PRP0110canonicalv1CRT-Goldbach Duality
CRT-Goldbach local solvability: for any even n≥4 and prime p≥3, ∃r with both r and n-r nonzero mod p. CRT guarantees independent local solutions.
Payload
CRT-Goldbach Duality
CRT-Goldbach local solvability: for any even n≥4 and prime p≥3, ∃r with both r and n-r nonzero mod p. CRT guarantees independent local solutions.
CRT-Goldbach Duality
Summary
CRT-Goldbach local solvability: for any even n≥4 and prime p≥3, ∃r with both r and n-r nonzero mod p. CRT guarantees independent local solutions.
Statement
\label{prop:crt-goldbach}
For any even $n \ge 4$ and any prime $p \ge 3$, there exists $r \in [1, p-1]$
with both $r$ and $n - r$ nonzero modulo $p$. This is the \emph{local
solvability} condition: at each prime, Goldbach has a solution. CRT
guarantees that local solutions exist independently.
\textbf{Lean:} \texttt{crt\_goldbach\_duality\_3}.\quad
\textbf{Registry:} III.P43.
Proof / Justification
No immediate manuscript proof block was extracted in this pilot run.
Source Context
- Registry source:
book-03.jsonlline 264 - Manuscript source:
2nd-edition/book-iii-categorical-spectrum/02_mainmatter/part10/ch81-additive-conjectures-deep.texlines 203-211
Lean / Formalization Notes
- Formalization:
formalized - Module:
TauLib.BookIII.Spectral.GoldbachDeep - Name:
crt_goldbach_duality_3
Dependencies
- Canonical: III.T10, III.D95
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.P43crt-goldbach-dualityprop:crt-goldbachRelease 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.