THM0205canonicalv1Partition Growth
Partition growth: r(M_{k+1}) > r(M_k) for k=2..4. Goldbach representations increase with primorial depth.
Payload
Partition Growth
Partition growth: r(M_{k+1}) > r(M_k) for k=2..4. Goldbach representations increase with primorial depth.
Partition Growth
Summary
Partition growth: r(M_{k+1}) > r(M_k) for k=2..4. Goldbach representations increase with primorial depth.
Statement
\label{thm:partition-growth}
The partition count grows with primorial depth:
$r(M_{k+1}) > r(M_k)$ for $k = 2, 3, 4$.
\textbf{Lean:} \texttt{partition\_growth\_4}.\quad
\textbf{Registry:} III.T70.\quad
\textbf{Scope:} $\tau$-effective.
Proof / Justification
No immediate manuscript proof block was extracted in this pilot run.
Source Context
- Registry source:
book-03.jsonlline 262 - Manuscript source:
2nd-edition/book-iii-categorical-spectrum/02_mainmatter/part10/ch81-additive-conjectures-deep.texlines 178-185
Lean / Formalization Notes
- Formalization:
formalized - Module:
TauLib.BookIII.Spectral.GoldbachDeep - Name:
partition_growth_4
Dependencies
- Canonical: III.D103
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.T70partition-growththm:partition-growthRelease 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.