Triple

T10973517
Position Surface form Disambiguated ID Type / Status
Subject John Tate E259307 entity
Predicate notableWork P4 FINISHED
Object Lubin–Tate formal groups
Lubin–Tate formal groups are a class of one-dimensional formal group laws over local fields that play a central role in local class field theory by providing explicit descriptions of abelian extensions.
E896826 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: Lubin–Tate formal groups | Statement: [John Tate, notableWork, Lubin–Tate formal groups]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Lubin–Tate formal groups
Context triple: [John Tate, notableWork, Lubin–Tate formal groups]
  • A. Drinfeld modules
    Drinfeld modules are algebraic structures that generalize elliptic curves to the setting of function fields, playing a central role in modern arithmetic geometry and the theory of automorphic forms.
  • B. Hasse–Arf theorem
    The Hasse–Arf theorem is a fundamental result in algebraic number theory that precisely characterizes the jumps in the ramification filtration of abelian extensions of local fields, showing they occur at integer values.
  • C. Shafarevich group of a torus
    The Shafarevich group of a torus is an arithmetic invariant measuring the failure of local-global principles for principal homogeneous spaces under an algebraic torus over a global field.
  • D. Furtwängler’s theorem in class field theory
    Furtwängler’s theorem in class field theory is a fundamental result in algebraic number theory that refines the principal ideal theorem by describing how ideal classes capitulate (become principal) in certain abelian extensions of number fields.
  • E. Iwasawa theory
    Iwasawa theory is a branch of number theory that studies the growth of arithmetic invariants in infinite towers of number fields, particularly using p-adic methods.
  • 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: Lubin–Tate formal groups
Triple: [John Tate, notableWork, Lubin–Tate formal groups]
Generated description
Lubin–Tate formal groups are a class of one-dimensional formal group laws over local fields that play a central role in local class field theory by providing explicit descriptions of abelian extensions.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Lubin–Tate formal groups
Target entity description: Lubin–Tate formal groups are a class of one-dimensional formal group laws over local fields that play a central role in local class field theory by providing explicit descriptions of abelian extensions.
  • A. Drinfeld modules
    Drinfeld modules are algebraic structures that generalize elliptic curves to the setting of function fields, playing a central role in modern arithmetic geometry and the theory of automorphic forms.
  • B. Hasse–Arf theorem
    The Hasse–Arf theorem is a fundamental result in algebraic number theory that precisely characterizes the jumps in the ramification filtration of abelian extensions of local fields, showing they occur at integer values.
  • C. Shafarevich group of a torus
    The Shafarevich group of a torus is an arithmetic invariant measuring the failure of local-global principles for principal homogeneous spaces under an algebraic torus over a global field.
  • D. Furtwängler’s theorem in class field theory
    Furtwängler’s theorem in class field theory is a fundamental result in algebraic number theory that refines the principal ideal theorem by describing how ideal classes capitulate (become principal) in certain abelian extensions of number fields.
  • E. Iwasawa theory
    Iwasawa theory is a branch of number theory that studies the growth of arithmetic invariants in infinite towers of number fields, particularly using p-adic methods.
  • 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_69d6aa895f4c8190887a15460ef622f4 completed April 8, 2026, 7:20 p.m.
NER Named-entity recognition batch_69d7719c16648190ab5a87abb1c61990 completed April 9, 2026, 9:30 a.m.
NED1 Entity disambiguation (via context triple) batch_69e2d7a0b3dc819084fbda3227caf5b5 completed April 18, 2026, 1 a.m.
NEDg Description generation batch_69e2ff211ae88190a40380cd25a61812 completed April 18, 2026, 3:48 a.m.
NED2 Entity disambiguation (via description) batch_69e32634397481908284c04448274b25 completed April 18, 2026, 6:35 a.m.
Created at: April 8, 2026, 9:24 p.m.