Triple
T11971701
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Ilya Piatetski-Shapiro |
E284934
|
entity |
| Predicate | notableWork |
P4
|
FINISHED |
| Object |
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.
|
E957159
|
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: Automorphic Forms and Representations | Statement: [Ilya Piatetski-Shapiro, notableWork, Automorphic Forms and Representations]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Automorphic Forms and Representations Context triple: [Ilya Piatetski-Shapiro, notableWork, Automorphic Forms and Representations]
-
A.
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.
-
B.
Euler products for automorphic L-functions
Euler products for automorphic L-functions are infinite product expansions attached to automorphic representations that encode deep arithmetic information and generalize the classical Euler product of the Riemann zeta function to a broad class of L-functions in the Langlands program.
-
C.
Hecke theory
Hecke theory is a branch of number theory centered on Hecke operators and modular forms, providing powerful tools to study arithmetic properties of modular forms and related objects.
-
D.
Galois representations
Galois representations are homomorphisms from Galois groups of field extensions into matrix groups that encode deep arithmetic information and link number theory with algebraic geometry and modular forms.
-
E.
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.
- 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: Automorphic Forms and Representations Triple: [Ilya Piatetski-Shapiro, notableWork, Automorphic Forms and Representations]
Generated description
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.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Automorphic Forms and Representations Target entity description: 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.
-
A.
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.
-
B.
Euler products for automorphic L-functions
Euler products for automorphic L-functions are infinite product expansions attached to automorphic representations that encode deep arithmetic information and generalize the classical Euler product of the Riemann zeta function to a broad class of L-functions in the Langlands program.
-
C.
Hecke theory
Hecke theory is a branch of number theory centered on Hecke operators and modular forms, providing powerful tools to study arithmetic properties of modular forms and related objects.
-
D.
Galois representations
Galois representations are homomorphisms from Galois groups of field extensions into matrix groups that encode deep arithmetic information and link number theory with algebraic geometry and modular forms.
-
E.
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.
- 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_69d6ab2eaeb881909f7914758f859413 |
completed | April 8, 2026, 7:23 p.m. |
| NER | Named-entity recognition | batch_69d9037d32e88190b1509285dc907d29 |
completed | April 10, 2026, 2:04 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69f4597cf818819089b0d897c236b87b |
completed | May 1, 2026, 7:42 a.m. |
| NEDg | Description generation | batch_69f45f89d5b08190a87312d96e61898a |
completed | May 1, 2026, 8:08 a.m. |
| NED2 | Entity disambiguation (via description) | batch_69f464a5191881908e291943996169cb |
completed | May 1, 2026, 8:30 a.m. |
Created at: April 8, 2026, 9:46 p.m.