Triple
T37259247
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Schur’s lemma |
E924214
|
entity |
| Predicate | firstSchurLemmaStatement |
P205800
|
FINISHED |
| Object | if V and W are irreducible representations and T:V→W is a nonzero homomorphism then T is an isomorphism |
—
|
LITERAL FINISHED |
How this triple was built (2 steps)
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.
NER
Named-entity recognition
gpt-5-mini
Instruction
Given a phrase, classify it is english named entity (e.g., persons, organizations, works of art) in Latin script, or not (e.g., literals, dates, URLs, verbose phrases). For disambiguation, the statement where the phrase occurs as object is also given. Please return a JSON object with `phrase` (string, the phrase being analyzed) and `is_ne` (boolean, indicating whether the phrase is a Named Entity).
Input
Phrase: if V and W are irreducible representations and T:V→W is a nonzero homomorphism then T is an isomorphism | Statement: [Schur’s lemma, firstSchurLemmaStatement, if V and W are irreducible representations and T:V→W is a nonzero homomorphism then T is an isomorphism]
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 (4 batches)
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. |
| NER | Named-entity recognition | batch_6a037cad051c8190b28b354b89208574 |
completed | May 12, 2026, 7:17 p.m. |
| PD | Predicate disambiguation | batch_6a037a11efc08190bb7cacc1325b4dc6 |
completed | May 12, 2026, 7:05 p.m. |
| PDg | Predicate description generation | batch_6a037c842b2c819082f1d2db995ac2eb |
completed | May 12, 2026, 7:16 p.m. |
Created at: May 3, 2026, 4:15 p.m.