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)

Abstract. This work presents a discrete-mathematical framework anchored on
objective difference as its sole first-cause anchor, with the trinity of existence–
difference–change as its ontological principle, and it explicitly grades the rigor of
every claim on a unified L0–L5 scale. The General Volume states the ontological
principle, the ontological status of mathematics, the methodological canon, the
axioms, meta-rules and boundaries; Volume 1 builds the difference-operator axiom
system and a translation programme (not a fidelity theorem) into ZFC under three
restrictions; Volume 2 geometrizes number theory, gives a universal affirmative
geometric definition of primes, renames the "prime-vacancy triangle" as the
multiplicative-triangle canonical form (its hard core being the natural-number edge,
the square edge, and the per-level products up to that level's square), and
systematically incorporates classical number theory; the self-made b*-truncation ζ_n
is moved to a separate short paper (the volume lists it only once under future work),
and the Riemann Hypothesis serves as an end-of-volume external comparator and a
bridge/whetstone for formalization (open, not a proof, with zero dependence of the
volume on RH); Volume 3 applies the framework reflexively to epistemology, yielding,
under the single postulate of a finite-bandwidth physical information channel, a
three-level conditional statement of "cognition as boundedness" (the categorical
boundary is fixed, trends are statistically fixed, concrete trajectories are not), re-
grounding the bounds of truth, the thing-in-itself, consciousness and digital/artificial
cognition (whose engineered form is the author's Anchor-Matching, AM, paradigm),
and culminating in a three-level attitude toward the unknown, high-fidelity cognitive
transmission, and the altruistic expansion of the collective pool of human cognition.
Mathematics is characterized as a fidelity-preserving projection of the quantitative
aspect of dimensional reality—a "discovered invention" (the symbolic encoding is
invented, while the quantitative relations it tracks are discovered)—whose objective is
high-fidelity derivability of quantitative relations rather than complete replication or
self-justification; Gödel's theorems (which already hold in a system as weak as
Robinson arithmetic Q) therefore function not as a premise of the framework but as
an independently, strictly proven corroboration, within classical arithmetic, of the
projective boundary that no closed static projection can completely seal off open
diachronic generation. The theorems are neither overturned nor claimed exempt, and
incompleteness receives a diachronic reinterpretation. The operator-theoretic core of
RH is left as an open problem.

摘要:本全集提出⼀套以客观差异为唯⼀第⼀因锚点、以"存在—差异—变化"三位⼀体为本体论原
则的离散数学框架,并明确区分框架中不同命题的严格度等级。全集由总卷与三卷构成,构
成⼀个⾃我限定、边界清晰的逻辑闭环:
•总卷确⽴三位⼀体的本体论原则、数学的本体论身份、⽅法论总纲、三条核⼼公理与统⼀
的严格度分级判准,说明体系的元规则与边界;
•第⼀卷建⽴以差异算⼦ Δ 为核⼼的离散数学公理系统,给出关系算术、⼆维离散域、两类
原⽣遍历坐标系,以及传统 ZFC 集合论在固定差异集、规律遗忘、潜⽆穷三项限定下的翻
译纲领(对应词典),并把形式逻辑明确定位为现实逻辑在同时性静态截⾯上的特例;
•第⼆卷完成数论的⼏何化重构:给出素数的通范肯定性⼏何定义,把"素数缺位三⻆"正名
为乘法三⻆规范形(硬核⼼为⾃然数边、平⽅数边与每阶乘积到该阶平⽅截⽌),并体系化
收编经典数论;⾃制 b* 截断 ζ_n 构造已移出另⽴⼩论⽂(本卷仅在"后续⼯作"列⼀⾏);
黎曼猜想在本卷是卷末外部对照与形式化衔接的桥梁/磨⼑⽯(开放、⾮证明、本卷对 RH
零依赖);
•第三卷把框架反身⽤于认识论,以有限带宽物理信息通道为唯⼀公设,给出"认知即注定"
的三级条件性命题(范畴边界注定、趋势统计注定、轨迹不注定),重构真理、物⾃体、意
识等概念,标明数字⼈⼯认知的第⼀因边界(⼯程化形态即作者的锚匹配 AM 范式),并
以"⾯对未知"的三级态度、⾼保真认知传承与⼈类总认知池的利他拓展为最终导向。
必须诚实声明:本体系是⼀套奠基性框架与研究纲领。其中既有可枚举复现、可标准证明的
结果,也有公设、本体论⽴场、未证明的猜想与说明性模型;全书以统⼀的 L0–L5 严格度
分级逐条标注(判准⻅卷⾸《判准与体例》)。本体系把数学定位为实存量纲之"量"的保真
投影(发现的发明),其⽬标是纯量关系层的⾼保真可推导,⽽⾮完备复制现实或在系统内
⾃证完备。据此,哥德尔不完备定理(在罗宾逊算术 Q 这样弱的系统中即成⽴)不是本体
系的前提,⽽是"封闭静态投影不可能在⾃身内完备封死开放历时⽣成"这⼀投影边界在经典
算术内被⽴严格证实的⼀次应验;本体系不推翻它、也不申请豁免,⽽是对不完备性给出
历时性根源重释(完整论述⻅总卷第七章)。黎曼猜想的本体性命题(临界线上的算⼦⾃伴
性)作为开放问题悬挂,不宣称已证。所有结论的第⼀因均可回溯⾄不可否认的客观差异,
⽆任何额外特设假设。