TheoremStatement: Literature-sourcedProof: AI-generatedprecheck passjudge pass (gpt-5.6-terra)audited 2026-09-01

How statement and proof provenance work

The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.

Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.

These labels describe origin, not correctness: citations and verification chips remain separate evidence.

The weak Whitney immersion theorem

Every smooth $n$ -manifold admits a smooth immersion into $R^{2 n}$ .

Given: A smooth $n$ -manifold $M$ .

[F1]

The classical Whitney immersion theorem says that every smooth $n$ -manifold admits a smooth immersion into $R^{2 n}$ .

technique · direct

1.1

By [F1], the smooth manifold $M$ admits a smooth immersion into $R^{2 n}$ .

F1given

2.1

This is exactly the claimed statement.

step 1.1∎

Used by

Nothing. This result depends on no other item in the library.