THM0209canonicalv1HL Constant Convergence
Hardy-Littlewood C₂(k) decreasing for k=2..5. Each factor p(p-2)/(p-1)² < 1.
Payload
HL Constant Convergence
Hardy-Littlewood C₂(k) decreasing for k=2..5. Each factor p(p-2)/(p-1)² < 1.
HL Constant Convergence
Summary
Hardy-Littlewood C₂(k) decreasing for k=2..5. Each factor p(p-2)/(p-1)² < 1.
Statement
\label{thm:hl-decreasing}
$C_2(k)$ is decreasing for $k = 2, \ldots, 5$. Each factor
$p(p-2)/(p-1)^2 < 1$ for $p \ge 3$, so the sequence is monotonically
decreasing toward $C_2 \approx 1.3203$.
\textbf{Lean:} \texttt{hl\_constant\_decreasing\_5}.\quad
\textbf{Registry:} III.T74.
Proof / Justification
No immediate manuscript proof block was extracted in this pilot run.
Source Context
- Registry source:
book-03.jsonlline 271 - Manuscript source:
2nd-edition/book-iii-categorical-spectrum/02_mainmatter/part10/ch81-additive-conjectures-deep.texlines 268-275
Lean / Formalization Notes
- Formalization:
formalized - Module:
TauLib.BookIII.Spectral.TwinPrimeDeep - Name:
hl_constant_decreasing_5
Dependencies
- Canonical: III.D106
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.T74hl-constant-convergencethm:hl-decreasingRelease 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.