Corpus corollary canonical 2026-05-27T20:53:50+00:00
Corpus v3 · Corollary cid001002COR0003canonicalv1

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).

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.jsonl line 205
  • Manuscript source: 2nd-edition/book-i-categorical-foundations/02_mainmatter/part18/ch81-ontic-identity-invariance.tex lines 659-687

Lean / Formalization Notes

  • Formalization: formalized
  • Module: TauLib.BookI.MetaLogic.OnticInvariance
  • Name: Tau.MetaLogic.no_identity_decoherence

Dependencies

  • Canonical: I.T46, I.D89

Generated by later projection phases.

Generated by later projection phases.

Revision Notes

  • 2026-04-24: Initial pilot migration.

Identifiers

  • Corpus ID cid001002
  • Primary alias COR0003
  • Type Corollary
  • Status canonical
  • Visibility public
  • Version v1

Aliases & legacy IDs

I.C03no-identity-decoherencecor:no-identity-decoherence

Release lines

corpus_v3_workingcorpus_v2

Relations

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

  • Monograph cid000023Book I, Part 18, Chapter 81 (Part XVIII)

Version & History

  • v1 · 2026-05-10 imported from v2 registry
  • v1 · 2026-05-10 wired formalized by in wave 5

Status disclaimer

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