Triple
T11219353
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Milnor K-theory |
E265518
|
entity |
| Predicate | usesConcept |
P531
|
FINISHED |
| Object |
Steinberg relations
Steinberg relations are algebraic identities in Milnor K-theory that impose the condition that symbols of pairs of field elements summing to one vanish, playing a central role in defining the structure of these K-groups.
|
E911353
|
NE FINISHED |
How this triple was built (4 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: Steinberg relations | Statement: [Milnor K-theory, usesConcept, Steinberg relations]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Steinberg relations Context triple: [Milnor K-theory, usesConcept, Steinberg relations]
-
A.
Dolan–Grady relations
The Dolan–Grady relations are algebraic commutation relations between two operators that generate the Onsager algebra and play a key role in the study of exactly solvable models in statistical mechanics.
-
B.
The Poincaré-Birkhoff-Witt theorem in ring theory
"The Poincaré-Birkhoff-Witt theorem in ring theory" is a mathematical work, attributed here to N. G. de Bruijn, that studies and applies the Poincaré–Birkhoff–Witt theorem in the context of associative and Lie-theoretic ring structures.
-
C.
Schur–Weyl duality
Schur–Weyl duality is a fundamental result in representation theory that links representations of the symmetric group and the general linear group via their commuting actions on tensor powers of a vector space.
-
D.
Rota–Baxter algebra
A Rota–Baxter algebra is an associative algebra equipped with a linear operator satisfying a specific integration-like identity that generalizes the properties of integral and summation operators in algebraic form.
-
E.
Zassenhaus conjecture
The Zassenhaus conjecture is a prominent open problem in group theory concerning the structure of units in integral group rings and their relation to the underlying finite group.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NEDg
Description generation
gpt-5.1
Instruction
Generate a one-sentence description of the target entity. You are given a context triple in the form (subject, predicate, object), where the object is the target entity. # Instructions Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. Avoid repeating the information from the triple, unless really essential. # Response Format Return only the sentence: "Description: [one-sentence description of the target entity]"
Input
Entity: Steinberg relations Triple: [Milnor K-theory, usesConcept, Steinberg relations]
Generated description
Steinberg relations are algebraic identities in Milnor K-theory that impose the condition that symbols of pairs of field elements summing to one vanish, playing a central role in defining the structure of these K-groups.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Steinberg relations Target entity description: Steinberg relations are algebraic identities in Milnor K-theory that impose the condition that symbols of pairs of field elements summing to one vanish, playing a central role in defining the structure of these K-groups.
-
A.
Dolan–Grady relations
The Dolan–Grady relations are algebraic commutation relations between two operators that generate the Onsager algebra and play a key role in the study of exactly solvable models in statistical mechanics.
-
B.
The Poincaré-Birkhoff-Witt theorem in ring theory
"The Poincaré-Birkhoff-Witt theorem in ring theory" is a mathematical work, attributed here to N. G. de Bruijn, that studies and applies the Poincaré–Birkhoff–Witt theorem in the context of associative and Lie-theoretic ring structures.
-
C.
Schur–Weyl duality
Schur–Weyl duality is a fundamental result in representation theory that links representations of the symmetric group and the general linear group via their commuting actions on tensor powers of a vector space.
-
D.
Rota–Baxter algebra
A Rota–Baxter algebra is an associative algebra equipped with a linear operator satisfying a specific integration-like identity that generalizes the properties of integral and summation operators in algebraic form.
-
E.
Zassenhaus conjecture
The Zassenhaus conjecture is a prominent open problem in group theory concerning the structure of units in integral group rings and their relation to the underlying finite group.
- F. None of above. chosen
Provenance (5 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_69d6aac59460819089b9848b27f57848 |
completed | April 8, 2026, 7:21 p.m. |
| NER | Named-entity recognition | batch_69d7e8eb84c48190b4f3bede254afde2 |
completed | April 9, 2026, 5:59 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69e4976f38788190855aed6338d819b7 |
completed | April 19, 2026, 8:50 a.m. |
| NEDg | Description generation | batch_69e49d37989881909c7e75ddfff06726 |
completed | April 19, 2026, 9:15 a.m. |
| NED2 | Entity disambiguation (via description) | batch_69e49f41a1f8819087cc15527dc7ff63 |
completed | April 19, 2026, 9:24 a.m. |
Created at: April 8, 2026, 9:30 p.m.