Consider a statement without proof in a paper, with the following assumptions:

- it is unknown,
- it is unused in the paper,
- it is not written as a theorem (or proposition, or lemma…), but just a free sentence in a paragraph,
- the proof
*exists*somewhere but is unpublished (say just handwritten).

The author just wants to inform about something new that might interest the reader, but whose proof would not fit in the paper. The proof may appear in a future paper, or not.

The statement cannot be considered as known without a published proof, but it also cannot be considered as open.

**Question**: How does the mathematical community tolerate this kind of intermediate status for a statement?

Relaxing the third assumption, one famous example in my subject is the statement 4.5 in Subfactors and classification in von Neumann algebras by Sorin Popa, about subfactor indices gap (after more than 30 years, the proof is still unpublished).

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