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.