而平衡式的历史读数方向只作为信息注记保留。The position of the universe on a one-dimensional health axis obeys a law that is not chosen but forced. Among rational flows with a single zero, poles at both window edges and odd behaviour under reflection, the lowest-order admissible law is unique, and the exponent of the approach to the edge is fixed rather than free. What is not derived is stated with the result: the isolated calibration value cancels from every dimensionless prediction, and the historical reading direction of the balance is retained only as an informational note.
zenodo.23240992这篇讲的是禁闭平时只是个数值结论（格点模拟给出弦张力和谱），而这里它在一个被钉住的有限三对角谱族里被证明成定理。作者特意让定理非平凡：手征定理说，两个最大格点幅值之差在零钉扎时精确为零，原因是二分结构把特征值配对、迫使配对的特征向量幅值相同。全态定理给出一个无量纲间隙值，并标明这个值来自姊妹算术链，与 QCD 色单态约束的对应仍属开放。Confinement is usually a numerical statement, with lattice simulations supplying a string tension and a spectrum; here it is proved as a theorem inside one pinned tridiagonal spectral family. The author makes the theorem non-vacuous: the chirality theorem shows the difference between the two largest site magnitudes vanishes exactly at zero pinning, because the bipartite structure pairs eigenvalues and forces paired eigenvectors to share magnitudes. A full-state theorem gives one dimensionless gap value, imported from the companion chain, and the identification with QCD's colour-singlet constraint remains open.
zenodo.23240995这篇讲的是 QCD 里那个人人都在用、却没人能解释的单圈系数。作者说明色扇区不是独立输入，而是密封 SU(5) 结构的一个投影：把骨架限制到色块上，不需要新参数就复现出 SU(3) 的结构常数，单圈系数也随之在扇区内算出，渐近自由在给定条件下成立。文章接着追问那个著名的「11」是否就是密封测度里的同一个 11，答案是否定的，并按五条反复现标准登记为一次否证，而不是把它当作巧合收起来。This tackles the one-loop coefficient of QCD, a number every practitioner uses and no framework inside it explains. The colour sector is shown to be a projection of a sealed SU(5) structure rather than an independent input: restricting the skeleton to its colour block reproduces the SU(3) structure constants with no new parameters, and the coefficient follows in-sector. The paper then asks whether the famous eleven is the same eleven as the sealed measure's spectral quantity and answers negatively, registering a falsification under five anti-recurrence criteria rather than filing it as a coincidence.
zenodo.23240998这篇讲的是把一个理论「算不出来」的自认，变成一条定理。对自由与密封的两个 Jacobi 算子，它们的系数偏离项可以求和，因此两者之差是迹类算子，这一点来自结构而不是假设；于是 Krein 谱移函数存在且唯一，矩序列与谱移函数携带同样的信息。作者据此说明数值层是一道可证明的信息守恒边界，而不是技术上的空缺，并附上一条归档定理：这种钉扎在本框架内不可判定。This turns a theory's prose admission that it cannot compute something into a theorem. For the free and the sealed Jacobi operator the coefficient deviation is summable, so the difference is trace-class structurally rather than by assumption; the Krein spectral-shift function therefore exists and is unique, and the moment sequence and the shift function carry equal information. The numerical layer is thus a provable information-conservation boundary rather than a technical gap, and an archived theorem records that the pinning is undecidable within the framework.
zenodo.23241002这篇讲的是这套理论的实现层，也就是训练那一侧，而不是物理那一侧。训练动态里出现的权重与序参量跟理论层的联系只是记号上的，作者把它们的等级照实登记为记号身份，没有升级成推导。算术权重是精确的，对齐权重与谱链值重合被当作两个独立方向的会合点，而不是单向推导；序参量则收敛到一个被钉住的小极限，其存在性、唯一性和钉扎值都在动态内部按定理级建立。This is about the implementation side of the framework, the training side rather than the physical side. The weights and the order parameter that appear there connect to the theory layer through notation rather than derivation, and they are registered at exactly that grade rather than promoted. The arithmetic weight is exact, the agreement of the alignment weight with the spectral-chain value is a meeting point of two independent sides rather than a one-way derivation, and the order parameter converges to a pinned limit whose existence, uniqueness and value are established at theorem level inside the dynamics.
zenodo.23241007这篇讲的是宇宙常数问题。通常它被说成真空能量估计与观测膨胀率之间差着一百多个数量级，而在这套框架里，比较化约成一个不含拟合量的精确有理数：理论真空能量除以一个密封有理数之后落进观测区间。作者说明这个有理数的三个组成部分都是结构计数，但它究竟是「落位机制」还是仅仅碰巧坐在正确区间里的算术恒等式，仍然开放，因此只作为候选提出，并配有事先登记的可否证检验方案。This is the cosmological constant problem. It is usually stated as a mismatch of more than a hundred orders of magnitude; here the comparison reduces to one exact rational with no fitted quantity in it, and the theory's vacuum energy divided by a single sealed rational lands inside the observed band. Its three components are independent structural counts, but whether it is the mechanism of the placement or an arithmetic identity that happens to sit in the right band remains open, so it is put forward as a candidate with a pre-registered falsifiable test protocol.
zenodo.23241029这篇讲的是电子与 μ 子的质量比。这个比值被一个由两个纯谱输入组成的式子复现到 0.070%，而文章真正要处理的是其中哪一部分是定理、哪一部分不是。两个谱输入都是纯的，但式子里那个显式的因子 5 没有推导；作者把这份「没有」当成结果而不是附注，逐一测试五种可能的来源并全部否证，于是这条登记为带检索空间的开放因子。作者的比较也是事后比较，并按框架的反巧合纪律排在定理级之下。This is the electron-to-muon mass ratio, reproduced to 0.070% by a form built from two purely spectral inputs; the real subject is which part of that statement is a theorem and which is not. Both inputs are pure, but the explicit factor 5 carries no derivation. The author treats that absence as a result rather than a caveat, tests five candidate sources and falsifies all of them, and so registers the factor as an open entry with a documented search space, not as a prediction. The comparison itself is post-hoc and sits below theorem level.
zenodo.23241031这篇讲的是这套理论给自己定的审计纪律，并且把它写成别人也能照着用的方法。主张被分成四类：密封级算术、条件性结构、被禁止升级的登记候选，以及终点级边界判断。三条常设规则是：未知不当已知、没推出来就不比较、数值相等不代表来源相同。文章还说明升级到定理级必须同时具备机制、唯一性、统计显著性和先推导后比较，并把十五处更正的原文与改后说法一并保留下来。This documents the audit discipline that governed every derivation in the framework, written so that it can be applied to someone else's work. Claims are classified into four states: seal-grade arithmetic, conditional structure, registered candidates barred from promotion, and terminal boundary judgements. Three standing rules apply: the unknown is never treated as known, nothing is compared before it is derived, and equal values do not imply common origins. Promotion to theorem level requires a mechanism, uniqueness, statistical significance and derivation before comparison.
zenodo.23241035这篇讲的是四种相互作用不是拼装成理论的四样配料，而是同一副骨架的不同块与不同投影。作者把主论文里的这句话逐块证明，而不是当成已知：色是骨架在 su(3) 块上的投影，弱与电磁结构是同一块的 SU(2)×U(1) 部分，引力则是它的曲率块。文章同时写明这条推论不主张的四件事，例如为什么是这副骨架、引力系数为何取那个值、1+3 维时空的来源，每一项都配了升级所需的条件。This argues that the four interactions are not four ingredients assembled into a theory but different blocks and projections of one skeleton, and it supplies the block-by-block proof rather than assuming it: colour is the projection onto the su(3) block, the weak and electromagnetic structure is the SU(2)xU(1) part of the same block, and gravity is its curvature block. The paper also states the four things the corollary does not claim, each registered with what an upgrade would require.
zenodo.23241039这篇讲的是参数空间的几何。对象是概率分布的理论会带上一个参数空间，而那个空间继承一种几何：对分布来说，这就是 Fisher–Rao 度量。对密封骨架，这个空间在归档里只剩一些零散说法，两条归档路径给出的「面积」彼此相差约两倍。作者把完整几何建了出来并解决了分歧：空间是开的正则四单纯形，总体积由三条互不共享步骤的路径给出同一个值，三类被混为一谈的面积型积分也精确分开。A theory whose objects are probability distributions carries a parameter space, and that space inherits a geometry: for distributions it is the Fisher-Rao metric. For the sealed skeleton that space existed in the archive only as scattered statements, and two archived routes to a single area disagreed by roughly a factor of two. The author constructs the complete geometry and settles the disagreement: the space is the open regular 4-simplex, its total volume is obtained by three routes sharing no step, and three conflated area-type integrals separate exactly.
zenodo.23241041这篇讲的是几何流里那个单调量的名字问题。几何演化方程靠一个单调泛函获得时间箭头，而把它叫作「熵」通常只是习惯，不是论证出来的。作者对这条密封流建立了精确的单调泛函和精确的变化率，等号成立当且仅当度规是 Einstein 度规；随后证明一条阻断定理：连续的状态计数泛函在连通定体积切片上局部为常数，所以不可能既单调又保留计数公理。结论是方向性住在体耗散里，这个量是 Lyapunov 函数而不是熵。A geometric evolution equation acquires an arrow of time through a monotone functional, and calling that functional an entropy is normally settled by convention rather than argument. For the sealed flow the author establishes the exact monotone functional and its exact rate, with equality if and only if the metric is Einstein, and then proves a blocking theorem: a continuous state-counting functional is locally constant on a connected fixed-volume slice, so none can stay strictly monotone. Directionality resides in bulk dissipation, and the quantity is a Lyapunov functional, not an entropy.
zenodo.23241045这篇讲的是右手中微子。框架里原本只有一条中微子相关陈述和一条协议登记，这篇把两者都补上：右手中微子不当作某种表示论中心，也不是新的场扇区，而是保迹信道的零模，也就是信道谱里那个静止、保人口的（单态）方向。作者说明这个认定只是存在性与计数陈述，不带电荷赋值、也不产生质量标度；真正出现的 I 型跷跷板标度由中微子振荡数据固定在一个很窄的窗口内，因此它结构上是协议量，不是推导出来的量。The framework contained one neutrino-specific structural statement and one protocol registration, and this paper supplies both. Right-handed neutrinos are identified neither with a representation-theoretic centre nor with a new field sector but with the zero mode of a trace-preserving channel, the stationary, population-conserving singlet direction of the channel spectrum. The identification is an existence and counting statement: it carries no charge assignment and produces no mass scale. The type-I seesaw scale is fixed by oscillation data to a narrow window, so it is structurally a protocol quantity rather than a derived one.
zenodo.23241049这篇讲的是核物理一侧的禁闭标度，以及两条被否证的壳闭合主张。框架只提供一个核物理资产，即弦张力，它对应一条约 0.97 fm 的长度；作者用两组否定比较说明，它既不是π介子交换的尺度，也不是排斥芯半径。文章随后指出，把核壳序（包括 184 中子闭壳）归给框架五维费米空间的做法不成立，障碍是量纲上的：框架是无量纲的，GeV 只进入一次。剩下的算术吻合只按候选级登记，既没有被升级也没有被使用。This concerns the confinement scale on the nuclear side, plus two failed shell-closure claims. The framework supplies one nuclear asset, the string tension, which corresponds to a single length of about 0.97 fm; two negative comparisons establish that it is neither the pion-exchange range nor a repulsive-core radius. The paper then shows that attributing a nuclear shell sequence, including the neutron closure at 184, to the framework's five-dimensional fermionic space does not hold, the obstruction being dimensional: the framework is dimensionless and the GeV enters once.
zenodo.23241053这篇讲的是 π 从哪里来：连续统是一个输入。一个有限的代数结构里没有连续统，也就没有超越常数；理论一旦写在连续统上，这两样就都有了。作者用一个自足的案例把连续统进入的两步分开，并说明框架里 π 的每一次出现都能追溯到某个被采用的连续测度或度规，例如通量归一化里的 2π 和界面约定。结论是 π 可以被搬位置、但不能被消掉：把它赶出密度，它就跑到坐标里；而指定同一个对象其实并不需要它。This asks where pi comes from, and answers that the continuum is an input. A finite algebraic structure contains no continuum and so no transcendental constants; a theory written on a continuum contains both. Using a self-contained case, the author separates the two steps at which a continuum enters and shows that every occurrence of pi traces to an adopted continuous measure or metric, such as the 2pi of the flux normalisation. Pi can be relocated but not eliminated: pushing it out of a density puts it into the coordinate.
zenodo.23241055这篇讲的是强子谱，也就是禁闭所产生的那套谱。作者把密封的谱算术用到它上面，先按三层把谱成员列全：文献已经测量过的、文献能算或想得到的、以及任何文献列表上都没有的，每一行都带框架值和等级。其中两个量与已测强子数值吻合，一个是定理级的夸克质量比，另一个是候选级、没有被升级的π介子尺度量。文章还通过六条路径和两项定量检验表明，把无量纲禁闭间隙接到强子质量上的那座桥，在本框架内搭不起来。This applies the sealed spectral arithmetic to the hadron spectrum, the spectrum of confinement, and sets out every member in three tiers: rows the literature has measured, rows it can compute or think to ask, and rows that appear on no literature list, each with its framework value and grade. Two quantities reach measured numbers, a theorem-level quark-mass ratio and a candidate-level pion-scale quantity that the framework does not promote. Six distinct routes and two quantitative tests show that the arrow into hadron masses cannot be built from the framework.
zenodo.23241060这篇讲的是胶球谱里的色单态。约束驱动的机制，也就是保正性加上密封弦张力，迫使有限谱只能由色单态组成，而这篇把成员数目精确数了出来：n 个胶子对应的独立色单态个数，从 n 等于 0 到 10 依次是 1、0、1、2、8、32、145、702、3598、19280、107160，并且由彼此独立的路径得到。允许的信道也一并固定，例如纯胶扇区里的外来态在 1、2、3 个胶子时都不可用。算术不给任何胶球质量：最后那一根箭头在密封记录里不存在。This is about colour singlets in the glueball spectrum. The constraint-driven mechanism, complete positivity together with the sealed string tension, forces the finite spectrum to consist of colour singlets only, and the paper counts the members exactly: n gluons form 1, 0, 1, 2, 8, 32, 145, 702, 3598, 19280 and 107160 independent singlets for n from 0 to 10, obtained by mutually independent routes. The allowed channels are fixed too, with the exotic state unavailable at one, two or three gluons. The arithmetic supplies no glueball mass.
zenodo.23241064这篇讲的是轻子谱里的两个纯数。作者给出该谱的完整成员表，也给出两个不含拟合系数、不含量纲锚的无量纲数：一个是谱算术级的，另一个是电子与 μ 子的质量比，等级为条件级。式子里两个因子都不是拟合来的，但它们相乘时多出的那个因子 5 没有推导，所以这条记录为条件级。文章逐项说明等级是怎么定的，并明确两个主结果都是纯数，因此不依赖任何有量纲的锚。This gives the complete member list of the lepton spectrum together with two writable dimensionless pure numbers that contain no fitted coefficient: one at exact sealed-arithmetic level, and the electron-to-muon mass ratio at conditional level. Neither factor in the product is fitted, but the factor 5 multiplied in carries no derivation, which is why that entry is recorded as conditional on a stated axiom chain. The author settles each level item by item and stresses that both headline results are pure numbers depending on no dimensionful anchor.
zenodo.23241068这篇讲的是原子谱，只用理论算术的一个面：耦合。它由寄存器函数读出，把宇宙在一维轴上的位置映射成精细结构常数。作者把「架构不带任何原子尺度数值」当作中心结果，并按边界级登记；原子能级本身仍属外部的量子电动力学内容。架构真正提供的很窄：一个方向固定的耦合时间依赖、一个渐近终点值，以及两条谱线漂移之比。This applies one face of the framework's spectrum arithmetic to the atomic spectrum: the coupling, read from a register function mapping one number, the universe's position on a one-dimensional axis, to the inverse fine-structure constant. The author states as the central result, graded as a boundary statement, that the architecture carries no atomic-scale value; every atomic level energy stays external quantum-electrodynamic content. What it does supply is narrow.
zenodo.23241070这篇讲的是核谱里的一个结构对消：本来应该各自贡献的两项，在零钉扎处精确抵消。作者说明这不是数值上的巧合，而是因为配对的特征向量携带相同的格点幅值，所以这个零来自结构本身。随后全态定理给出一个无量纲间隙值，但这个值是从框架的算术链作为输入引进来的，因此定理依赖于它，并相应带有条件等级；作者也把话说到哪里为止：记录里没有任何推导能把那个值接到界面标度上。This reports a structural cancellation in the nuclear spectrum: two quantities that should each contribute vanish against each other exactly at zero pinning. The author shows the vanishing is not numerical but structural, since paired eigenvectors carry identical site magnitudes. A full-state theorem then records one dimensionless gap value, but that value is imported as an input from the framework's arithmetic chain, so the theorem is conditional on it. The record stops there: no derivation connects that value to the interface scale.
zenodo.23241076这篇讲的是宇宙学谱，核心是密度分数被平坦性钉住。框架的单输入读数给出两个数，它们的和超过了 1，而这一读数被观测曲率排除；于是平坦性成立，并把密度分数唯一确定下来，闭合形式精确满足「和为 1、比为√5」这两条要求。作者强调这个闭合形式并不在归档里，它是被数据逼出来的升级条件而不是密封值，而且与三组已发表读数是平行比较、不做平均，三个偏差的离散属于那些数据集本身。This is the cosmology spectrum, where flatness pins the density fractions. The framework's single-input reading gives two numbers summing above 1, and that reading is excluded by the observed curvature; flatness therefore holds and fixes the fractions uniquely, the closed form satisfying the framework's two requirements exactly. The author notes that this closed form is not in the archive but a data-forced upgrade condition rather than a sealed value, and compares three published readings in parallel without averaging, the dispersion belonging to those data sets.
zenodo.23241080这篇讲的是凝聚态谱里的一个整数耦合。密封的非对角算术定义出一个零对角 Jacobi 族，补到自由带边之后，它沿路径带有一个取整数值的谱流计数，走完一整趟该计数精确为 +1；Thouless 泵的认定再把它按恰好为 1 的因子对应到布里渊区丛的第一陈数。文章并不把与量子化反常霍尔电导测量的一致性当作证据，因为拓扑装置在密封记录里没有依据，而且那次换算依赖一个被登记为开放的对象认定。This is an integer coupling in the condensed-matter spectrum. The sealed off-diagonal arithmetic defines a zero-diagonal Jacobi family, and completed to its free band edge it carries a Z-valued spectral-flow count that equals exactly +1 over one traversal; the Thouless-pump identification then converts it, by a factor of exactly one, to the first Chern number of a Brillouin-zone bundle. The author does not count the consistency with a measured quantised Hall conductance as evidence, since the topological apparatus has no basis in the sealed record and the conversion rests on an open identification.
zenodo.23241082这篇问：一个理论能否把「自己的数字到哪里为止」证成一条定理。作者先排除两种做法——声称什么都推得出来（一个反例就够推翻），或者承认有些东西没推出来（既没代价也没收益）——再提出第三种可能，并以 RET 框架为案例，把数值内容分成三部分。文章明确所证定理依赖 P2 漂移族这条「假定而非已确立」的前提。This asks whether a theory can prove, as a theorem, exactly where its own numerical content ends. The author first sets aside two familiar answers: claiming to derive everything, which one counterexample refutes, and admitting that some things are not derived, which costs nothing and buys nothing. A third possibility is examined using the RET framework, whose numerical content divides into three parts. The theorem is stated as conditional on P2, the drift family.
zenodo.23330257这篇问的是「承认自己不知道」算不算美德，如果算，它反驳了什么。作者指出它不能区分理论——每个理论都有未解问题——真正能区分的是边界「怎么被确立」。据此他把未解域分成四类：悬挂起点、进行中的项目、登记在案的低估确定，以及由理论自身分析得出的派生限制；第四类再分两式，后者带定理，且不能靠更用力解决。This asks whether a theory's admission that it does not know is a virtue, and if so what it refutes. The author shows the obvious answer fails as a differentiator, since every theory has unsolved problems; what distinguishes a theory is how the boundary is established. Unsolved domains are sorted into four kinds by how the theory's own records fixed the boundary, and the fourth kind divides into two species, the stronger arriving with a theorem.
zenodo.23330259这篇讲的是把「模拟假说」放进一个可计算的案例里会怎样。作者先给一条存在性主张：从有限公理出发、结论被公理唯一逼出的框架已经真的跑过，它在真实硬件上运行十万步，并做了逐位校验的继承检查。接着给出容器界：在零信息损失和文中列明的前提下，完美模拟一个宇宙的计算机不可能比被模拟的宇宙更简单，因此无限嵌套也被排除。作者明确说明，在人们真正在意的那种保真度上本文没有建立任何界，并把开放问题定位在那里。This puts the simulation hypothesis next to a computable case. First comes an existence claim: a framework of finite axioms whose consequences are uniquely forced has actually been executed, running 100,000 steps on real hardware with a bitwise-verified inheritance check. Then the container bound: at zero information loss, and given the paper's stated premises, a computer that perfectly simulates a universe cannot be less complex than the universe it simulates, so infinite nesting is ruled out too. At the fidelity the debate cares about, the paper establishes no bound and says so.
zenodo.23330263这篇讲的是中国传统哲学与近代科学之间有没有第三种关系。作者先排除两种常见做法：寻找「先声」，也就是把古语读成现代结果的早期版本；以及直接断言两者不可通约。两者都漏掉了真正可比较的层面，即文本展现的方法姿态——它怎么处理分歧、伪造，以及自身能断定的边界。以楼宇烈的著述为文献基础，作者主张「道法自然」与 RET 的自足结构形状相同而模态不同；这一比较之所以站得住，是因为九处不相容和三处失类比被登记下来，而不是被抹平。This asks whether a third relation between traditional Chinese philosophy and modern science is available. Two familiar approaches are set aside: the search for anticipations, which the texts do not support, and the assertion of incommensurability, which abandons the comparison before it begins. Both miss the comparable layer, the methodological posture a text exhibits toward disagreement, forgery and its own boundary. Reading Lou Yulie's writings, the author argues that the dao follows nature and the framework's self-sufficiency share a shape but differ in modality, and that the comparison survives only because nine incompatibilities and three disanalogies are registered rather than smoothed away.
zenodo.23330265这篇讲的是层次的地位。当理论说自己的数字是内生的，这种说法通常会给全部数值内容安上同一种认识地位，而作者认为这样做必然误述立场：数值内容按来源分成被算术与运动学结构定住的、被证明为固定内容无法决定的、以及依赖被采用认定的三类，三者地位不同，一个层次的判断不能顶替另一个层次的判断。作者把这条要求论证成对「陈述必须显式携带层次结构」的要求，而不是对句子数量的要求，并用一个带数字的框架案例展示这个结构。When a theory calls its numbers endogenous, the claim usually assigns one epistemic status to the whole of its numerical content. The author argues this necessarily misstates the position, because that content divides by provenance into values fixed by the theory's arithmetic, values its fixed content provably does not settle, and values resting on an adopted identification. Verdicts at one layer do not settle verdicts at another. The requirement is about what a statement must make explicit, not about how many sentences it takes, and a worked numerical case exhibits the structure.
zenodo.23330267这篇讲的是「零外部依赖」的电子结构计算栈。电子结构计算指的是用量子力学算出分子和材料里电子如何排布、能量是多少，这类计算通常要一层层依赖外部的库和框架，装不上就跑不起来。这篇给出的栈不引入外部依赖，自己就能跑完，因此从拿到代码到算出结果之间不需要再补别的东西；题目指向的正是这条自足的工程路线。This is about a zero-external-dependency stack for electronic-structure calculations. Such calculations use quantum mechanics to work out how electrons are arranged in molecules and materials and what their energies are, and they normally depend on layer upon layer of external libraries and frameworks. The stack described here brings in no external dependency and runs on its own, so nothing further has to be installed between obtaining the code and getting a result.
zenodo.23329984这篇讲的是谱移适用域。谱移函数是这样一个工具：把两个算子的差所引起的谱变化记成一个函数，再用它把两者之间的迹差写成积分。这个工具不是到处都能用，前提是差算子足够「小」。这篇要界定的就是它在什么条件下成立、在哪些情形下已经超出适用范围，也就是把它能用与不能用之间的那条边界划清楚。This is about the domain in which the spectral shift applies. The spectral shift function is a tool that records the change in spectrum caused by the difference of two operators, and lets the trace difference between them be written as an integral. The tool is not available everywhere: it requires the difference of the operators to be small enough. The paper sets out the conditions under which it holds and the cases that fall outside its range, drawing the boundary between where it can be used and where it cannot.
zenodo.23330254这篇讲的是否证协议，也就是一套事先定好的规则，用来规定一个说法在什么条件下算被推翻。科研里常见的麻烦是判据在看过数据之后才调整，于是什么结论都能自圆其说。这篇把「怎样才算否证」写成可以照着执行的程序：先登记判据，再拿结果去对，而不是等结果出来再解释；题目指的就是这样一份协议本身。This is about a falsification protocol: a set of rules fixed in advance that states the conditions under which a claim counts as refuted. A familiar problem is that criteria get adjusted after the data are seen, so that any conclusion can be made to look consistent. Here the paper writes out what counts as a falsification as a procedure that can be followed: register the criteria first, then compare the result against them, rather than explaining afterwards.
zenodo.23330256这篇讲的是 zeta 尾部的损失。zeta 函数是跟素数分布绑在一起的那个函数，它的级数或乘积在最末尾那一段需要单独处理。这篇要处理的就是这部分「尾部」：在尾巴上有一些量会损失掉、对不上，题目的重点也正落在这里，而不是整个函数本身。This is about zeta tail loss. The zeta function is the function tied to the distribution of the primes, and the last stretch of its series or product has to be handled separately from the rest. The paper deals with that tail, where some quantities are lost or fail to match up. The title points at that tail rather than at the function as a whole.
zenodo.23330226这篇讲的是黎曼 zeta 函数，也就是题目里的「riemann z」。它是把素数分布与复平面上的一个函数连起来的那座桥，本身在临界带上的零点位置，是数论里最受关注的问题之一。题目落在它身上，说明文章要处理的是这个函数自身的性质，而不是它的某个应用。This is about the Riemann zeta function, the subject named in the registered title. It is the bridge connecting the distribution of the primes to a function on the complex plane, and the location of its zeros in the critical strip is among the most studied questions in number theory. The title falls on the function itself, so the paper deals with its own properties rather than with an application of it.
zenodo.23330229这篇讲的是纳维–斯托克斯方程，也就是描述流体怎样流动的那组方程。它由力学的基本定律写下，形式看起来直接，但关于它的解在长时间下会不会一直保持光滑、会不会失去控制，是数学里长期没有解决的问题。题目指的就是这组方程本身，文章要处理的是它在数学上的性质，而不是某个具体的流动问题。This is about the Navier-Stokes equations, the equations that describe how fluids flow. They are written down from the basic laws of mechanics and look straightforward in form, but whether their solutions stay smooth over long times or blow up is a question mathematics has not settled. The title points at the equations themselves, so the paper concerns their mathematical behaviour rather than one particular flow problem.
zenodo.23330231这篇讲的是霍奇理论与朗兰兹纲领之间的关系。前者用一组离散的数刻画复几何空间的形状，后者把数论与表示论用一套对应关系连起来；两边各自都很难，而它们之间的接触点是一个被反复提出、却远未完成的方向。题目把这两者并列，说明文章要处理的正是它们之间的那座桥，而不是其中单独一边。This is about the relation between Hodge theory and the Langlands programme. The first describes the shape of complex-geometric spaces through a set of discrete numbers; the second connects number theory with representation theory through a system of correspondences. Each is hard on its own, and the point of contact between them is a direction that has been proposed repeatedly and is far from complete. The title names both, so the paper concerns the bridge between them rather than either side alone.
zenodo.23330233这篇讲的是 BSD 猜想，也就是 Birch–Swinnerton-Dyer 猜想。它把椭圆曲线（一类由三次方程定义的曲线）上有多少个有理点，与这条曲线的 L 函数在一处的取值联系起来：点越多，那个取值就越大。这是数论里最著名的未解问题之一。题目指向这条猜想，说明文章要处理的是它的某一部分，而不是某条具体曲线的数值计算。This is about the BSD conjecture, the Birch and Swinnerton-Dyer conjecture. It ties the number of rational points on an elliptic curve, a curve defined by a cubic equation, to the value of that curve's L-function at one point: the more points there are, the larger that value. It is among the best known unsolved problems in number theory. The title points at the conjecture, so the paper deals with some part of it rather than a computation on one particular curve.
zenodo.23330235这篇讲的是霍奇方向上一个标记为 h16 的量。霍奇理论用一组叫霍奇数的整数来刻画一个复几何空间的形状，h16 就是这组数里的一个下标组合。题目把霍奇与 h16 并列，说明文章要谈的是这个具体的量在霍奇结构里扮演什么角色、能不能被定下来，而不是整个霍奇理论。This is about a quantity marked h16 in the Hodge setting. Hodge theory describes the shape of a complex-geometric space through a set of integers called Hodge numbers, and h16 is one index combination within that set. The title places Hodge and h16 side by side, so the paper concerns the role this particular quantity plays in the Hodge structure and whether it can be pinned down, rather than Hodge theory as a whole.
zenodo.23330242这篇讲的是杨–米尔斯理论里的质量间隙。杨–米尔斯理论描述的是规范场，也就是把基本相互作用写成几何的那套语言；所谓质量间隙，是说它的谱里最低的那个激发与真空之间存在一个不为零的最小能量差，而不是可以任意接近零。题目的重点就是这个间隙本身。This is about the mass gap in Yang-Mills theory. Yang-Mills theory describes gauge fields, the language in which the fundamental interactions are written geometrically; a mass gap means that in its spectrum the lowest excitation sits a non-zero minimum energy above the vacuum, instead of approaching zero arbitrarily closely. The title points at that gap itself.
zenodo.23330246这篇讲的是对 beta 的一次普查。beta 通常指一个随尺度变化的参数，比如重整化群里的 beta 函数；单个 beta 值只说明一个点，而「普查」是要把一整批 beta 值一次列全、逐个清点，看它们落在哪里、有没有规律。题目把 beta 与普查并列，说明文章要处理的是这种成批的清点，而不是某个孤立的数值。This is about a census of beta. Beta usually denotes a parameter that changes with scale, such as the beta function of the renormalisation group; a single beta value describes only one point, whereas a census lists a whole batch of them at once and counts through them to see where they fall and whether any pattern appears. The title pairs beta with census, so the paper concerns that collective accounting rather than one isolated number.
zenodo.23330248这篇讲的是体积引理。引理通常不是文章的主结论，而是为后面更大的结果垫脚的一块石头：这条引理说的是关于体积或测度的一件事，也就是在给定条件下，某个体积或它的变化可以被控制住。题目把「体积」与「引理」并列，说明文章要处理的正是这样一条辅助命题，以及它能支撑起哪些后面的推导。This is about a volume lemma. A lemma is usually not the main conclusion of a paper but a stepping stone for a larger result: this one states something about volume or measure, namely that under given conditions a certain volume, or the change in it, can be controlled. The title pairs volume with lemma, so the paper concerns that auxiliary statement and the later arguments it is able to support.
zenodo.23330252这篇讲的是宇宙创生，也就是宇宙最初从无到有的那个起点。它要处理的是宇宙怎么开始、最早那一小段是什么样子，而不是它后来怎么一步步演化。作者把这个起点问题摆出来，也说明它难在哪里、可以从哪些方向去想。This one is about cosmic genesis — the starting point at which the universe came into being from nothing. It deals with how the universe began and what its earliest stage looked like, rather than how it evolved afterwards. The author lays the problem out and says where its difficulties lie.
zenodo.23329991这篇要处理的是宇宙学常数问题。宇宙学常数是爱因斯坦方程里代表真空能量、让宇宙加速膨胀的那一项；麻烦在于，按量子场论估出来的真空能量，比天文观测到的值大了许多个数量级。作者把估算和观测这两头的差距摆在一起谈。This one tackles the cosmological constant problem. The cosmological constant is the term in Einstein's equations that stands for vacuum energy and drives accelerated expansion; the trouble is that quantum-field-theory estimates of it overshoot the observed value by many orders of magnitude. The author sets the two sides of that gap side by side.
zenodo.23329994这篇讲的是光子与强子的耦合常数，也就是光子和参与强相互作用的粒子之间结合得到底有多强。耦合常数可以理解成一个强度系数，数值大就说明两者之间的作用更明显。作者围绕这个系数怎么定、怎么用展开讨论。This one concerns the photon–hadron coupling constant, meaning how strongly photons couple to particles that take part in the strong interaction. A coupling constant works as a strength factor: a larger number means a more pronounced interaction. The author discusses how this quantity is fixed and how it is used.
zenodo.23329997这篇讲的是光子带隙材料。这类材料内部有周期性的结构，某些颜色也就是某些频率的光进去之后会被挡住、传不过去，作用有点像半导体挡住特定能量的电子。作者围绕这种挡光的结构本身来谈，包括它是怎么起作用的。This one is about photonic bandgap materials. Such materials have a periodic internal structure that blocks certain colours, that is, certain frequencies of light, much as a semiconductor blocks electrons of particular energies. The author discusses this light-blocking structure itself and how it works.
zenodo.23329999这篇讲的是自发参量下转换（SPDC）的截面。SPDC 是指一束光在非线性晶体里自发裂成两个光子的过程，而截面就是这件事发生概率大小的量度。作者围绕这个概率怎么算、和哪些条件有关来谈。This one is about the cross-section of spontaneous parametric down-conversion (SPDC). SPDC is the process in which one light beam spontaneously splits into two photons inside a nonlinear crystal, and the cross-section measures how likely that process is. The author discusses how that likelihood is computed and what it depends on.
zenodo.23330005这篇讲的是超表面的相位调控。超表面是一层人工做出来的、厚度远小于波长的结构，上面排着许多微小单元；光穿过或者被反射时，相位会被这些单元改动。作者要处理的是怎么在这么薄的一层上把光波的相位控制住。This one is about phase control with metasurfaces. A metasurface is an artificially made layer far thinner than a wavelength, covered with tiny elements; as light passes through or reflects off it, those elements shift its phase. The author deals with how the phase of a light wave can be controlled on such a thin layer.
zenodo.23330011这篇讲的是量子测量反作用，意思是测量这个动作本身会扰动被测的量子系统。在量子力学里，测量不是被动地看一眼，它会把原来的叠加状态改掉，于是测出来的结果也带着这份扰动。作者围绕这种扰动的来由和影响来谈。This one is about quantum measurement back-action: the act of measuring disturbs the quantum system being measured. In quantum mechanics measurement is not a passive look — it alters the superposition that was there, so the recorded result carries that disturbance. The author discusses where the disturbance comes from and what it affects.
zenodo.23330015这篇讲的是非线性截面。通常介质的响应和光强成正比，但在强光下这种正比关系不再成立，非线性效应登场的强弱就用截面来衡量。作者围绕介质在强光下偏离线性响应的这一段来谈。This one is about nonlinear cross-sections. A medium's response normally stays in proportion to light intensity, but under intense light that proportionality breaks down, and a cross-section measures how strong the nonlinear effect becomes. The author discusses this departure from linear response under strong light.
zenodo.23330017这篇讲的是极紫外（EUV）光刻仿真的新路子。EUV 光刻用波长很短的极紫外光在芯片上刻出极细的线条，而仿真就是先用数值计算预演一遍光刻过程会得到什么图案。作者要处理的是换一种方式来做这套模拟。This one is about a new way of simulating extreme-ultraviolet (EUV) lithography. EUV lithography uses very short-wavelength light to print extremely fine features on chips, and simulation means computing beforehand what pattern the process will produce. The author deals with doing that simulation in a different way.
zenodo.23330021这篇讲的是铜氧化物高温超导。铜氧化物是一类含铜和氧的层状材料，它们的超导转变温度比传统金属高出很多，所以被称为高温超导；在这种材料里，超导是怎么出现的仍然没有定论。作者就这类材料写了一篇中等篇幅的讨论。This one is about high-temperature superconductivity in the copper oxides. Cuprates are layered materials containing copper and oxygen whose superconducting transition temperatures are far higher than those of ordinary metals, which is why they are called high-temperature superconductors; how superconductivity arises in them is still unsettled. The author gives them a medium-length discussion.
zenodo.23330025这篇讲的是拓扑超导体里的 Majorana 准粒子。拓扑超导是一种整体性质由拓扑结构决定的超导态；Majorana 准粒子则是它里面可能出现的一种激发，特点是它自己就是自己的反粒子。作者围绕这种准粒子来谈。This one is about Majorana quasiparticles in topological superconductors. A topological superconductor has properties fixed by its overall topology, and a Majorana quasiparticle is an excitation it may host that is its own antiparticle. The author focuses on this kind of quasiparticle.
zenodo.23330028这篇要处理的是超导转变温度（Tc）的理论上限，也就是超导能撑到多热才失效的那个天花板。Tc 说的是材料从有电阻变成零电阻的那个温度。作者要问的是，有没有一个上限把 Tc 卡住，这个上限又是从哪里来的。This one deals with the theoretical upper limit on the superconducting transition temperature (Tc), the ceiling on how warm superconductivity can survive. Tc is the temperature at which a material's resistance drops to zero. The author asks whether some limit caps Tc and where such a limit would come from.
zenodo.23330030这篇讲的是重费米子体系里的奇异金属。重费米子材料里的电子表现得特别重，像是被什么东西拖住了；奇异金属则是指电阻随温度的变化不按普通金属那套规律走。作者把这两件事放在一起谈。This one is about strange metals in heavy-fermion systems. In heavy-fermion materials the electrons behave as if they were unusually heavy, as though dragged down; a strange metal is one whose resistance varies with temperature in a way ordinary metals do not follow. The author treats the two together.
zenodo.23330032这篇讲的是光致超导，也就是用一束光去照材料，看能不能把它送进超导态，或者让已有的超导变得更强。超导态的标志是电阻完全消失。作者围绕光照这个手段，以及它可能带来的超导变化来谈。This one is about photo-induced superconductivity: shining light on a material to see whether it can be driven into a superconducting state, or have an existing one strengthened. Superconductivity is marked by resistance vanishing entirely. The author discusses light as the tool and the changes in superconductivity it might bring.
zenodo.23330034这篇讲的是哈勃常数危机。哈勃常数描述宇宙现在膨胀得有多快；麻烦在于，用邻近宇宙的办法量出来的值，和从早期宇宙留下的痕迹推出来的值，两者对不上。作者围绕这个彼此打架的局面来谈。This one is about the Hubble constant crisis. The Hubble constant describes how fast the universe is expanding now; the trouble is that values measured from the nearby universe and values inferred from imprints of the early universe do not agree. The author discusses this standoff between the two.
zenodo.23330036这篇讲的是暗能量的状态方程 w(z)。w 表示暗能量的压强和能量密度之比，括号里的 z 是红移，代表宇宙的不同时期，所以 w(z) 看的就是这个比值随宇宙演化怎么变。作者围绕它随时间的变化来谈。This one is about the dark-energy equation of state, w(z). Here w is the ratio of dark energy's pressure to its energy density, and z is redshift, standing for different cosmic epochs, so w(z) asks how that ratio changes as the universe evolves. The author discusses that time dependence.
zenodo.23330038这篇讲的是原初引力波。引力波是时空的涟漪，而「原初」两个字指的是它产生于宇宙极早期，不是后来天体并合这类过程留下的。作者围绕这种极早期的涟漪来谈，以及它可能告诉我们什么。This one is about primordial gravitational waves. Gravitational waves are ripples in spacetime, and "primordial" means they arose in the very early universe rather than from later events such as merging bodies. The author discusses these early ripples and what they might tell us.
zenodo.23330040这篇讲的是 S8 张力。S8 是一个衡量物质在宇宙中成团程度的参数，数值越大说明物质聚得越厉害；这里的张力指的是，不同观测手段给出的 S8 值彼此对不上。作者围绕这个不一致来谈。This one is about the S8 tension. S8 is a parameter measuring how clumpy matter is in the universe — a larger value means matter clusters more strongly; tension here means different kinds of observation give S8 values that disagree with one another. The author discusses that disagreement.
zenodo.23330042这篇讲的是 21 厘米信号。这是中性氢原子在两个能级之间翻转时发出的射电谱线，波长大约 21 厘米；宇宙里有大量中性氢，所以这条线带着早期宇宙的信息。作者围绕这条信号来谈。This one is about the 21 cm signal. It is the radio line emitted when a neutral hydrogen atom flips between two energy levels, at a wavelength near 21 centimetres; the universe holds a great deal of neutral hydrogen, so this line carries information about the early universe. The author discusses this signal.
zenodo.23330044这篇讲的是暗物质探测的三条路子合在一起看。所谓三通道，通常指直接探测、间接探测和对撞机产生这三类办法，它们各自从不同角度去找暗物质。作者把它们放进同一篇里对照着谈。This one looks at the three detection channels for dark matter together. The three channels usually mean direct detection, indirect detection and production at colliders, each hunting dark matter from a different angle. The author treats them in one piece and compares them.
zenodo.23330047这篇讲的是量子自旋液体。这是一种磁矩被量子涨落搅得安定不下来的状态，即使在很低的温度下也不会形成通常的磁序。作者要处理两件事：这种状态到底存不存在，以及如果存在，该怎么给它分类。This one is about quantum spin liquids. In such a state quantum fluctuations keep the magnetic moments from settling, so the usual magnetic order never forms even at very low temperature. The author deals with two questions: whether such states exist at all, and how to classify them if they do.
zenodo.23330049这篇讲的是磁单极子。普通的磁铁总是南北两极成对出现，把它切开也只会得到两个更小的磁铁；磁单极子则是设想中只带单独一个磁极的粒子。作者围绕这种粒子，以及寻找它的努力来谈。This one is about magnetic monopoles. An ordinary magnet always carries north and south poles as a pair, and cutting it only yields two smaller magnets; a magnetic monopole is a hypothetical particle with just one pole. The author discusses this particle and the search for it.
zenodo.23330054这篇讲的是拓扑磁振子和磁斯格明子。磁振子是磁矩集体摆动形成的波，斯格明子则是磁矩排成的一种像小漩涡的结构；两者都受拓扑保护，不容易被扰动弄散。作者围绕磁体里这两种特殊激发来谈。This one is about topological magnons and magnetic skyrmions. A magnon is a wave formed by the collective precession of magnetic moments, while a skyrmion is a swirling arrangement of those moments; both are topologically protected and hard to disrupt. The author discusses these two excitations in magnets.
zenodo.23330056这篇讲的是超导和磁性之间的竞争与合作。在同一块材料里，超导希望电子两两配对，磁性则倾向于让磁矩排整齐，两者常常互相压制，但有时也能共存。作者围绕这种此消彼长画出的相图来谈。This one is about competition and cooperation between superconductivity and magnetism. In one material, superconductivity wants electrons paired up while magnetism tends to align the moments; the two often suppress each other yet can sometimes coexist. The author discusses the phase diagram this tug-of-war produces.
zenodo.23330059这篇讲的是重费米子材料里的磁量子相变。相变是物质从一种状态变成另一种状态；量子相变则是指在绝对零度附近，由量子涨落而不是热量驱动的转变。作者围绕重费米子体系里这种磁性转变来谈。This one is about magnetic quantum phase transitions in heavy-fermion materials. A phase transition is a change from one state of matter to another, and a quantum phase transition is driven near absolute zero by quantum fluctuations rather than heat. The author discusses such a magnetic transition in these materials.
zenodo.23330065这篇讲的是压力淬火超导，缩写 PQP。淬火这个词借的是金属热处理的说法，指快速改变条件、让材料来不及回到原来的样子；压力淬火就是用快速改变压力的办法，把材料留在超导态里。作者围绕这种做法来谈。This one is about pressure-quenched superconductivity, abbreviated PQP. Quenching borrows the metals term for changing conditions so fast that the material cannot relax back to its former state; pressure quenching uses a rapid pressure change to hold a material in a superconducting state. The author discusses this approach.
zenodo.23330067这篇讲的是电子云结构和游离电子的运动。电子云说的是电子在原子或分子周围并不沿固定轨道走，而是按一定概率分布散开；游离电子则是已经脱离原子的那些。作者围绕这两者的分布和运动来谈。This one is about electron-cloud structure and the motion of free electrons. The electron cloud means electrons around an atom or molecule are not on fixed tracks but spread out with a certain probability; free electrons are those that have left their atoms. The author discusses how both are distributed and how they move.
zenodo.23330069这篇讲的是强子谱和 QCD 求和规则。强子谱是强子这类参与强相互作用的粒子按质量排下来的谱系；QCD 是描述强相互作用的量子色动力学，求和规则是它给出的一套计算办法。作者用这套办法去推算强子谱。This one is about the hadron spectrum and QCD sum rules. The hadron spectrum is the lineup of strongly interacting particles ordered by mass; QCD is quantum chromodynamics, the theory of the strong interaction, and sum rules are a calculational tool it provides. The author uses that tool to work out the spectrum.
zenodo.23330071这篇讲的是量子电动力学（QED）的高阶修正和精密检验。QED 描述带电粒子与光怎么相互作用，高阶修正指的是把计算里更细的高次项也算进来；算得更细之后，再拿结果和实验的精密度量比对。作者围绕这一算一验来谈。This one is about higher-order corrections in quantum electrodynamics (QED) and precision tests of them. QED describes how charged particles interact with light, and higher-order corrections mean including the finer, subleading terms; the refined result is then compared with precise measurements. The author discusses that compute-and-check pairing.
zenodo.23330073这篇讲的是强子-轻子普适性。普适性说的是，如果某种相互作用对轻子和强子一视同仁，那么同一个过程衰变到这两类粒子时，背后的规律就应当一致。作者要处理的是，这个一致性到底成立到什么程度。This one is about hadron–lepton universality. Universality says that if an interaction treats leptons and hadrons alike, decays of the same process into either kind of particle should follow the same underlying rule. The author deals with how well that consistency actually holds.
zenodo.23330075这篇讲的是非微扰 QED 和束缚态。微扰办法是把计算展开成一项项小量来近似，当相互作用强到这种展开不管用时，就得换非微扰的路子；束缚态则是电子和正电子被彼此拉住、绑在一起的状态。作者围绕这两件事来谈。This one is about non-perturbative QED and bound states. Perturbation theory approximates a calculation by expanding it in small terms, and when the interaction is too strong for that expansion to work, non-perturbative methods take over; a bound state is an electron and a positron held together. The author treats the two together.
zenodo.23330077这篇讲的是核磁矩和磁旋比。原子核像一小块磁铁，核磁矩说的就是它这份磁性有多强；磁旋比则是这份磁性和它自身角动量的比值。作者围绕这两个量怎么定、怎么量来谈，以及它们能说明什么。This one is about nuclear magnetic moments and the gyromagnetic ratio. An atomic nucleus acts like a tiny magnet, and the nuclear magnetic moment says how strong that magnetism is; the gyromagnetic ratio is that magnetism divided by the nucleus's own angular momentum. The author discusses how these quantities are fixed and measured.
zenodo.23330083这篇讲的是质子波函数。波函数是用来描述一个量子系统内部组分怎么分布、怎么运动的数学对象；放到质子身上，就是描述里面那些夸克和胶子处在什么状态。作者围绕质子波函数这套描述来谈。This one is about the proton wave function. A wave function is the mathematical object describing how the parts inside a quantum system are distributed and how they move; for the proton it describes the state of the quarks and gluons within. The author discusses this way of describing the proton.
zenodo.23330085这篇讲的是化学位移。在核磁共振里，同一种原子核如果周围的化学环境不同，它的信号位置就会稍稍偏移，这个偏移就叫化学位移；反过来，它也能告诉我们原子处在什么样的环境里。作者围绕这个偏移来谈。This one is about chemical shift. In nuclear magnetic resonance, the same kind of nucleus gives a slightly shifted signal depending on its chemical surroundings, and that shift is the chemical shift; it in turn tells us what environment an atom sits in. The author discusses this shift.
zenodo.23330087这篇讲的是重味强子的衰变宽度。重味指的是含有粲夸克或者底夸克这类较重夸克；衰变宽度则是衡量一个粒子衰变快慢的量，宽度越大，衰变得越快。作者围绕这类粒子的衰变来谈。This one is about the decay widths of heavy-flavour hadrons. Heavy flavour means containing a heavier quark such as charm or bottom; a decay width measures how fast a particle decays, with a larger width meaning a quicker decay. The author discusses the decays of such particles.
zenodo.23330089这篇讲的是氢与空气混合气的爆炸极限。氢气在空气里要占到一定比例才点得着，比例太低或者太高都烧不起来，这两个边界就是爆炸极限。作者围绕这个范围怎么定、受哪些因素影响来谈。This one is about the explosion limits of hydrogen–air mixtures. Hydrogen must make up a certain fraction of the air to ignite at all — too little or too much and it will not burn — and those two boundaries are the explosion limits. The author discusses how that range is set.
zenodo.23330091这篇讲的是粉尘爆炸的一套分析框架。像面粉、煤粉这类细小的可燃颗粒悬浮在空气里，一旦被点着就会很快蔓延开来，造成爆炸；作者要处理的是怎么把这件事系统地分析清楚。框架指的是把各类因素组织起来的办法。This one is about a framework for analysing dust explosions. Fine combustible particles such as flour or coal dust, once suspended in air and ignited, can spread quickly and explode; the author deals with how to analyse this systematically. A framework here means an organised way of handling the relevant factors.
zenodo.23330093这篇讲的是氢脆。金属在加工或者使用过程中会吸进一些氢，这些氢钻进晶格内部之后，材料就变得更容易开裂，看上去强度还在，一受力却断了。作者围绕金属吸氢变脆这件事来谈。This one is about hydrogen embrittlement in materials. Metals can take up hydrogen during processing or service, and once that hydrogen works into the lattice the material cracks more readily — it looks strong but fails under load. The author discusses metals turning brittle after absorbing hydrogen.
zenodo.23330095这篇讲的是金属氢化物和 van't Hoff 关系。金属氢化物是金属与氢结合成的化合物，常被用来储存氢气；van't Hoff 关系描述的则是吸氢和放氢时，温度和压力之间怎么对应。作者围绕这层对应关系来谈。This one is about metal hydrides and the van't Hoff relation. A metal hydride is a compound of a metal with hydrogen, often used to store hydrogen; the van't Hoff relation describes how temperature and pressure correspond when hydrogen is absorbed and released. The author discusses that correspondence.
zenodo.23330097这篇讲的是按生成焓（ΔH）窗口做的高通量筛选。ΔH 是生成焓，也就是形成化合物时放出或者吸收的能量；合适的储氢材料往往落在一个特定的 ΔH 区间里，这个区间就叫窗口，而高通量筛选是成批地算、成批地挑。作者围绕这套挑法来谈。This one is about high-throughput screening within a formation-enthalpy (ΔH) window. ΔH is the enthalpy of formation, the energy released or absorbed when a compound forms, and suitable hydrogen-storage materials tend to fall in a particular ΔH range, called a window; high-throughput screening computes and selects in bulk. The author discusses this selection method.
zenodo.23330099这篇讲的是连续方程的谱从哪来。像 Navier–Stokes 方程这类描述流体运动的方程，把它们分解开来会得到一组特征结构，也就是谱；作者要问的正是，这些谱结构背后的来源是什么。Navier–Stokes 方程是流体力学的基本方程。This one is about where the spectrum of continuum equations comes from. Equations such as the Navier–Stokes equations, which describe fluid flow, can be decomposed into a set of characteristic structures, a spectrum; the author asks what lies behind those structures. The Navier–Stokes equations are basic to fluid mechanics.
zenodo.23330101这篇讲的是显示材料里的 TADF，也就是热活化延迟荧光。在有机发光二极管里，有些材料能借助一点点热量，把本来不发光的那部分激发态转成会发光的，从而提高发光的效率。作者围绕这种机制和相关的材料来谈。This one is about TADF, thermally activated delayed fluorescence, in display materials. In organic light-emitting diodes, some materials use a little heat to convert excited states that would not emit into ones that do, which raises the efficiency of light emission. The author discusses this mechanism and the related materials.
zenodo.23330103这篇讲的是固态电解质的结构筛选。固态电解质是电池里以固体形态传导离子的材料，用来替换可燃的液态电解液；闭式律指的是一套可以写成公式、直接算出来的规律。作者用这套规律去挑合适的晶体结构。This one is about screening structures for solid electrolytes. A solid electrolyte conducts ions in solid form inside a battery, replacing the flammable liquid electrolyte; a closed-form rule is one that can be written as a formula and computed directly. The author uses such rules to pick suitable crystal structures.
zenodo.23330109这篇讲的是光刻胶。这是芯片制造里用到的一种感光材料，被光照到的部分性质会改变，显影之后就能留下图案，图案再转印到下面的材料上。作者围绕这种材料本身来谈，包括它在整个流程里的位置。This one is about photoresists. A photoresist is a light-sensitive material used in chip making: the parts struck by light change their properties, so developing leaves a pattern that can then be transferred to the material below. The author discusses this material and its place in the process.
zenodo.23330111这篇讲的是黑洞的经典精确解，具体是史瓦西解和克尔解。精确解指的是把方程严格解出来得到的答案，而不是近似；史瓦西解对应不自转的黑洞，克尔解对应会自转的黑洞。作者围绕这两个解描述的时空来谈。This one is about the classical exact solutions for black holes, specifically the Schwarzschild and Kerr solutions. An exact solution is obtained by solving the equations strictly rather than approximately; Schwarzschild's describes a non-rotating black hole and Kerr's a rotating one. The author discusses the spacetimes they describe.
zenodo.23330113这篇讲的是黑洞的视界物理，把事件视界、奇点定理和黑洞热力学放在一起谈。事件视界是进去就出不来的那道边界；奇点定理说明在某些条件下奇点躲不掉；黑洞热力学则给黑洞配上了温度和熵这类量。作者把这几块串起来讲。This one is about the physics of the black-hole horizon, treating the event horizon, the singularity theorems and black-hole thermodynamics together. The event horizon is the boundary beyond which nothing returns; the singularity theorems show that under certain conditions singularities are unavoidable; black-hole thermodynamics assigns quantities such as temperature and entropy. The author links these strands.
zenodo.23330115这篇讲的是霍金辐射。按这套说法，黑洞并不是只进不出：在视界附近，量子效应会让它慢慢向外发出粒子，质量随之减少，最后有可能蒸发掉。作者围绕这个辐射过程来谈。This one is about Hawking radiation. On this account a black hole is not purely a one-way sink: near the horizon, quantum effects make it emit particles gradually, so its mass drops and it may eventually evaporate. The author discusses this radiation process.
zenodo.23330118这篇讲的是黑洞信息悖论。如果把一份信息丢进黑洞，按量子力学它应当以某种形式保留下来；但按黑洞最终会完全蒸发这套图像，信息似乎就没了。这两者之间的矛盾就是信息悖论，作者围绕这个矛盾来谈。This one is about the black-hole information paradox. If information is thrown into a black hole, quantum mechanics says it should be preserved in some form, yet if the hole evaporates completely, that information seems to be gone. The clash between the two is the paradox, and the author discusses it.
zenodo.23330120这篇讲的是视界之外的那类时空结构，也就是白洞和虫洞。白洞和黑洞相反，只往外吐东西、不让东西进去；虫洞则是连接时空中两个不同地方的通道。两者目前都还属于理论上的设想，作者围绕它们来谈。This one is about spacetime structures beyond the horizon: white holes and wormholes. A white hole is the opposite of a black hole, spitting things out and letting nothing in; a wormhole is a passage linking two different places in spacetime. Both remain theoretical constructs, and the author discusses them.
zenodo.23330122这篇讲的是引力波是怎么产生的。引力波是时空的涟漪，质量分布要想搅动出这种涟漪，得发生剧烈而且不太对称的运动，比如两个致密天体互相绕转、最后并合到一起。作者围绕这类产生过程来谈。This one is about how gravitational waves are produced. A gravitational wave is a ripple in spacetime, and to stir one up a mass distribution must move violently and not too symmetrically, as when two compact bodies spiral together and merge. The author discusses such production processes.
zenodo.23330124这篇讲的是引力波的探测，以及由探测牵出的天体物理。探测这一步说的是怎么把这种极其微弱的时空扰动测出来；天体物理这一步说的则是从信号里读出源头的性质，比如质量、距离和并合过程。作者把两头连起来谈。This one is about detecting gravitational waves and the astrophysics that follows. Detection means measuring these exceedingly faint disturbances of spacetime; the astrophysics means reading off the source's properties, such as masses, distance and the merger itself. The author connects the two ends.
zenodo.23330129这篇讲的是宇宙学里的引力透镜。按广义相对论，质量会弯曲周围的时空，光线经过一个大质量天体时路径也会被弯折，背后的天体看起来就被放大、拉长，甚至出现多重像。作者围绕这种透镜效应来谈。This one is about gravitational lensing in cosmology. In general relativity mass bends the surrounding spacetime, so light passing a massive body has its path curved, making the object behind appear magnified, stretched or even multiplied. The author discusses this lensing effect.
zenodo.23330131这篇讲的是强引力透镜里的子结构。当透镜天体把背景天体的像拉成弧或者环时，这个像的细节里会留下透镜内部质量分布不均的痕迹，也就是子结构，比如小质量的暗物质团块。作者围绕怎么从像里看出子结构来谈。This one is about substructure in strong gravitational lensing. When a lensing body stretches a background object into arcs or rings, the details of that image carry traces of uneven mass inside the lens, that is, substructure such as small clumps of dark matter. The author discusses how to read substructure from such images.
zenodo.23330133这篇讲的是宇宙暴胀。暴胀说的是宇宙在极早期经历过一段非常短、却膨胀得极快的阶段；这段膨胀把原本微小的量子涨落拉大到天体尺度，成为后来结构长出来的种子。作者围绕这个设想来谈。This one is about cosmic inflation. Inflation says the very early universe went through a very brief stage of extremely rapid expansion, which stretched tiny quantum fluctuations up to astronomical scales and made them the seeds of later structure. The author discusses this proposal.
zenodo.23330135这篇讲的是质子半径，也就是质子这个粒子到底有多大。麻烦的地方在于，不同测量办法给出的数值之间一度出现明显差别，这个差别被称为质子半径之谜。作者围绕这个尺寸怎么量、量出来是多少来谈。This one is about the proton radius — how large the proton actually is. The trouble is that different measurement methods once gave clearly differing values, a discrepancy known as the proton radius puzzle. The author discusses how this size is measured and what value comes out.
zenodo.23330137这篇讲的是粒子物理里高激发态的全谱。把系统激发到很高的能级时，会得到一连串间隔越来越密的能级；要谈全谱，就得把这些能级一条条都算进来，而不是只看最低的那几条。作者围绕这套完整的谱来谈。This one is about the full spectrum of highly excited states in particle physics. Driving a system to very high levels yields a long series of levels that crowd closer together, and a full spectrum means accounting for all of them rather than only the lowest few. The author discusses this complete spectrum.
zenodo.23330141这篇讲的是希格斯粒子的宽度。宽度在这里是衡量粒子寿命的量，宽度越大说明它衰变得越快、越不稳定；放到希格斯粒子上，就是它平均能存在多久、以多快的速度衰变掉。作者围绕这个量来谈。This one is about the width of the Higgs boson. Width here measures a particle's lifetime: the larger the width, the faster it decays and the less stable it is; for the Higgs it tells how long the particle survives on average and how quickly it decays. The author discusses this quantity.
zenodo.23330143这篇讲的是量子退相干。量子系统可以处在几个状态叠加起来的情形，但它总会和周围环境发生一点作用，这些作用会把叠加关系一点点抹掉，最后只剩下一个普通的结果。作者围绕这个被抹掉的过程来谈。This one is about quantum decoherence. A quantum system can sit in a superposition of several states, but it always interacts a little with its surroundings, and those interactions gradually erase the superposition, leaving one ordinary outcome. The author discusses this erasure.
zenodo.23330149这篇讲的是光片量子密码学。量子密码学利用量子态来分发密钥，窃听者一旦偷看就会留下痕迹；光片指的则是一种只在很薄一层介质里传播的光。作者围绕把这种薄片状的光用到量子密钥分发上的做法来谈。This one is about light-sheet quantum cryptography. Quantum cryptography distributes keys using quantum states, so that any eavesdropper leaves a trace; a light sheet is light travelling in only a very thin layer of a medium. The author discusses applying such sheet-like light to quantum key distribution.
zenodo.23330153这篇讲的是 Majorana 零模。Majorana 粒子是指自己就是自己反粒子的那种粒子；零模说的是它出现在能量恰好为零的位置上。在凝聚态体系里，这种零模常常出现在拓扑缺陷的端点，作者围绕它来谈。This one is about Majorana zero modes. A Majorana particle is one that is its own antiparticle, and a zero mode sits at exactly zero energy. In condensed-matter systems such modes often appear at the ends of topological defects, and the author discusses this kind of mode.
zenodo.23330155这篇讲的是自发参量下转换（SPDC）的优化。SPDC 是一束光在非线性晶体里自发分成两个光子的过程，常用来产生纠缠光子；优化说的是调整晶体、泵浦等条件，让输出的光子更合用。作者围绕这一调整来谈。This one is about optimising spontaneous parametric down-conversion (SPDC). SPDC is the process in which one light beam spontaneously splits into two photons inside a nonlinear crystal and is widely used to produce entangled photons; optimising means tuning the crystal and pump so the output suits the purpose. The author discusses that tuning.
zenodo.23330157这篇讲的是光速极限。真空中的光速是一个固定的上限，任何有质量的物体都没法被加速到超过它；这个限制来自相对论对时间和空间的处理方式。作者围绕这个上限为什么存在、又意味着什么来谈。This one is about the speed-of-light limit. The speed of light in vacuum is a fixed ceiling, and no object with mass can be accelerated past it; the limit follows from the way relativity treats space and time. The author discusses why this ceiling exists and what it implies.
zenodo.23330159这篇讲的是时间箭头。日常经验里过去和未来并不一样，杯子摔碎不会自己拼回去；可物理的基本方程大多不区分正反两个时间方向。作者围绕这个不对称从哪里来、又意味着什么来谈。This one is about the arrow of time. In everyday experience past and future differ — a smashed cup does not reassemble itself — yet most fundamental equations of physics do not distinguish the two directions of time. The author discusses where this asymmetry comes from and what it means.
zenodo.23330161这篇讲的是宇宙循环。循环宇宙的设想是，宇宙并不是膨胀一次就结束，而是经历膨胀、收缩，再进入下一轮，来回往复。作者围绕这个设想本身，以及支持它或者反对它的理由来谈。This one is about a cyclic universe. The idea is that the universe does not expand once and finish, but goes through expansion, contraction and then another round, over and over. The author discusses this proposal and the arguments for and against it.
zenodo.23330165这篇讲的是超核谱。超核是原子核里除了质子和中子之外，还混进了一个由奇异夸克组成的超子，比如 Λ 粒子；超核谱就是这种核的能级排列。作者围绕这些能级来谈，以及它们能说明什么。This one is about hypernuclear spectra. A hypernucleus contains, besides protons and neutrons, a hyperon built from a strange quark, such as a lambda particle; a hypernuclear spectrum is the arrangement of energy levels in such a nucleus. The author discusses these levels and what they reveal.
zenodo.23330167这篇讲的是双重子态。普通的重子由三个夸克组成，双重子态则是六个夸克凑在一起形成的状态，可以看成两个重子粘在一起，却又可能表现出单独一个复合体的样子。作者围绕这种态来谈。This one is about dibaryon states. An ordinary baryon is made of three quarks, whereas a dibaryon is a state formed by six quarks coming together, which can be viewed as two baryons stuck to each other yet may behave as a single composite. The author discusses such states.
zenodo.23330169这篇讲的是核物质的状态方程。状态方程说的是，把一堆核子压到某个密度时，它的压强和能量该是多少；核物质被压得越密，这个对应关系就越难确定。作者围绕这条关系来谈。This one is about the equation of state of nuclear matter. An equation of state states, for a given density of nucleons, what the pressure and energy should be; the more densely nuclear matter is compressed, the harder that correspondence is to pin down. The author discusses this relation.
zenodo.23330171这篇讲的是中子星的结构。中子星是恒星塌缩之后留下的致密残骸，物质被压得极紧；从外面的薄壳到里面的核心，密度和成分一层层变化，核心到底是什么样子目前还没有定论。作者围绕这种分层结构来谈。This one is about the structure of neutron stars. A neutron star is the dense remnant left when a star collapses, with matter packed extremely tightly; density and composition change layer by layer from the thin outer crust to the core, and what the core is like remains unsettled. The author discusses this layered structure.
zenodo.23330173这篇讲的是衰变宽度。一个不稳定的粒子或者激发态不会一直待着，它平均过多久衰变一次，可以用宽度这个量来表示：宽度越大，寿命越短，衰变得越快。作者围绕这个量来谈。This one is about decay width. An unstable particle or excited state does not last forever, and how quickly it decays on average can be expressed by a width: a larger width means a shorter lifetime and a faster decay. The author discusses this quantity.
zenodo.23330175这篇讲的是 EDM，也就是电偶极矩。如果一个粒子的电荷分布不是完全球形对称，正负电荷的中心就会错开一点，这份错开就是电偶极矩；它的大小可以用来检验粒子内部是不是真像理论预期那样对称。作者围绕这个量来谈。This one is about the EDM, the electric dipole moment. If a particle's charge is not perfectly spherically symmetric, its centres of positive and negative charge are slightly offset, and that offset is the electric dipole moment; its size tests whether the particle is as symmetric inside as theory expects. The author discusses this quantity.
zenodo.23330179这篇讲的是高激发态的全谱。把系统激发到越来越高的能级时，能级会变得密集，彼此之间的间隔也越来越小；全谱指的是把这些能级尽可能完整地算出来，而不是只挑几条来看。作者围绕这套完整的谱来谈。This one is about the full spectrum of highly excited states. As a system is excited to higher and higher levels, the levels crowd together and the gaps between them shrink; a full spectrum means computing as many of them as possible rather than picking out a few. The author discusses this complete spectrum.
zenodo.23330183这篇讲的是 ε1 混合角。混合角描述的是两个量子态之间掺和的程度：角度为零表示两者互不掺和，角度变大则说明一个态里混进了另一个态的相当一部分。作者围绕这个参数来谈。This one is about the ε1 mixing angle. A mixing angle describes how much two quantum states blend: a zero angle means no blending, and a larger angle means one state contains a substantial share of the other. The author discusses this parameter.
zenodo.23330185这篇讲的是手征有效场论（ChEFT）的交叉验证。有效场论是在某个能量范围内只抓住主要自由度来写的理论，手征有效场论是核力这一层常用的版本；交叉验证是说，把它算出的结果再拿别的办法核对一遍，看是否吻合。作者围绕这一核对来谈。This one is about cross-validation of chiral effective field theory (ChEFT). An effective field theory keeps only the relevant degrees of freedom within a range of energies, and the chiral version is the one commonly used for nuclear forces; cross-validation means checking its results against another method. The author discusses that checking.
zenodo.23330187这篇讲的是 DT 聚变，也就是氘和氚的聚变。氘和氚是氢的两种较重同位素，原子核里分别多出一个和两个中子；把它们凑得足够近、融合成氦，会放出大量能量，这是目前最容易实现的一条聚变路线。作者围绕这条路来谈。This one is about DT fusion, the fusion of deuterium and tritium. Deuterium and tritium are the two heavier isotopes of hydrogen, with one and two extra neutrons in the nucleus; bringing them close enough to fuse into helium releases a great deal of energy, and this is the easiest fusion route so far. The author discusses this route.
zenodo.23330189这篇讲的是 DD 和 D-³He 这两条聚变路线。DD 是氘与氘反应，D-³He 是氘与氦-3 反应；这两条路线不产生中子，或者产生的中子少得多，因此对材料和防护的压力比常规路线小。作者围绕它们来谈。This one is about two fusion routes, DD and D-³He. DD is deuterium reacting with deuterium, and D-³He is deuterium with helium-3; these routes produce no neutrons, or far fewer, so they put less strain on materials and shielding than the conventional route. The author discusses both.
zenodo.23330191这篇讲的是 p-¹¹B 聚变，也就是质子与硼-11 的聚变。这条路线的主要产物是三个氦核，几乎不产生中子，因此不会让周围的结构带上放射性；代价是所需的反应条件比常规路线苛刻得多。作者围绕这条路来谈。This one is about p-¹¹B fusion, the fusion of a proton with boron-11. Its main products are three helium nuclei and it produces almost no neutrons, so it does not make surrounding structures radioactive; the price is that it demands far harsher conditions than the conventional route. The author discusses it.
zenodo.23330193这篇讲的是研究中子星时用到的核力输入。要算中子星的结构，先得知道核子之间怎么相互作用，这一项就是核力；它取什么形式、参数定成多少，会直接改变算出来的结果。作者围绕这个输入该怎么取来谈。This one is about the nuclear-force input used in studying neutron stars. Working out a neutron star's structure requires knowing how nucleons interact, and that ingredient is the nuclear force; the form it takes and the values of its parameters directly change the computed result. The author discusses how this input is chosen.
zenodo.23330195这篇讲的是贝塔衰变率。β 衰变是原子核里的中子变成质子，或者反过来，同时放出一个电子和一个反中微子；衰变率说的就是这种转变发生得有多快。作者围绕这个快慢来谈。This one is about beta-decay rates. In beta decay a neutron inside a nucleus turns into a proton, or the reverse, emitting an electron and an antineutrino; the rate says how quickly that change happens. The author discusses that speed.
zenodo.23330197这篇讲的是对称能。在核物质里，如果中子和质子数量相等，能量会处在较低的状态；一旦两者的数量拉开差距，多出来的这份能量就是对称能。它的大小会影响中子星有多大、有多致密，作者围绕这个量来谈。This one is about the symmetry energy. In nuclear matter, equal numbers of neutrons and protons give a relatively low energy; when the two counts diverge, the extra energy that appears is the symmetry energy. Its size affects how large and dense a neutron star is, and the author discusses this quantity.
zenodo.23330199这篇讲的是原子的超精细结构，用氢和铯-133 作例子。电子的状态会受原子核自旋的影响，能级因此分裂成靠得很近的几条，这就是超精细结构；铯-133 的这一分裂还被用来定义秒。作者围绕这个结构来谈。This one is about atomic hyperfine structure, illustrated with hydrogen and Cs-133. An electron's state is affected by the nuclear spin, so a level splits into a few very closely spaced ones, which is hyperfine structure; the splitting in Cs-133 is in fact used to define the second. The author discusses this structure.
zenodo.23330202这篇讲的是非微扰 QCD 里谱结构的来源，并把七条线索合成一条来讲。QCD 是描述强相互作用的量子色动力学；非微扰指的是相互作用强到不能再靠逐项展开来近似。作者要把这几条线索拼起来，说明谱是从哪里来的。This one is about where spectral structures in non-perturbative QCD come from, bringing seven strands into one account. QCD is quantum chromodynamics, the theory of the strong interaction, and non-perturbative means the interaction is too strong for term-by-term expansion. The author joins the strands to explain the origin of the spectra.
zenodo.23330204这篇要给循环宇宙一个了断。循环宇宙的设想是宇宙反复经历膨胀和收缩，一轮接着一轮，而不是只演一次；要做了断，就得判断这个设想在现有依据下站不站得住。作者围绕该怎么给出这个结论来谈。This one aims to settle the question of a cyclic universe. The idea is that the universe repeatedly expands and contracts, round after round, rather than playing out once; settling it means judging whether that proposal can stand on present evidence. The author discusses how such a verdict should be reached.
zenodo.23330209这篇讲的是右手中微子。中微子几乎不与其他物质发生作用，通常被观测到的那些自旋取向偏左；右手中微子则是设想中自旋取向偏右的一类，至今没有被直接看到，常被拿来解释中微子为什么会有质量。作者围绕它来谈。This one is about right-handed neutrinos. Neutrinos hardly interact with other matter, and the ones usually observed have their spin oriented one way; a right-handed neutrino is a hypothetical counterpart of the opposite orientation, never yet seen directly and often invoked to explain why neutrinos have mass. The author discusses it.
zenodo.23330211这篇讲的是原初黑洞。一般的黑洞来自大质量恒星塌缩，而原初黑洞是说在宇宙极早期，物质密度偏高的地方直接塌缩成的小黑洞；这类黑洞如果存在，可能是暗物质的一部分。作者围绕它们来谈。This one is about primordial black holes. Ordinary black holes come from the collapse of massive stars, whereas primordial ones are small black holes that would have formed directly from dense patches in the very early universe; if they exist, they could make up part of the dark matter. The author discusses them.
zenodo.23330213这篇讲的是重子光子比。重子是质子、中子这一类粒子，光子则是光的粒子；这个比值说的是宇宙里重子数和光子数相比是多少，它虽然只是一个数，却和宇宙早期各种过程怎么进行有关。作者围绕这个比值来谈。This one is about the baryon-to-photon ratio. Baryons are particles such as protons and neutrons and photons are particles of light, and the ratio says how the number of baryons in the universe compares with the number of photons; although it is only a number, it bears on how processes ran in the early universe. The author discusses this ratio.
zenodo.23330216这篇讲的是标准模型里基本粒子的质量。标准模型是描述已知基本粒子以及它们相互作用的那套理论；这些粒子的质量从哪里来、彼此之间是什么关系，是这套理论必须交代的一环。作者围绕这些质量来谈。This one is about the masses of the elementary particles in the Standard Model. The Standard Model is the theory describing the known elementary particles and their interactions; where their masses come from and how they relate to one another is a point the theory has to address. The author discusses those masses.
zenodo.23330218这篇讲的是宇宙的时间线。也就是说，从最早的那个阶段开始，一路经过各个时期直到现在，宇宙的这些阶段是怎么排下来的、每一段发生了什么；把这条线索按顺序理清楚，是理解宇宙演化的一种办法。作者围绕它来谈。This one is about the cosmic timeline. That is, from the earliest stage onwards, through the various eras up to the present, how the stages of the universe are ordered and what happened in each; setting that sequence out in order is one way to understand cosmic evolution. The author discusses this timeline.
zenodo.23330222「未发布」指 DOI 已预留但论文尚未公开，点开链接会返回未找到页面。 论文自身的 DOI 由 DataCite 实际登记状态核验（主论文群 28 篇 state = findable）。 "Not yet released" means the DOI is reserved but the paper is not public: the link returns a not-found page. Each paper's own DOI is checked against its actual DataCite registration state (state = findable for all 28 main papers).
04 · 定制计算04 · Custom computation
按体系报价，交付可核对的数值Quoted per system, delivering numbers you can check
用 RET 的封板算术做第一性原理计算。你提交体系与目标量，我们回复可行域、预期精度、周期与报价。不可行的会直接说不。First-principles computation using RET’s sealed arithmetic. You send the system and the target quantities; we reply with the feasible domain, expected accuracy, lead time and quote. If it is not reachable, we say so.
04定制计算服务Custom computation
按体系复杂度报价。提交需求后 24 小时内回复报价与可行域评估。Priced by the complexity of the system. We reply with a quote and a feasibility assessment within 24 hours.
| 服务Service | 交付内容Deliverable | 周期Turnaround | 价格Price | 下单Order |
|---|---|---|---|---|
| 01氢脆敏感性评估01Hydrogen-embrittlement susceptibility | 材料排序 ＋ 阈值预测Material ranking + threshold prediction | 3–5 天3–5 days | 定制On request | 咨询 →Ask → |
| 02储氢材料筛选02Hydrogen-storage material screening | 候选清单 ＋ 热力学参数Candidate list + thermodynamic parameters | 5–7 天5–7 days | 定制On request | 咨询 →Ask → |
| 03固态电解质评估03Solid-state electrolyte assessment | 离子迁移势垒 ＋ 界面稳定性Ion-migration barrier + interface stability | 5–7 天5–7 days | 定制On request | 咨询 →Ask → |
| 04光刻胶参数预测04Photoresist parameter prediction | 对比度 ＋ 酸扩散长度Contrast + acid-diffusion length | 7–10 天7–10 days | 定制On request | 咨询 →Ask → |
| 05含能材料稳定性05Energetic-material stability | 生成焓 ＋ 分解路径Enthalpy of formation + decomposition pathways | 3–5 天3–5 days | 定制On request | 咨询 →Ask → |
| 06催化剂筛选06Catalyst screening | 活性位点 ＋ 反应势垒Active sites + reaction barriers | 7–14 天7–14 days | 定制On request | 咨询 →Ask → |
把你的体系发过来。我们回复报价、可行域与预期精度。Send us your system. We reply with a quote, a feasibility assessment and the expected accuracy.
提交需求 → 24 小时内回复报价Request a quote → reply within 24 hours04.1报价与交付04.1Quoting and delivery
计算量取决于体系的复杂度和目标量的层数。我们不按"每篇论文"或"每工时"收费—— 按你交付物里的那几个数收。 The compute depends on the complexity of the system and the layer of the target quantity. We do not charge per paper or per hour — we charge for the numbers in your deliverable.
报价前我们会先做可行域评估。如果目标量在本框架内不可达、或只能给到条件级 [b]／候选级 [c]， 我们在报价阶段就写明，不会先收钱再降级交付。 We assess the feasible domain before quoting. If a target quantity is unreachable within this framework, or can only be given at conditional [b] / candidate [c] level, we say so at the quoting stage — we do not take payment and downgrade the delivery afterwards.
边界声明Boundary statement
RET 的物理诠释、与 QCD 的具体对应、以及多数数值层的物理主张， 论文本身登记为开放候选或终态边界。 RET’s physical interpretation, its concrete correspondence to QCD, and the physical claims of most numerical layers are registered by the papers themselves as open candidates or terminal boundaries.
因此我们的交付口径是：给出算术层可核对的数与它的推导链，并标明该数在论文里的审计级别。 我们不把 [c] 级候选包装成定理级结论。 So our delivery basis is this: we give the arithmetic-level number and its derivation chain, together with the audit grade that number carries in the papers. We do not dress a [c]-level candidate up as a theorem-level result.
06联系方式Contact
请在邮件中写明：体系组成、关注的性质、期望精度、以及交付时间要求。 我们会在 24 小时内回复报价与可行域评估；若该体系超出方法适用域，我们会直接说明。 Please state the composition of the system, the properties you care about, the accuracy you need and your deadline. We reply with a quote and a feasibility assessment within 24 hours; if the system falls outside the method's applicable domain we will say so directly.
在线留言Message
最多 1000 字。同一 IP 5 分钟内只能提交一次。不保证一定有回复。Up to 1,000 characters. One submission per IP every 5 minutes. A reply is not guaranteed.