PRP0081canonicalv1Defect Contractivity
For τ-admissible data, the defect functional is contractive: Δ(f, n+1) ≤ κ · Δ(f, n) for some κ < 1. Key estimate driving regularity. The contraction constant κ comes from the divergence of ∑1/p.
Payload
Defect Contractivity
For τ-admissible data, the defect functional is contractive: Δ(f, n+1) ≤ κ · Δ(f, n) for some κ < 1. Key estimate driving regularity. The contraction constant κ comes from the divergence of ∑1/p.
Defect Contractivity
Summary
For τ-admissible data, the defect functional is contractive: Δ(f, n+1) ≤ κ · Δ(f, n) for some κ < 1. Key estimate driving regularity. The contraction constant κ comes from the divergence of ∑1/p.
Statement
\label{prop:defect-contractivity}
Let $f$ be $\tau$-admissible fluid data (Definition~\ref{def:tau-admissible-fluid-data}, Ch.~34). There exists a contraction factor $\kappa = \kappa(k) < 1$, depending only on the primorial depth $k$ of the initial data, such that for all $n \geq k$:
\begin{equation}
\Delta(f, n+1) \;\leq\; \kappa \cdot \Delta(f, n).
\label{eq:ch35-defect-contractivity}
\end{equation}
Proof / Justification
No immediate manuscript proof block was extracted in this pilot run.
Source Context
- Registry source:
book-03.jsonlline 93 - Manuscript source:
2nd-edition/book-iii-categorical-spectrum/02_mainmatter/part05/ch35-fluid-sectors-and-the-defect-functional.texlines 165-173
Lean / Formalization Notes
- Formalization:
formalized - Module:
TauLib.BookIII.Physics.PositiveRegularity - Name:
defect_contractivity_check
Dependencies
- Canonical: III.D39, III.T07, III.T14
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.P14defect-contractivityprop:defect-contractivityRelease 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.
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Version & History
Status disclaimer
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