Corpus v3 · Definition
cid001446
DEF0216canonicalv1Goldbach Obstruction
Obstruction at prime p for even n: |O_p(n)|=1 if p|n, 0 otherwise. Each prime blocks at most one Goldbach pair.
Payload
Goldbach Obstruction
| Obstruction at prime p for even n: | O_p(n) | =1 if p | n, 0 otherwise. Each prime blocks at most one Goldbach pair. |
Goldbach Obstruction
Summary
| Obstruction at prime p for even n: | O_p(n) | =1 if p | n, 0 otherwise. Each prime blocks at most one Goldbach pair. |
Statement
\label{def:goldbach-obstruction}
At prime $p$, the obstruction count for even~$n$ is
$|O_p(n)| = \begin{cases} 1 & \text{if } p \mid n, \\ 0 & \text{otherwise.}\end{cases}$
\textbf{Lean:} \texttt{goldbach\_obstruction\_count}.\quad
\textbf{Registry:} III.D104.
Proof / Justification
This item is definitional. No manuscript proof is required.
Source Context
- Registry source:
book-03.jsonlline 259 - Manuscript source:
2nd-edition/book-iii-categorical-spectrum/02_mainmatter/part10/ch81-additive-conjectures-deep.texlines 187-193
Lean / Formalization Notes
- Formalization:
formalized - Module:
TauLib.BookIII.Spectral.GoldbachDeep - Name:
goldbach_obstruction_count
Dependencies
- Canonical: 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.D104goldbach-obstructiondef:goldbach-obstructionRelease 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.