Triple
T12735396
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Euler products for automorphic L-functions |
E304347
|
entity |
| Predicate | builtFrom |
P11047
|
FINISHED |
| Object |
local Langlands correspondence
The local Langlands correspondence is a deep conjectural (and in many cases proven) framework in number theory that relates representations of local Galois or Weil–Deligne groups to admissible representations of reductive groups over local fields, forming the local building blocks of global automorphic theory.
|
E753154
|
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: local Langlands correspondence | Statement: [Euler products for automorphic L-functions, builtFrom, local Langlands correspondence]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: local Langlands correspondence Context triple: [Euler products for automorphic L-functions, builtFrom, local Langlands correspondence]
-
A.
Langlands classification
The Langlands classification is a fundamental framework in representation theory that systematically describes all irreducible admissible representations of a real or p-adic reductive group in terms of data from its parabolic subgroups and their characters.
-
B.
Langlands program
The Langlands program is a far-reaching web of conjectures and theories in number theory and representation theory that seeks deep connections between Galois groups and automorphic forms, unifying many areas of modern mathematics.
-
C.
Deligne–Lusztig theory
Deligne–Lusztig theory is a framework in algebraic geometry and representation theory that constructs and studies representations of finite groups of Lie type using varieties defined over finite fields.
-
D.
Automorphic Forms and Representations
Automorphic Forms and Representations is a foundational mathematical monograph that develops the theory of automorphic forms and their connections to representation theory and number theory.
-
E.
Representation Theory and Automorphic Functions
"Representation Theory and Automorphic Functions" is a seminal mathematical work by Israel Gelfand that develops the connections between representation theory of groups and the theory of automorphic forms, with deep applications in number theory and harmonic analysis.
- 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: local Langlands correspondence Triple: [Euler products for automorphic L-functions, builtFrom, local Langlands correspondence]
Generated description
The local Langlands correspondence is a deep conjectural (and in many cases proven) framework in number theory that relates representations of local Galois or Weil–Deligne groups to admissible representations of reductive groups over local fields, forming the local building blocks of global automorphic theory.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: local Langlands correspondence Target entity description: The local Langlands correspondence is a deep conjectural (and in many cases proven) framework in number theory that relates representations of local Galois or Weil–Deligne groups to admissible representations of reductive groups over local fields, forming the local building blocks of global automorphic theory.
-
A.
Langlands classification
The Langlands classification is a fundamental framework in representation theory that systematically describes all irreducible admissible representations of a real or p-adic reductive group in terms of data from its parabolic subgroups and their characters.
-
B.
Langlands program
chosen
The Langlands program is a far-reaching web of conjectures and theories in number theory and representation theory that seeks deep connections between Galois groups and automorphic forms, unifying many areas of modern mathematics.
-
C.
Deligne–Lusztig theory
Deligne–Lusztig theory is a framework in algebraic geometry and representation theory that constructs and studies representations of finite groups of Lie type using varieties defined over finite fields.
-
D.
Automorphic Forms and Representations
Automorphic Forms and Representations is a foundational mathematical monograph that develops the theory of automorphic forms and their connections to representation theory and number theory.
-
E.
Representation Theory and Automorphic Functions
"Representation Theory and Automorphic Functions" is a seminal mathematical work by Israel Gelfand that develops the connections between representation theory of groups and the theory of automorphic forms, with deep applications in number theory and harmonic analysis.
- F. None of above.
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_69d7bdf1426c8190a4402e1c4cdec33a |
completed | April 9, 2026, 2:55 p.m. |
| NER | Named-entity recognition | batch_69d9646b3ca08190b239f0736a01169d |
completed | April 10, 2026, 8:58 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69f67c8e2dbc81909c1c85ca699a2679 |
completed | May 2, 2026, 10:37 p.m. |
| NEDg | Description generation | batch_69f67d888d7c8190b9aaeb877984a403 |
completed | May 2, 2026, 10:41 p.m. |
| NED2 | Entity disambiguation (via description) | batch_69f67e12b8148190958b63ba114d6221 |
completed | May 2, 2026, 10:43 p.m. |
Created at: April 9, 2026, 5:26 p.m.