DEF0002canonicalv1Five Generators
The five generators {alpha, pi, gamma, eta, omega} with canonical roles: radial seed, prime base, exponent channel, tetration channel, fixed-point absorber.
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Five Generators
The five generators {alpha, pi, gamma, eta, omega} with canonical roles: radial seed, prime base, exponent channel, tetration channel, fixed-point absorber.
Five Generators
Summary
The five generators {alpha, pi, gamma, eta, omega} with canonical roles: radial seed, prime base, exponent channel, tetration channel, fixed-point absorber.
Statement
\label{def:generators}
The five \textbf{generators} of Category~$\tau$ are the constant symbols
\[
\alpha, \quad \pi, \quad \gamma, \quad \eta, \quad \omega.
\]
They are the only primitive objects of the theory.
All other objects will be produced by applying the
progression operator $\rho$ to these generators (Part~II).
Proof / Justification
This item is definitional. No manuscript proof is required.
Source Context
- Registry source:
book-01.jsonlline 2 - Manuscript source:
2nd-edition/book-i-categorical-foundations/02_mainmatter/part01/ch01-five-generators.texlines 83-92
Lean / Formalization Notes
- Formalization:
formalized - Module:
TauLib.BookI.Kernel.Signature - Name:
Tau.Kernel.Generator
Dependencies
- Canonical: I.K0
Related Results
Generated by later projection phases.
Related Publications
Generated by later projection phases.
Revision Notes
- 2026-04-24: Initial pilot migration.
Identifiers
Aliases & legacy IDs
I.D01five-generatorsdef:generatorsRelease lines
corpus_v3_workingcorpus_v2Relations
Appears in (1)
Sources
Version & History
Status disclaimer
A Corpus Item page reports the program's current internal record for this item. It does not imply external verification, scientific consensus, or final proof unless explicitly stated. Read it together with its dependencies, formalization status, and the program's overall stance.