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 partition (5,3,3,2,1) decomposes by its Durfee square

Example

For

$λ = (5, 3, 3, 2, 1),$

the Durfee length is $3$ , so the upper-left $3 \times 3$ square is the Durfee square.

The cells to the right of that square form the partition

$α = (2),$

and the cells below it form the partition

$β = (2, 1) .$

Thus $λ$ is rebuilt from the $3 \times 3$ square together with one partition having at most $3$ parts and one partition with parts at most $3$ .

Depends on

Durfee-square decomposition of the partition series

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

5 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.