The G0-Lattice_ An Axiomatic Derivation of a 4×7 Dimensional Knowledge Topology

Abstract Current knowledge classification systems such as the Chinese Library Classification and Dewey Decimal Classification are established through empirical induction, lacking rigorous a priori axiomatic foundations. This paper proposes the G0-Lattice Theory. Starting from a single primitive axiom of void self-reference (G0), we derive a complete 4×7-dimensional knowledge topological space via six-order deductive derivation (G0–G6) without injecting any empirical data. We define seven-dimensional wave coordinates as fundamental invariants of knowledge entities, and strictly prove that all human abstract activities can be projected into 28 irreducible resonant windows (4 universes × 7 degrees of freedom). By contradiction, this paper verifies that the set of 28 windows satisfies orthogonality and self-limitation. This research constructs a purely formal underlying coordinate system for interdisciplinary knowledge mapping, independent of specific physical carriers and computational implementations. 摘要现有中图法、杜威十进分类法等知识组织体系均依托经验归纳构建,不具备严格先验公理基底。本文提出G0 - 格理论,以单一虚无自指元公理 G0 为逻辑原点,通过 G0 至 G6 六阶演绎体系,在零经验数据输入条件下推导出完备 4×7 维知识拓扑空间。 本文确立七维波坐标 作为知识实体不变量,严格证明人类全部抽象认知活动均可映射至28 组不可约谐振窗口(4 宇宙维度 ×7 自由维度),并通过反证法完成该窗口集合正交性与自限性证明。本成果为跨学科知识融合搭建纯形式化底层坐标体系,脱离物理载体与工程实现范畴。