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.

Donaldson's ADHM matrix equations in the source convention

Definition

Let $V = C^{k}$ and $W = C^{N}$ with their standard Hermitian inner products. Write $α_{1}, α_{2} \in {End}_{C} (V)$ , $P : W \to V$ , and $Q : V \to W$ . The Donaldson source convention for these four matrices is

$[α_{1}, α_{2}] + P Q = 0, [α_{1}, α_{1}^{†}] + [α_{2}, α_{2}^{†}] - P P^{†} + Q^{†} Q = 0.$

The second equality is an equality of Hermitian endomorphisms of $V$ . It is an algebraic convention from the displayed source equations; it does not by itself assert the full-rank condition on the source's ADHM linear map or an identification with the run's raw moment maps.

Definition references

Donaldson, §6, printed pp. 10–11

Dependency tree · 0 levels

Nothing. This result depends on no other item in the library.

Sources

Simon K. Donaldson, The ADHM construction of Yang-Mills instantons