DEF0219canonicalv1CRT 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.jsonlline 268 - Manuscript source:
2nd-edition/book-iii-categorical-spectrum/02_mainmatter/part10/ch81-additive-conjectures-deep.texlines 277-284
Lean / Formalization Notes
- Formalization:
formalized - Module:
TauLib.BookIII.Spectral.TwinPrimeDeep - Name:
crt_twin_admissible
Dependencies
- Canonical: III.T10
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.D107crt-twin-admissibilitydef:crt-twin-admissibleRelease lines
corpus_v3_workingcorpus_v2Relations
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
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.