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.