Triple
T37259247
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Schur’s lemma |
E924214
|
entity |
| Predicate | firstSchurLemmaStatement |
—
|
GENERATED |
| Object | if V and W are irreducible representations and T:V→W is a nonzero homomorphism then T is an isomorphism |
—
|
UNRECOGNIZED GENERATED |
How this triple was built (1 step)
Every LLM step that produced this triple, in pipeline order — named-entity classification, the disambiguation choices (the exact options shown, with the pick highlighted), and the generated description. The batch + timestamp of each is in the Provenance table below.
PD
Predicate disambiguation
gpt-5-mini-2025-08-07
Target predicate: firstSchurLemmaStatement Context triple: [Schur’s lemma, firstSchurLemmaStatement, if V and W are irreducible representations and T:V→W is a nonzero homomorphism then T is an isomorphism]
-
A.
secondSchurLemmaStatement
Indicates that, under the conditions of the second Schur lemma, any homomorphism between two irreducible representations is either zero or an isomorphism.
-
B.
isSymmetrizationOf
Indicates that one object or structure is the result of transforming another into a symmetric form, typically by averaging or otherwise enforcing symmetry with respect to some operation or group.
-
C.
hasUniqueIrreducibleUnitaryRepresentationUpToEquivalence
Indicates that there exists exactly one irreducible unitary representation of the entity (up to unitary equivalence), so any two such representations are equivalent.
-
D.
firstCongruence
Indicates that one entity is the initial or primary instance in a set of congruent (equivalent in form or measure) entities or relationships.
-
E.
satisfiesUnitarityRelationWith
Indicates that one entity and another are related in such a way that together they fulfill a required unitarity condition or constraint.
- F. None of above. chosen
Provenance (1 batch)
The batch behind each pipeline step, in order, with when it ran. Timestamps are batch-level — stages were processed in waves, so the object chain (NER → NED1 → NEDg → NED2) reads in order, but predicate / elicitation batches can sit in a different wave.
| Step | Stage | Batch ID | Status | When |
|---|---|---|---|---|
| creating | Elicitation | batch_69f76eabd6c481909d414a80a1345c98 |
completed | May 3, 2026, 3:50 p.m. |
Created at: May 3, 2026, 4:15 p.m.