Traditional Chinese categories (Dao, yin-yang, the four images, the eight trigrams, the Five Phases) are technical terms with precise formal meanings here, not metaphors. Which trigram corresponds to which object, however, is a convention: not unique, and never a basis for calculation.
Basic categories
Generation (shēng)
The iterative operator of qualitative change and emergence, Xₙ₊₁ = S(Xₙ), required to produce finite cycles.
Rotor (xuánjī)
A self-sustaining cycle containing a method of distinction that establishes invariant relations among the distinguished; the basic category of the science of generation.
Mutual arising
Two poles emerge in one differentiation event and define each other; A = S(B), B = S(A), hence A = S(S(A)).
Dao
The unnamed whole before differentiation; a generating operation, not a being. It cannot be axiomatised, only operationalised.
Proper class
A circular, self-nesting structure that presupposes itself, excluded by the Axiom of Foundation; its mathematical home is the terminal coalgebra νF.
Circular recognition
Divide the whole, distinguish within, fix the relations — members and relations are generated together; there is no cognitive origin.
Structure and form
Yin-yang track
The 2ⁿ nesting track in which one generates two; period 2; handles hierarchical nesting and the unity of opposites.
Five-Phase track
The five-element track in which two generates three; n = 5 is the smallest integer carrying two directed Hamiltonian cycles at once, generation (step 1) and overcoming (step 2). Theorem
Overcoming = generation²
Overcoming is the square of generation; the Five Phases do not reduce to binary (5 ∤ 2ᵏ). Theorem
Terminal coalgebra νF
The coalgebra with F(νF) ≅ νF; the mathematical home of proper classes — one appearance of the Dao, not the Dao itself.
Bisimulation
The criterion of identity on the side of images; decidable in finite cases by Paige–Tarjan partition refinement. Theorem
Primordial equation
A fixed-point equation that replaces an axiom; used with coinduction and bootstrapping.
Epistemology
Downward generation / upward abstraction
Downward is the determinate application of one principle (a forward problem); upward infers the principle from its products (an inverse problem), so its conclusions are always probabilistic.
Boundary postulate
“Entities do not carry information about their generative path”; a founding statement about the side of being, not an internal axiom of the science of generation. Postulate
Generation-preserving
Inference that preserves the type of generative structure; a lexical-level counterpart of truth preservation.
The full glossary, with the claims linked to each term, is in the public claim base.