COR0003canonicalv1No Identity Decoherence
No Identity Decoherence: the diagonal resonance pattern (L+E+P) cannot occur at the ontic level in tau, because K5 blocks (L), NF-Confluence blocks (E), and the star-autonomous structure blocks (P).
Payload
No Identity Decoherence
No Identity Decoherence: the diagonal resonance pattern (L+E+P) cannot occur at the ontic level in tau, because K5 blocks (L), NF-Confluence blocks (E), and the star-autonomous structure blocks (P).
No Identity Decoherence
Summary
No Identity Decoherence: the diagonal resonance pattern (L+E+P) cannot occur at the ontic level in tau, because K5 blocks (L), NF-Confluence blocks (E), and the star-autonomous structure blocks (P).
Statement
%
\label{cor:no-identity-decoherence}
The diagonal resonance pattern
(Definition~\ref{def:diagonal-resonance}, I.D89)
--- the three-component splice
of free contraction (L),
equality-as-congruence (E),
and primitive self-products (P) ---
cannot occur at the ontic level in $\tau$.
Its three prerequisites are individually blocked:
\begin{enumerate}[\normalfont(i)]
\item (L) is blocked by $\KAxiom{5}$
(Definition~\ref{def:diagonal-discipline}, I.D03).
\item (E) is blocked by NF-Confluence
(Lemma~\ref{lem:nf-confluence}, I.L02)
and three-level equality
(Definition~\ref{def:three-equality}, I.D15).
\item (P) is blocked by the star-autonomous structure
(Theorem~\ref{thm:k5-structural-exclusion}, I.T39).
\end{enumerate}
Therefore, identity slippage
(Definition~\ref{def:identity-slippage}, I.D90)
is zero, shadow identities
(Definition~\ref{def:shadow-identity}, I.D91)
do not arise,
and ontic identity coherence
is maintained at 100\% under every admissible construction.
Proof / Justification
Diagonal resonance (I.D89) requires
the simultaneous presence of (L), (E), and (P).
Theorem~\ref{thm:ontic-identity-invariance} (I.T46)
established that each component
is individually blocked by the coherence kernel:
(L) by K5, (E) by NF-Confluence, (P) by star-autonomy.
Since the resonance pattern cannot assemble
without all three components,
it cannot occur.
Without diagonal resonance,
identity slippage (I.D90) has no source,
shadow identities (I.D91) have no mechanism
of generation,
and the identity coherence of
Theorem~\ref{thm:ontic-identity-invariance}
is maintained without exception.
Source Context
- Registry source:
book-01.jsonlline 205 - Manuscript source:
2nd-edition/book-i-categorical-foundations/02_mainmatter/part18/ch81-ontic-identity-invariance.texlines 659-687
Lean / Formalization Notes
- Formalization:
formalized - Module:
TauLib.BookI.MetaLogic.OnticInvariance - Name:
Tau.MetaLogic.no_identity_decoherence
Dependencies
- Canonical: I.T46, I.D89
Related Results
Generated by later projection phases.
Related Publications
Generated by later projection phases.
Revision Notes
- 2026-04-24: Initial pilot migration.
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I.C03no-identity-decoherencecor:no-identity-decoherenceRelease lines
corpus_v3_workingcorpus_v2Relations
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Downstream uses (computed) (2)
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