DefinitionDefinition: Literature-sourcedProof: Not applicablePipeline-generatedjudge pass (gpt-6-luna)

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.

Jones–Wenzl recursion in the nonvanishing-denominator range

Definition

Let $δ \in C$ and use the quantum integers of Temperley–Lieb quantum integers and quantum characteristic. Define $p_{0} = 1 \in {T L}_{0}$ and $p_{1} = 1 \in {T L}_{1}$ . If $[2]_{δ}, \dots, [n]_{δ}$ are nonzero, define recursively, for $1 \leq r < n$ ,

$P_{r} = p_{r} \otimes 1 \in {T L}_{r + 1}, p_{r + 1} = P_{r} - \frac{[r]_{δ}}{[r + 1]_{δ}} P_{r} d_{r} P_{r} .$

The element $p_{n}$ defined by this recursion is the Jones–Wenzl element in the nonvanishing-denominator range. This definition makes no assertion that failure of the displayed recursion implies nonexistence of any idempotent.

Depends on

Used by

Dependency tree · two levels

7 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.

Sources

Joshua Chen, The Temperley-Lieb Categories and Skein Modules (standard reference, not scraped)