Static Kernel tau_0

tau_0 = the static kernel: 5 generator objects + K1-K6 axioms + rho. The complete specification before the generative act.

Static Kernel tau_0

Summary

tau_0 = the static kernel: 5 generator objects + K1-K6 axioms + rho. The complete specification before the generative act.

Statement

%
\label{def:tau-zero}
The \textbf{static kernel} $\tau_0$ is the first-order theory
with signature $\Sigma_\tau = (\alpha, \pi, \gamma, \eta, \omega, \rho, {<})$,
the universe postulate $\KAxiom{0}$,
and structural axioms $\KAxiom{1}$--$\KAxiom{6}$:
\[
    \tau_0 \;:=\; (\Sigma_\tau,\; \KAxiom{0}, \KAxiom{1}, \KAxiom{2},
    \KAxiom{3}, \KAxiom{4}, \KAxiom{5}, \KAxiom{6}).
\]

Proof / Justification

This item is definitional. No manuscript proof is required.

Source Context

• Registry source: book-01.jsonl line 5
• Manuscript source: 2nd-edition/book-i-categorical-foundations/02_mainmatter/part01/ch04-closure-tau-zero.tex lines 223-234

Lean / Formalization Notes

• Formalization: formalized
• Module: TauLib.BookI.Kernel.Signature
• Name: Tau.Kernel.tau_zero

Dependencies

• Canonical: I.D01, I.D02, I.K1, I.K2, I.K3, I.K4, I.K5, I.K6

Related Results

Generated by later projection phases.

Related Publications

Generated by later projection phases.

Revision Notes

• 2026-04-24: Initial pilot migration.