ExampleConstruction: AI-generatedVerification: Not suppliedSession-authored (Fable 5 assisted)judge pass (gpt-5.6-terra)audited 2026-08-28

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 partitions of 7 into distinct parts and into odd parts match

Example

The partitions of $7$ into distinct parts are

$7, 6 + 1, 5 + 2, 4 + 3, 4 + 2 + 1.$

The partitions of $7$ into odd parts are

$7, 5 + 1 + 1, 3 + 3 + 1, 3 + 1 + 1 + 1 + 1, 1 + 1 + 1 + 1 + 1 + 1 + 1.$

Glaisher's map pairs them as

$7 \leftrightarrow 7, 5 + 1 + 1 \leftrightarrow 5 + 2, 3 + 3 + 1 \leftrightarrow 6 + 1,$

$3 + 1 + 1 + 1 + 1 \leftrightarrow 4 + 3, 1 + 1 + 1 + 1 + 1 + 1 + 1 \leftrightarrow 4 + 2 + 1.$

Depends on

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

6 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.