Corpus definition canonical 2026-05-27T20:53:50+00:00
Corpus v3 · Definition cid001449DEF0219canonicalv1

CRT Twin Admissibility

Twin-admissible residues mod M_k: r with neither r nor r+2 ≡ 0 (mod p_i) for all i≤k. Always nonempty.

Payload

CRT Twin Admissibility

Twin-admissible residues mod M_k: r with neither r nor r+2 ≡ 0 (mod p_i) for all i≤k. Always nonempty.

CRT Twin Admissibility

Summary

Twin-admissible residues mod M_k: r with neither r nor r+2 ≡ 0 (mod p_i) for all i≤k. Always nonempty.

Statement

\label{def:crt-twin-admissible}
A residue $r \bmod M_k$ is \emph{twin-admissible} if for every
prime $p_i$ ($i \le k$): $r \not\equiv 0 \pmod{p_i}$ and
$r + 2 \not\equiv 0 \pmod{p_i}$.

\textbf{Lean:} \texttt{crt\_twin\_admissible}.\quad
\textbf{Registry:} III.D107.

Proof / Justification

This item is definitional. No manuscript proof is required.

Source Context

  • Registry source: book-03.jsonl line 268
  • Manuscript source: 2nd-edition/book-iii-categorical-spectrum/02_mainmatter/part10/ch81-additive-conjectures-deep.tex lines 277-284

Lean / Formalization Notes

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

Dependencies

  • Canonical: III.T10

Generated by later projection phases.

Generated by later projection phases.

Revision Notes

  • 2026-04-24: Initial pilot migration.

Identifiers

  • Corpus ID cid001449
  • Primary alias DEF0219
  • Type Definition
  • Status canonical
  • Visibility public
  • Version v1

Aliases & legacy IDs

III.D107crt-twin-admissibilitydef:crt-twin-admissible

Release lines

corpus_v3_workingcorpus_v2

Relations

Formalized by (2)

Appears in (1)

Downstream uses (computed) (4)

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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