Finite weighted ensemble and covariance

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.