Triple
T14438335
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Iwasawa theory |
E358023
|
entity |
| Predicate | coreConcept |
P533
|
FINISHED |
| Object |
Selmer group
A Selmer group is an arithmetic invariant in number theory that encodes obstructions to local-global principles for Galois representations or abelian varieties, playing a central role in studying Diophantine equations and Iwasawa theory.
|
E1099328
|
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: Selmer group | Statement: [Iwasawa theory, coreConcept, Selmer group]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Selmer group Context triple: [Iwasawa theory, coreConcept, Selmer group]
-
A.
Weil group
The Weil group is an extension of the absolute Galois group introduced by André Weil to refine class field theory and play a central role in the formulation of the local and global Langlands correspondences.
-
B.
Whitehead groups
Whitehead groups are algebraic K-theory invariants associated with groups that measure the failure of certain projective modules or h-cobordisms to be trivial, playing a central role in high-dimensional topology and geometric group theory.
-
C.
Segal conjecture
The Segal conjecture is a fundamental result in algebraic topology that relates the Burnside ring of a finite group to the stable cohomotopy of its classifying space, profoundly influencing equivariant stable homotopy theory.
-
D.
Abelian groups
Abelian groups are algebraic structures in which the group operation is commutative, meaning the order of combining elements does not affect the result.
-
E.
Grothendieck group
The Grothendieck group is an algebraic construction that formally turns a commutative monoid (often arising from isomorphism classes of objects like vector bundles or modules) into an abelian group, playing a central role in K-theory and modern algebraic geometry.
- 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: Selmer group Triple: [Iwasawa theory, coreConcept, Selmer group]
Generated description
A Selmer group is an arithmetic invariant in number theory that encodes obstructions to local-global principles for Galois representations or abelian varieties, playing a central role in studying Diophantine equations and Iwasawa theory.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Selmer group Target entity description: A Selmer group is an arithmetic invariant in number theory that encodes obstructions to local-global principles for Galois representations or abelian varieties, playing a central role in studying Diophantine equations and Iwasawa theory.
-
A.
Weil group
The Weil group is an extension of the absolute Galois group introduced by André Weil to refine class field theory and play a central role in the formulation of the local and global Langlands correspondences.
-
B.
Whitehead groups
Whitehead groups are algebraic K-theory invariants associated with groups that measure the failure of certain projective modules or h-cobordisms to be trivial, playing a central role in high-dimensional topology and geometric group theory.
-
C.
Segal conjecture
The Segal conjecture is a fundamental result in algebraic topology that relates the Burnside ring of a finite group to the stable cohomotopy of its classifying space, profoundly influencing equivariant stable homotopy theory.
-
D.
Abelian groups
Abelian groups are algebraic structures in which the group operation is commutative, meaning the order of combining elements does not affect the result.
-
E.
Grothendieck group
The Grothendieck group is an algebraic construction that formally turns a commutative monoid (often arising from isomorphism classes of objects like vector bundles or modules) into an abelian group, playing a central role in K-theory and modern algebraic geometry.
- 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_69d8279402a88190821ffa39ae15bccf |
completed | April 9, 2026, 10:26 p.m. |
| NER | Named-entity recognition | batch_69de914a45ec81909ab8ccf302047d7f |
completed | April 14, 2026, 7:11 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69fd5bd7f46881908df1a1cea7b6af9b |
completed | May 8, 2026, 3:43 a.m. |
| NEDg | Description generation | batch_69fd5d585cc08190908bc5f9b8abdb82 |
completed | May 8, 2026, 3:49 a.m. |
| NED2 | Entity disambiguation (via description) | batch_69fd5e0bbd6c8190b14039b3335692c7 |
completed | May 8, 2026, 3:52 a.m. |
Created at: April 10, 2026, 1:18 a.m.