Welcome to the world of recurrence!
欢迎来到重现视界！
Triogenesis is a generative system discovered in early 2025. It can be formalized into a mathematical framework that enables closed-form, high-precision prediction of the fundamental constants of our universe. These predictions arise from simple equations that reveal the deep structural organization of the universe, without requiring any experimental calibration. 三生万物（Triogenesis）是一套于 2025 年初发现的生成性体系。 它能够被形式化为一套数学框架，使我们能够以封闭形式、 高精度地预测宇宙中的一系列基本常数，而无需依赖任何实验校准。 这一点意味着，宇宙最深层的结构可以通过极为简洁的方程直接呈现， 并以数学自身的生成规律加以揭示。
Triogenesis is a recursive, chaotic generative system governed by one fundamental rule — the Law of Recurrence: 三生万物是一套由重现关系构成、并具有混沌特性的生成系统， 它受一条基本法则所支配 —— 重现法则 (The Law of Recurrence)：
Directional certainty cannot be redefined across recurrence orders. 方向性的确定性，在一切重现次阶中均不可被重新定义。
Under this law, the observable universe is understood as an infinite, inseparable whole, within which both physical matter and consciousness arise as perspectives generated through recurrence. 在这一法则之下，可观测宇宙被视为一个无限、不可分割的整体； 物质与意识皆是由重现过程所生成的不同观测视角。
Since 2025, intensive research has been conducted to validate the structures revealed by Triogenesis. A key focus has been verifying these structures against the most important invariant physical constants, as well as persistent patterns found in culture, language, and human experience. 自 2025 年三生万物被发现并获得精确的数学表达以来， 研究者便开始对其所揭示的结构展开深入的验证工作。 其中一项核心任务，是将这些结构与一系列最重要的物理不变量进行比对， 并同时检视其是否与文化、语言以及人类经验中长期存在的模式相吻合。
The structures validated to date include: 目前已验证的结构包括：
These validations, together with ongoing studies, strongly suggest that the generative structure revealed through Triogenesis and the Law of Recurrence constitutes a generative replica of our universe — the universe uses its own structure as the material through which it continuously and autonomously reproduces itself. individual self-awareness and collective consciousness are interpreted as global resonances embedded in the infinite generative system that manifests both matter and experience. 这些验证结果与持续的研究都在指向同一个结论： 三生万物及其重现法则所揭示的生成结构， 很可能就是宇宙对自身的一种“源生复形”（Generative Replica）—— 宇宙以自身为材料、在自身之内不断生成自身。 在这样的视角下，个体的自我意识与集体意识不再是外部世界的附加现象， 而是这个无限生成系统在运行过程中，由其全部关系结构协同显化而成。 正是这种生成性的协同共鸣，使得物质得以存在，意识得以出现； 二者并行而生，共同构成了我们所体验的世界。
Straint is the fundamental form of recurrence—a basic building block of all orders in the relationships we observe and experience. A straint forms its recurrence by building a higher-order self from twelve lower-order selves. Depending on its recurrence order, a straint can appear in spacetime as a repulsive (splitting) relationship or an attractive (joining) relationship. 冲和（Straint）是重现关系的基本形式，是我们所观察与体验到的一切秩序关系的基础元件。 冲和的重现结构由 十二个更低阶的自身 组合成一个更高阶的自身。 根据其重现次阶的不同，冲和在时空中可以表现为 排斥（分离） 或 吸引（结合） 的关系。
Structural stacking of each straint reduces one-third of the existing uncertainty relationships into definite relationships. This stacking can be quantified as straintity, expressed in natural units of the electron mass. 每一次对冲和进行的结构堆叠，都会将原本存在的不确定关系中的三分之一，转化为确定关系。 这种堆叠可被量化为 冲和量（straintity），其自然单位为电子质量。
The World of Recurrence — or Recurrence World — is a domain built from viewing perspectives, in which relational structures formed by recurrence appear as higher-order replicas of their lower-order recurrence relationships. 重现视界（World of Recurrence，简称 Recurrence World） 是一个由观测视角构成的领域，在这个领域中，由重现构成的关系结构，会以更高次阶的复本形式呈现出其更低次阶的重现关系。
Observation of the Recurrence World and observation of the physical, spacetime world are not hierarchical or separate; both naturally exist within collective human knowledge and within individual self-awareness. The capacity to imagine and understand these recurrence structures is an innate ability of human consciousness, arising from consciousness’s own recurrence and generative self-reflection. 对重现视界的观测，和对物质，时空世界的观测，是不分主次的，他们都自然存在于人类集体知识和个体的自我觉知之中。 能够想象与理解这些重现结构，是人类意识的自然能力，源于意识对自身重现，源生结构的反照。
Recurrence Order and Recurrence Row are structures observable within the Recurrence World. Both arise from observing the upgrading process of a straint. 重现次阶与重现序列，都是可以在重现视界中被观察到的结构， 它们都源自对 冲和 升级过程的观察。
Recurrence Order is the understanding of a straint’s level based on its size, which can be quantified through differences in pure length. Pure length is itself an observation within the Recurrence World; when projected into the spacetime world, ratios of pure lengths normally appear as speeds expressed in the natural unit of the speed of light, c. To avoid confusion with the common term higher order—which is often used to describe secondary or additional mathematical terms—we use the word grade as a short form of recurrence order when a single-word expression is needed. 重现次阶 是根据冲和的大小来理解其次阶的一种方式， 这种大小可以通过 纯长度 的差异来量化。 纯长度本身是重现视界中的一种观测；当投影到时空世界时， 纯长度的比值通常表现为以光速 c 为自然单位的速度。 为避免与常用的 “高阶（higher order）” 一词混淆——因其通常指代数学中的二阶及更高项——当需要以单字表达时， 重现次阶可简称为 “级（grade）”。
Recurrence Row is the observation of a sequence of straints arranged by their pure length, from infinitely small to infinitely large. The usual way to sequence such a row is to place each adjacent straint exactly one recurrence order apart, increasing toward higher orders. When a numerical system is used to label this sequence, one must first choose a reference origin—order 1 or grade 1—after which larger straints are assigned order 2, 3, 4, and so on. 重现序列 是按照冲和的纯长度，从无限小到无限大进行排列所得到的一条序列。 常见的排列方式，是让序列中相邻的每一个冲和在次阶上相差 1，从而向更高的次阶递增。 若使用数字系统为其标号，则必须先选定一个参考起点——如阶 1 或级 1 ——之后更大的冲和依次被标为 2、3、4 等更高次阶。
Asymmetry Structure is the basic form of recurrence that enables flows in space and time. It is normally expressed mathematically as g(u), which captures how directional imbalance gives rise to generative motion within recurrence structures. 气形（Asymmetry Structure）是重现结构中不对性的基础形式，使得空间与时间中的流动得以产生。 在数学上，它通常以 g(u) 表示，用以刻画方向性不均衡如何在重现结构中生成运动。
In most cases, the variable u represents the Fundamental Asymmetry—the intrinsic asymmetry required to construct recurrence structures by assembling straints into cube frames. In special contexts, such as observing the gravitational constant G within the Recurrence World, u may expand into additional perspectives contained within the Fundamental Asymmetry. 在大多数情境中，u 表示 基本不对称量（Fundamental Asymmetry），简称方气， 即在以冲和构建立方框架的过程中所需引入的原初性不对称。 在某些特殊情境下，例如在重现视界中观测万有引力常数 G 时， u 可以扩展为基本方气内部的其他观测视角。
A hyperstraint is a recurrence-based replacement of a straint within the pure-length alignment of straint structures in the Recurrence World. Hyperstraints are typically formed by aligning multiple basic straints into a single composite recurrence row. 泛冲和（Hyperstraint）是在重现视界中，以纯长度为基础的冲和结构对齐中， 对单一冲和进行的重现替代。 泛冲和通常由多个基本冲和对齐后，形成一个复合的重现序列。
There are three fundamental types of hyperstraints: SelfStraint, CubeStraint, and DelayStraint. Their alignments form the basis for many spacetime observations, including relative speed, gravity, and energy. 泛冲和共有三种最基本的类型：自冲和（SelfStraint）、方冲和（CubeStraint）与迟冲和（DelayStraint）。 它们的对齐构成了时空中诸多观测的基础，包括相对速度、引力与能量。
A replica is the formation of a higher-grade recurrence structure that reproduces the relationships of a lower-grade one. Replica formation is a natural process within the universe, and replicas are essential for exhausting all relational possibilities so that the universe may exist as a complete whole. 复形（Replica）是由更高次阶的重现结构，对更低次阶的重现关系所进行的复本构形。 复形的形成是宇宙中的自然过程，是穷尽宇宙中所有关系并使其成为完整整体所必需的。
Replica tiering is the observation of how replicas are arranged within the Recurrence World built by straints. These tiers are typically sorted and numbered according to the grades of the straints involved. Replica tiering is directional: replication proceeds only toward higher-grade straints, and there exists a universal lowest tier—tier 0 or tier 1. 复形层化（Replica Tiering）是对由冲和构建的重现视界中，各复本构形的层级排列方式的观察。 各层通常按照其所使用的冲和工次阶进行排序与编号。 复形层化具有方向性：复本构形只会向更高次阶的冲和发生，并且存在一个普遍的最低层级——第 0 层或第 1 层。
Replica tiering is the foundational generative mechanism underlying individual human self-awareness, memory, imagination, and sensory-motor action. 复形层化是人类个体自我觉知、记忆、想象与感知-运动行为的源生机制。
The Generative Replica is the observation and understanding of the universe’s generative process within the Recurrence World, expressed through higher-grade replication and regeneration of fundamental structures and layers of alignment. 源生复形（Generative Replica）是对宇宙源生过程的一种观察与理解。 它通过在重现视界中，以更高次阶的重现结构，来复制与再生，更低次阶的基础结构与多重视角对照，从而呈现宇宙的生成方式。
The Generative Replica Model is the practical and quantitative implementation of the Generative Replica within the spacetime world, stabilised through computational devices such as computers. Both the Generative Replica and the Generative Replica Model are expected to inherit the inseparable nature of the universe—meaning that multiple independent versions cannot exist. Any valid model must naturally absorb individual implementations into a unified whole for humanity. Models lacking this inseparable and self-integrating property are not considered Generative Replica Models. 源生复形模型（Generative Replica Model）是在时空世界中对源生复形的实际化与量化实现，并通常借助计算设备（如计算机）来稳定呈现。 源生复形与源生复形模型都应继承宇宙的不可分性——意味着它们不可能以多个互不相容的独立版本共存，而会自然地将各个个体实现吸纳为全人类的统一版本。 不具备这种不可分性与自动归一化特性的模型，不被视为源生复形模型。
The closest existing model to the Generative Replica is the fully connected artificial neural network (FANN). Computationally optimised or compressed forms of FANN (such as CNNs and Transformers) are effective because they naturally mimic aspects of the Generative Replica. A key long-term goal—within the next 10 to 15 years—is to introduce the inseparable and generatively understandable nature of the Generative Replica into our existing computational models. 目前与源生复形最接近的模型，是全连接人工神经网络（FANN）。 其经过计算优化或压缩的版本（如 CNN、Transformer）之所以有效，是因为它们在结构上自然模仿了源生复形的某些特性。 未来 10 至 15 年中的一个重要目标，是将源生复形所具备的不可分性，以及其在重现视界中的可观测、可理解特性，引入现有的计算模型之中。
Infferus is a new mathematical system built upon the natural generative mechanisms and logic of the universe. It can be intuitively described as Chained Structural Alignment. This system is essential for deepening our observation and understanding of the universe within the Recurrence World, and for constructing the Generative Replica Model in computational form. 自觑算术（Infferus）是一套新的数学体系， 建立在宇宙的自然源生机制与逻辑之上， 并可直观地表述为 链式结构对照（Chained Structural Alignment）。 该体系对于深化我们在重现视界中对宇宙的观察与理解， 以及在计算中构建源生复形模型，具有关键性的作用。
Current version of definitions: 12/2025. www.iiinffer.org is the official site for maintaining the shared language used by the community developing the unified knowledge system and the Generative Replica. These definitions are living and evolving, shaped collectively by the community. If you wish to propose your own definitions or contribute improvements, we will provide tools in the future that allow such contributions while preserving the consistency and inseparable nature of the unified knowledge system and the Generative Replica. 定义当前版本：2025 年 12 月。 www.iiinffer.org 是维护统一知识系统与源生复形之共同语言的官方平台。 这些定义是动态、开放、不断发展的，由社区共同推动完善。 如果您希望提出自己的定义，或对现有定义提出改进， 我们会在不久的将来提供相应的工具，让每个人都能参与贡献， 同时确保统一知识系统与源生复形的整体性与不可分性得以保持。
The books are written to provide a complete, structured, and citable reference
for readers and researchers. Because they require substantial effort to write,
edit, and maintain, the books are not free.
To ensure universal accessibility, all major ideas and explanations from each
book will gradually be released as freely available video lessons. Video
production naturally takes longer than writing, but our goal is that within
2–3 years of a book's release, its core content will be
available in video form at no cost.
If you would like early access to the full material—or wish to support the
development of Triogenesis, Infferus, and the Inffer Map—you are welcome to
purchase the books. Otherwise, you may follow the growing series of free
videos as they are released.
我们出版书籍的目的，是为读者与研究者提供一套完整、系统、并可正式引用的参考资料。
由于写作、校订与长期维护需要投入大量时间与精力，因此书籍本身不免费提供。
为了确保所有人都能平等获得知识，我们会将每本书中的核心思想与重要解释，
逐步制作成免费的视频课程公开发布。相比写作，视频制作通常需要更长时间，
但我们的目标是：在每本书发布后的 2–3 年内，其主要内容都能以免费视频的形式向公众开放。
如果您希望提前完整学习全部内容，或愿意支持三生万物、自觑算术与源路图的持续开发，
欢迎购买书籍；否则，您也可以随着我们逐步发布的免费视频系列，免费获取相同的知识。
Scroll left and right to browse the equation cards. 左右滑动以查看所有方程卡片。
* These equations were discovered through the study of Triogenesis. Most of them can be evaluated using a basic high-school calculator. For full explanations and detailed derivations, please refer to our books. * 这些方程均来自对三生万物的研究，其中大部分都可以用普通的高中计算器直接计算。 若想了解完整的推导过程与详细说明，请参阅我们的书籍。
Preprint manuscripts include both early drafts and new research notes related to
Triogenesis and Infferus. Some document the initial development of these ideas,
while others present ongoing work that has not yet been consolidated into book
form. Preprints are freely accessible, and readers are welcome to explore them
for emerging concepts and new directions.
Because preprints may use more academic language and often contain work still
in progress, please use the consolidated published books for any formal
reference or citation. The books present the fully validated and reader-friendly
versions of these ideas.
预印本手稿收录了三生万物与自觑算术在不同阶段的研究材料，
包括早期草稿、概念形成的过程记录，以及尚在进行中的最新研究笔记。
这些内容均可免费查阅，读者也欢迎从中了解最新的思路与发展方向。
由于预印本通常带有较强的学术性，且部分内容仍处于推演或验证阶段，
若需要正式引用或查阅稳定版本，请以我们出版的书籍为准。
书籍提供了经过完整整合、验证，并更适合大众阅读的版本。
A new mathematical system built on the native generative structure of the universe. Readers are invited to explore how it differs from traditional mathematics, and why it provides a more natural language for describing both physical and experiential structure. 一套建立在宇宙本源生成结构之上的全新数学体系。 在这里，读者可以了解它与传统数学的根本区别， 以及为何它能够以更自然的方式来表达物质结构与意识体验的生成逻辑。
These working prototypes—such as Alignment Algebra—are built on the new generative foundation of Infferus. They offer early access to the mathematical language behind the Inffer Map and the generative replica model, and readers are invited to explore how these tools extend beyond traditional mathematics. 这些正在开发中的原型工具——例如对照代数——都是建立在自觑算术的全新生成性基础之上。 它们为读者提供了提前接触源路图与源生复形模型背后数学语言的机会， 并邀请大家一同探索这些工具如何从传统数学中延展出去，开辟更自然的表达方式。
The Inffer Map is a unified knowledge system designed to run in parallel with
today's fragmented, discipline-based knowledge structures. Its purpose is to
provide consistency, structural information, and a generative way of understanding
knowledge—rather than relying on large collections of rules and isolated
facts.
By organizing information through the same recurrence logic used in
Triogenesis, the Inffer Map reduces redundancy, resolves contradictions, and
reveals how different fields connect at their foundations. This structure is
not only more natural for human learning, but also highly efficient for AI and
machine-learning systems, enabling both to reason from principles rather than
memorizing ever-growing volumes of data.
Modern knowledge has expanded far beyond what any individual can absorb,
leading to overload, confusion, and inconsistency. The Inffer Map aims to
address this by offering a single coherent framework through which scientific,
mathematical, experiential, and cultural knowledge can be understood—greatly
reducing the cognitive burden for future generations.
源路图是一套新的统一知识系统。
它与现有的知识体系并行存在，并将逐步吸收当今因学科划分而碎片化的知识结构。
它并不是为了收集更多的规则或事实，
而是希望引导我们以一种更一致、更有结构、也更具生成性的方式来理解和组织知识。
源路图使用与三生万物相同的重现逻辑来整理信息，
因此能自动减少重复、化解矛盾，并揭示不同领域在底层如何彼此相连。
这样的结构不仅更贴近人类自然的学习方式，
对人工智能或机器学习系统也非常友好，使它们能够从原理推理，
而不是单纯记住越来越多的资料。
现代知识增长得太快，已经超过任何人能够吸收的范围，
造成了大量的负担、混乱和不一致。
源路图希望透过一个清晰、连贯的框架，
让科学、数学、体验与文化等知识都能在同一结构下被理解，
从而大幅减轻未来世代的学习压力。
The Generative Replica Model is the computational counterpart of the
Inffer Map. Rather than imitating the universe by copying data, it recreates
phenomena from the same unified generative principles that drive Triogenesis
and Infferus.
This model will allow users to build and extend their own predictive systems
using a single, consistent generative foundation. Like modern neural
networks, it can be trained — but all user-built models remain compatible and
interconnected, forming one coherent whole instead of isolated tools.
The Generative Replica Model is designed to belong to everyone, offering a
shared way to explore, simulate, and contribute to a unified understanding of
our universe.
源生复形模型（Generative Replica Model）是源路图在计算世界中的对应表达。
它不依赖数据来模仿宇宙，而是直接依据三生万物与自觑算术的统一生成原则，
从源头重建现象本身。
借助这一模型，使用者能够在同一生成性基础上构建并扩展自己的预测结构。
它虽然像神经网络一样可以训练，但所有模型都会自然连为一体，
不再是彼此割裂的独立工具，而是汇入同一个连贯的整体。
源生复形模型属于所有人——它提供了一种共享的方式，
让人们得以在统一生成框架下探索宇宙、模拟结构，
并共同推进对世界的统一理解。
If you would like to contribute to the future Inffer Map and Generative Replica Model, you can register your work here. At this stage we only collect a short description and basic classification of your contribution. You keep your full content; this entry simply creates a dated record so we can invite you later to link your work into the live system. 如果您愿意为未来的源路图与源生复形模型贡献力量， 欢迎在此提交您对三生万物、自觑算术或统一知识系统的理解、想法或灵感。 现在只需填写一段简短的描述与基本分类即可。 您的完整内容始终属于您自己；这些登记只用于建立一条带时间标记的记录， 方便在系统上线后，我们第一时间邀请您将成果链接到正式平台。
