Terms
Foundations
- Science of Being （存在之科学） — The science whose core operator is BE, studying well-founded beings; the degenerate projection of the science of generation as ι→1
- Dao （道） — The unnamed whole prior to differentiation; a generative operation, not a being; cannot be axiomatized, only operationalized
- boundary postulate （分界基设） — A foundational proposition about the BE side / degenerate projection; not an internal axiom
- proper class (project sense) （固有类） — A circular, self-embedding structure presupposing itself, excluded by the Axiom of Foundation; its mathematical home is νF
- containment asymmetry （涵摄非对称） — The one-way containment relation between the two systems
- mutual arising （互生） — Two poles emerge simultaneously in one differentiation event and define each other; A=S(S(A))
- Shēng （生） — The iterative operator of qualitative change and emergence, Xₙ₊₁=S(Xₙ), required to yield finite cycles
- Science of Generation （生之科学） — The science whose core operator is Shēng (generation), studying proper classes, i.e. generation itself
- rotor （旋机） — A self-sustaining cycle containing a method of distinction that establishes invariant relations among the distinguished; the basic category of the science of generation
Structure
- primordial equation （本原方程） — A fixed-point equation replacing an axiom
- bisimulation （互模拟） — The identity criterion on the image face; decidable in the finite case
- guardedness （守护性） — Each self-reference is guarded by an actual generation step; one of the two criteria of endogeneity
- Five-Phase track （五行轨） — The two-relation, five-element track; the minimal closed rotor carrying generation (step 1) and restraint (step 2) as irreducible relations
- yin-yang track （阴阳轨） — The one-generates-two track of 2ⁿ nesting, period 2, handling hierarchical nesting and unity of opposites
- terminal coalgebra （终余代数 νF） — F(νF)≅νF; the mathematical home of proper classes; one of the images of the Dao
- autologicality （自例化） — A principle is an instance of its own content; one of the two criteria of endogeneity
Epistemology
- generation-preserving （保生） — Preserving the type of generative structure in inference