AXM0007canonicalv1Beacon Non-Successor (K5)
omega is NOT in the image of rho restricted to any orbit ray; omega is unreachable by finite iteration.
Payload
Beacon Non-Successor (K5)
omega is NOT in the image of rho restricted to any orbit ray; omega is unreachable by finite iteration.
Beacon Non-Successor (K5)
Summary
omega is NOT in the image of rho restricted to any orbit ray; omega is unreachable by finite iteration.
Statement
\label{ax:beacon-non-succ}
For every generator $g \in \{\alpha, \pi, \gamma, \eta\}$
and every $n \geq 0$:
\[
\boxed{\rho^n(g) \neq \omega.}
\]
No finite iteration of $\rho$ on a non-$\omega$ generator reaches~$\omega$.
Proof / Justification
This item is an axiom. No manuscript proof is required.
Source Context
- Registry source:
book-01.jsonlline 10 - Manuscript source:
2nd-edition/book-i-categorical-foundations/02_mainmatter/part01/ch02-rho-omega.texlines 158-166
Lean / Formalization Notes
- Formalization:
formalized - Module:
TauLib.BookI.Kernel.Axioms - Name:
Tau.Kernel.K5_beacon_non_succ
Dependencies
- Canonical: I.D01, I.D02
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.K5beacon-non-successor-k5ax:beacon-non-succRelease 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.