AXM0005canonicalv1Orbit-Seeded Generation (K3)
Each generator g in {alpha, pi, gamma, eta} seeds its orbit ray O_g = {rho^n(g) : n >= 0}.
Payload
Orbit-Seeded Generation (K3)
Each generator g in {alpha, pi, gamma, eta} seeds its orbit ray O_g = {rho^n(g) : n >= 0}.
Orbit-Seeded Generation (K3)
Summary
Each generator g in {alpha, pi, gamma, eta} seeds its orbit ray O_g = {rho^n(g) : n >= 0}.
Statement
%
\label{ax:orbit-seeded}
For each generator $g \in \{\alpha, \pi, \gamma, \eta\}$:
\[
\boxed{%
g \in O_g, \quad\text{and}\quad
\rho^n(g) \in O_g \;\text{for all}\; n \geq 0.
}
\]
That is, $g$ belongs to its own orbit ray,
and $\rho$ maps $O_g$ into~$O_g$.
Proof / Justification
This item is an axiom. No manuscript proof is required.
Source Context
- Registry source:
book-01.jsonlline 8 - Manuscript source:
2nd-edition/book-i-categorical-foundations/02_mainmatter/part01/ch03-generation-cover.texlines 104-116
Lean / Formalization Notes
- Formalization:
formalized - Module:
TauLib.BookI.Kernel.Axioms - Name:
Tau.Kernel.K3_orbit_seeded
Dependencies
- Canonical: I.D01, I.D02, I.K1
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.K3orbit-seeded-generation-k3ax:orbit-seededRelease lines
corpus_v3_workingcorpus_v2Relations
Formalized by (1)
Appears in (1)
Downstream uses (computed) (2)
Items in the corpus that reference this one via load-bearing relations. Computed from the full corpus-v3 graph at build time.
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.