Corpus theorem canonical 2026-05-27T20:53:50+00:00
Corpus v3 · Theorem cid001665THM0208canonicalv1

Twin Density Primorial

Twin prime density positive at each primorial level k≥2 (up to depth 5).

Payload

Twin Density Primorial

Twin prime density positive at each primorial level k≥2 (up to depth 5).

Twin Density Primorial

Summary

Twin prime density positive at each primorial level k≥2 (up to depth 5).

Statement

\label{thm:twin-density}
At each primorial level $k \ge 2$, at least one twin prime pair
exists below $\min(M_k, 500)$.

\textbf{Lean:} \texttt{twin\_density\_primorial\_5}.\quad
\textbf{Registry:} III.T73.

Proof / Justification

No immediate manuscript proof block was extracted in this pilot run.

Source Context

  • Registry source: book-03.jsonl line 270
  • Manuscript source: 2nd-edition/book-iii-categorical-spectrum/02_mainmatter/part10/ch81-additive-conjectures-deep.tex lines 247-253

Lean / Formalization Notes

  • Formalization: formalized
  • Module: TauLib.BookIII.Spectral.TwinPrimeDeep
  • Name: twin_density_primorial_5

Dependencies

  • Canonical: III.D105

Generated by later projection phases.

Generated by later projection phases.

Revision Notes

  • 2026-04-24: Initial pilot migration.

Identifiers

  • Corpus ID cid001665
  • Primary alias THM0208
  • Type Theorem
  • Status canonical
  • Visibility public
  • Version v1

Aliases & legacy IDs

III.T73twin-density-primorialthm:twin-density

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 cid000024Book III, Part 10, Chapter 81 (Wave R1)

Version & History

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

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.

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