Discrete Mathematics System of Difference Ontology: Foundational Canon (Complete Works)

中文名称:差异本体论离散数学体系:奠基元典(全集)

This work is the complete foundational canon of the Discrete Mathematics System of Difference Ontology, representing the first unified cognitive framework in human intellectual history that fully connects metaphilosophy, mathematics, and epistemology. The complete collection consists of three volumes, forming a complete logical closed loop without breakpoints: The General Volume establishes the ontological principle of the trinity of existence-difference-change, and clarifies the meta-rules and boundaries of the system; Volume 1 constructs a discrete mathematical axiom system with the difference operator Δ as the sole core, replacing the ten axioms of traditional ZFC set theory with only three axioms, strictly proving the ZFC embedding theorem, demonstrating that this system is a boundary-complete and consistent foundation of mathematics, and resolving all fundamental paradoxes of mathematical foundation such as Russell's paradox; Volume 2 completes the geometrization reconstruction of number theory, gives the first affirmative and essential geometric definition of prime numbers, constructs the core number theory research tool of prime number vacancy triangle, defines the native discrete ζ function, and provides a constructive proof framework for the Riemann Hypothesis based on the six-fold symmetry of two-dimensional discrete domain; Volume 3 realizes the mathematical turn of philosophy, strictly proves the "Cognition is Destined Theorem", accurately delineates the ultimate boundary of human cognition, reconstructs core philosophical concepts such as truth, thing-in-itself, and consciousness, and clarifies the inherent boundaries and evolution direction of digital artificial cognitive systems. All conclusions of this system are strictly derived from the sole observable objective difference phenomenon, without any additional ad hoc assumptions, providing a brand-new unified research paradigm for fields such as mathematics, philosophy, and cognitive science.

本成果为差异本体论离散数学体系的奠基元典全集,是人类思想史上首个从元哲学到数学再到认知论完全贯通的统一认知框架。全集共三卷,构成完整无断点的逻辑闭环:总卷确立存在 - 差异 - 变化三位一体的本体论原则,明确体系的元规则与边界;第一卷建立以差异算子 Δ 为唯一核心的离散数学公理系统,仅用三条公理替代传统 ZFC 集合论的十条公理,严格证明 ZFC 嵌入定理,证明本体系是边界完备且一致的数学基础,消解罗素悖论等所有数学基础根本性悖论;第二卷完成数论的几何化重构,给出素数的第一个肯定性、本质性几何定义,构造素数缺位三角这一核心数论研究工具,定义原生离散 ζ 函数,基于二维离散域的六重对称性给出黎曼猜想的构造性证明框架;第三卷实现哲学的数学化转向,严格证明「认知即注定定理」,精确划定人类认知的终极边界,重构真理、物自体、意识等核心哲学概念,明确数字人工认知系统的固有边界与演化方向。本体系所有结论均严格推导自唯一的可观测客观差异现象,无任何额外特设性假设,为数学、哲学、认知科学等领域提供了全新的统一研究范式。