Input Contract

For each cited external theorem/lemma/definition:

Procedure

Query search_arxiv_theorems using the full referenced statement as query.
Inspect returned results and compare theorem text directly to the referenced statement in reasoning.
Expand the definitions and terminology appearing in the cited statement using the cited paper's context before deciding whether the theorem applies.
Check whether the same words in the current proof mean the same thing as they do in the cited paper. In mathematics, identical words can carry different definitions in different contexts.
Accept as matched and applicable only when both are true:
- the result clearly corresponds to the cited statement,
- the contextual definitions and hypotheses align with the current problem.
If the theorem exists but the current proof uses different definitions, hypotheses, or ambient objects, record a critical error for incorrect application.

Validate every external-paper reference used in the proof.

For each cited external theorem/lemma/definition:

Query search_arxiv_theorems using the full referenced statement as query.
Inspect returned results and compare theorem text directly to the referenced statement in reasoning.
Expand the definitions and terminology appearing in the cited statement using the cited paper's context before deciding whether the theorem applies.
Check whether the same words in the current proof mean the same thing as they do in the cited paper. In mathematics, identical words can carry different definitions in different contexts.
Accept as matched and applicable only when both are true:
- the result clearly corresponds to the cited statement,
- the contextual definitions and hypotheses align with the current problem.
If the theorem exists but the current proof uses different definitions, hypotheses, or ambient objects, record a critical error for incorrect application.