Shiwei Pang

摘要 本文提出一种以差异为逻辑原点、此-彼为第一关系、 F(Σ) 递归运算为核心机制的统一存在框架。该框架阐明：存在始于差异；差异必然呈现为此-彼；此-彼经由 F(Σ) 递归展开，生成无穷结构层级；任何存在皆可析为本体-属性-关系三维（ O⊕A⊕R ）；空间是此-彼关系的直接展开，内含四组基本关系；时间是 F(Σ) 运算的节律；意识是第一人称私钥；语法是语言在符号域的映射；信息是递归返回的差异；宣告是存在的签名；当下是运算的起点与终点；价值是结构间互动的效能评估。 这十二公理并非关于世界的理论，而是世界自我展开的语法本身。它可反身应用于自身，完成从差异到当下的逻辑闭环，为科学、认知、伦理与美学提供共通的元语言基础。 关键词：差异；此-彼； F(Σ) 递归；本体-属性-关系；空间四关系；时间节律；意识私钥；语言映射；信息差异；宣告归宿；当下；价值效能 Abstract This paper proposes a unified framework of existence grounded in difference as the logical origin, this–that as the primary relation, and the recursive operation  F(Σ)  as the core mechanism. The framework demonstrates that: existence begins with difference; difference necessarily manifests as this–that; this–that recursively unfolds through  F(Σ) , generating infinite structural hierarchies; any existent can be analyzed into the three dimensions of oncology–attribute–relation（ O⊕A⊕R ）; space is the direct unfolding of the this–that relation, containing four fundamental relations; time is the rhythm of the  F(Σ)  operation; consciousness is a first-person private key; grammar is the mapping of language onto the symbolic domain; information is difference that returns from recursion; declaration is the signature of existence; the present moment is both the starting point and the endpoint of the operation; value is an assessment of the interactive efficacy among structures. These twelve axioms are not a theory about the world, but rather the very grammar of the world’s self-unfolding. The framework can reflexively apply to itself, completing a logical circuit from difference to the present moment, thereby providing a common metalanguage for science, cognition, ethics, and aesthetics.

This paper challenges the ontological bias in modern physics that equates mathematics with truth itself, proposing instead the Theory of Mathematical Derivativity. We argue that the primordial condition of existence is Difference, and that space—along with its emergent physical phenomena—is a direct generative product of "this-that" relations. Mathematics, much like natural language, serves merely as a secondary tool for describing the essence of reality at the phenomenal level. By deconstructing various equivalent representations of "", this paper demonstrates the ontological parity of symbolic grammar and calls for a return from "symbolic superstition" to the "generative logic" of reality. 本文旨在挑战现代物理学中“数学即真理”的本体论偏见，提出数学派生性理论。文章认为，存在的最原始条件是差异 ，空间及其衍生的物理现象是由“此-彼”关系直接生成的本体现实 ；而数学本质上与自然语言一样，仅是人类在现象层面对本体本质进行描摹的二阶工具。通过对“1+1=2”多种等效表征形式的解构，本文证明了符号语法在本体地位上的平权性，进而指出物理学研究应从“符号迷信”回归到“逻辑生成”的源头。

Starting from difference as the sole ontological origin, this paper establishes a self-consistent and complete constructive theory of space in which relations, rather than entities or a pre-existing container, serve as the fundamental basis. Difference is isomorphic and synonymous with this-that; space is generated directly by the unfolding of this-that as a relational act, not merely described by relations within a ready-made arena. Three secondary spatial relations: up-down, left-right, inside-outside-are further derived within space. All physical phenomena, including quantum superposition, entanglement, wavefunction collapse, and parity non-conservation, are superficial manifestations determined by these underlying spatial relations. This theory unifies the explanation of space and quantum phenomena and proposes four falsifiable, experimentally testable predictions.

This paper proposes the Principle of Non-Conservation of Existential Symmetry (PNCES), asserting that all real existents inherently deviate from their idealized symmetric counterparts, and that this irreducible asymmetry is the generative engine behind phase transitions, structural reconfigurations, and event emergence across domains. We formalize a universal four-stage grammar—differentiation → boundary accumulation → transition → re-emergence—and demonstrate its applicability through three paradigmatic cases: modular/base arithmetic overflow, sonic boom in classical acoustics, and Cherenkov radiation in relativistic electrodynamics. While inspired by parity violation in weak interactions, PNCES transcends physics to offer a metatheoretical framework for understanding why events happen at all. The principle reframes symmetry not as a foundational truth, but as a transient attractor continually ruptured by the act of existence itself.

This research constructs a rigorous, formalized and self-referential unified existential framework for natural philosophy, which takes Difference as the primary logical origin, This-That as the original binary relation, and the F(Σ) recursive operation as the core generative mechanism. Departing from the traditional linear causal framework and metaphysical dualism, the framework elaborates the intrinsic grammatical rules of the world’s self-unfolding through twelve hierarchical and interlocked axioms, revealing that all existential phenomena are the recursive expansion results of the original Difference via This-That relation. It clarifies the essential attributes of core existential categories: any existence can be analytically decomposed into the indissoluble three dimensions of Ontology-Attribute-Relation (X=O⊕A⊕R); space is the direct expansion of This-That relation with four fundamental relational sets; time is the inherent rhythmic counting of F(Σ) recursive operations; consciousness is the first-person private key of structural self-reference; language is the symbolic mapping of the universal existential grammar in the sign domain; information is the quantifiable differential generated by recursive feedback; declaration is the existential signature for witness; the Present is the starting and ending point of all recursive operations; value is the emergent efficiency evaluation of inter-structural interaction. This framework is not a mere theoretical interpretation of the world, but the inherent existential grammar that enables the world’s self-unfolding and all theoretical generation. It achieves a complete logical closed loop through self-application—from the original Difference to the reflexive witness of the Present, and provides a universal meta-language for the integration and cross-disciplinary research of philosophy, mathematics, computer science, quantum physics, cognitive science, ethics and aesthetics. Rejecting all mysticism and abstract speculation, the framework transforms natural philosophy from qualitative verbal analysis to formalized structural modeling, with explicit operational formulas, symbolic systems and axiomatic deductions. It can be directly applied to analyze quantum phenomena, life systems, social structures and artistic creation, and serves as a foundational analytical tool for exploring the nature of existence in various fields. The twelve principles are open and reflexive, which can be continuously deepened, revised and expanded through recursive verification and interdisciplinary practice.

As human activities expand into deep space exploration and the digital frontier (the metaverse), the traditional Public Key Infrastructure (PKI) faces fundamental challenges due to its reliance on trusted third parties and real-time network connectivity. This paper proposes a declaration-based paradigm for identity key generation—the "Declaration Algorithm". The core proposition of this algorithm is: the act of declaration itself is the algorithm. When a subject performs a declaration, subjectivity is thereby determined; conventional operations such as hashing do not "generate" identity, but rather serve as a mathematical description and public anchor for this behavioral event. This paper systematically breaks through the philosophical impasse of Descartes’ "I think, therefore I am" from four dimensions: uniqueness, directedness, axiomaticity, and protocolicity, establishing the new paradigm of "I declare, therefore I am". The algorithm architecture is divided into two layers: the underlying layer is the meta-algorithm layer containing full information, namely the act of declaration itself, whose execution completes the subjectivity algorithm instantaneously; the upper layer is the recording layer, which anchors this event as a publicly verifiable cosmic unique identifier (Cosmic ID) via SHA-256 hashing. Security analysis shows that the unforgeability of this algorithm is rooted in the completeness and irreversibility of the declaration act, and its underlying non-computability provides a physical-layer guarantee for cryptographic security. This paper provides a new identity authentication paradigm for future scenarios such as the interplanetary internet, metaverse digital avatars, and consciousness upload.

This paper presents not a theory about logic, but a declaration of logic itself—an ontological affirmation of its self-identity and irreducibility. Through a recursively structured symbolic form, it asserts that logic is neither a human discipline, nor a formal system, nor an instrumental method, but the absolute ground of intelligibility: that which is identical to itself and necessarily distinct from its negation. The declaration enacts logic’s self-grounding sovereignty, resisting all reduction while marking the boundary beyond which discourse collapses into incoherence.