Daopology: An Axiomatic System for the Speakable Dao

The human knowledge system faces a fundamental tension: while the total volume of knowledge grows unprecedentedly, cross-disciplinary methodological transfer becomes increasingly difficult. Traditional disciplinary classification, while promoting specialization, has created knowledge islands that obstruct the reuse of structurally isomorphic methods. This paper proposes Daopology—a meta-discipline studying the generation, classification, measurement, and transfer of “the Dao that can be spoken.” Unlike previous versions, this paper does not treat generators, Heng families, kernels, and other concepts as empirically given taxonomies, but derives the entire system from two irreducible axioms. Axiom 1 (Dao-Name Axiom): The Constant Dao cannot be named; the speakable Dao can be named. Axiom 2 (Six-Act Axiom): The speakable Dao must be manifested by an observer through six acts: distinction, naming, determination, measurement, composition, and transfer. From the six acts, we derive:• From naming: 9 primitives (motion, transition, interaction, repetition, adaptation, computation, encoding, randomness, self-reference);• From measurement: 6 Heng families (information, thermodynamics, topology, symmetry, randomness, causality);• From composition: 6 Jiao families (additive, multiplicative, competitive, hierarchical, time-varying, feedback), generating 12 common combinations;• From determination: 8 Cha families, 7 Que families, 21 He families;• From distinction: a 9-layer framework;• From transfer: 4 transfer types. These seven categories constitute 79 minimal expressive parameters. We provide completeness and minimality proofs for each, and validate the system through cross-domain cases.