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.

Positive-energy module

Definition

For this page, an ordinary module of positive energy for a conformal vertex algebra of CFT type is a nonzero ordinary module as in Ordinary module for which there is a lowest weight $h \in C$ with $M_{h} \neq 0$ and

M = ⨁_{n \geq 0} M_{h + n} .

The eigenspaces are finite dimensional by ordinariness. This convention implies a lower bound on real parts. It does not impose unitarity, positivity of an inner product, a classification of simple modules, or semisimplicity of their category.

Depends on

Ordinary module

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

2 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

Antony Wassermann, Kac–Moody and Virasoro Algebras, Chapter III §2 (standard reference, not scraped)
Tomoyuki Arakawa and Anne Moreau, Arc Spaces and Vertex Algebras, §3.3 (standard reference, not scraped)