PRP0098canonicalv1Terminal Level Characterization
E₃ is terminal iff the self-modelling operator is idempotent: Enr(E₃) = E₃ means the self-model of the self-model is the self-model. This is the abstract characterization of why the ladder stops at four levels.
Payload
Terminal Level Characterization
E₃ is terminal iff the self-modelling operator is idempotent: Enr(E₃) = E₃ means the self-model of the self-model is the self-model. This is the abstract characterization of why the ladder stops at four levels.
Terminal Level Characterization
Summary
E₃ is terminal iff the self-modelling operator is idempotent: Enr(E₃) = E₃ means the self-model of the self-model is the self-model. This is the abstract characterization of why the ladder stops at four levels.
Statement
%
\label{prop:terminal-level-characterization}
An enrichment level~$\Elayer{k}$ is \textbf{terminal}
if and only if the self-modelling operator~$S_{k}$
is idempotent:
\[
S_{k} \circ S_{k} = S_{k}.
\]
Equivalently, $\Elayer{k}$ is terminal if and only if
every $\Elayer{k}$-observer's self-model
is already an $\Elayer{k}$-object.
Proof / Justification
No immediate manuscript proof block was extracted in this pilot run.
Source Context
- Registry source:
book-03.jsonlline 189 - Manuscript source:
2nd-edition/book-iii-categorical-spectrum/02_mainmatter/part10/ch72-saturation-why-e3-is-terminal.texlines 207-219
Lean / Formalization Notes
- Formalization:
formalized - Module:
TauLib.BookIII.Mirror.Saturation - Name:
terminal_level_check
Dependencies
- Canonical: III.T49, III.T03
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
III.P31terminal-level-characterizationprop:terminal-level-characterizationRelease lines
corpus_v3_workingcorpus_v2Relations
Formalized by (4)
Appears in (1)
Downstream uses (computed) (8)
Items in the corpus that reference this one via load-bearing relations. Computed from the full corpus-v3 graph at build time.
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Version & History
Status disclaimer
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