DefinitionDefinition: Literature-sourcedProof: Not applicablePipeline-generated

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.

Topological spin

Definition

For a simple charge $a$ in a unitary ribbon fusion category, the twist component is an endomorphism $θ_{a} \in End (a)$ . Since $End (a) = C {id}_{a}$ , there is a unique scalar $ϑ_{a} \in C$ such that

$θ_{a} = ϑ_{a} {id}_{a} .$

The scalar $ϑ_{a}$ is the topological spin of $a$ . Unitarity of the twist gives $∣ ϑ_{a} ∣^{2} {id}_{a} = θ_{a}^{†} θ_{a} = {id}_{a}$ ; since ${id}_{a} \neq 0$ , $∣ ϑ_{a} ∣ = 1$ .

Depends on

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

12 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

P. Etingof, S. Gelaki, D. Nikshych, and V. Ostrik, Tensor Categories, author final text (standard reference, not scraped)
Chetan Nayak et al., Non-Abelian Anyons and Topological Quantum Computation (standard reference, not scraped)