The five canonical generators (K1–K5)

K1–K5 are the five canonical generators of the τ-kernel — strict order, labelled boundary, composition, boundary identification, and generator closure. They are the structural atoms from which every τ-categorical invariant is built. The number five is not a parameter; the no-ω axiom (K6) proves that no sixth generator can be added.

Categorical invariant. Five distinguished generators on the τ-kernel, each axiomatized by one of the K1–K5 axioms, jointly satisfying the K6 closure.

Primary registry anchor: I.K1

Supporting items: I.K0, I.K2, I.K3, I.K4, I.K5, I.K6

1. I.K0 — Universe Postulate — the categorical kernel τ exists
2. I.K1 — K1: strict order on the kernel atoms
3. I.K2 — K2: labelled boundary as a structured Stone space
4. I.K3 — K3: composition (total and associative)
5. I.K4 — K4: boundary identification (universal property)
6. I.K5 — K5: generator closure (the five close under declared relations)

Lean modules referenced: TauLib.BookI.Kernel.Signature, TauLib.BookI.Kernel.Diagonal

Status: Formalized

Module: TauLib.BookI.Kernel.Signature

Lean kind: structure

Lean symbol: Tau.BookI.Kernel.Signature