Triple
T17671610
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Goro Shimura |
E440532
|
entity |
| Predicate | knownFor |
P22
|
FINISHED |
| Object |
Shimura lift
The Shimura lift is a fundamental construction in number theory that associates modular forms of half-integral weight to modular forms of integral weight, playing a key role in the theory of automorphic forms and L-functions.
|
E1281165
|
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: Shimura lift | Statement: [Goro Shimura, knownFor, Shimura lift]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Shimura lift Context triple: [Goro Shimura, knownFor, Shimura lift]
-
A.
Siegel modular form
A Siegel modular form is a type of complex analytic function defined on the Siegel upper half-space that generalizes classical modular forms to higher dimensions and plays a central role in number theory and algebraic geometry.
-
B.
Shimura varieties
Shimura varieties are higher-dimensional algebraic varieties that generalize modular curves and play a central role in the Langlands program by connecting number theory, automorphic forms, and arithmetic geometry.
-
C.
Eisenstein series
Eisenstein series are special types of complex analytic functions on the upper half-plane (or more general symmetric spaces) that play a central role in the theory of modular and automorphic forms, connecting number theory, representation theory, and harmonic analysis.
-
D.
Hecke eigenforms
Hecke eigenforms are special modular forms that are simultaneous eigenfunctions of all Hecke operators, playing a central role in modern number theory and the theory of automorphic forms.
-
E.
Hecke operators
Hecke operators are algebraic operators acting on modular forms that play a central role in number theory, particularly in understanding congruences, L-functions, and the arithmetic of modular forms.
- 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: Shimura lift Triple: [Goro Shimura, knownFor, Shimura lift]
Generated description
The Shimura lift is a fundamental construction in number theory that associates modular forms of half-integral weight to modular forms of integral weight, playing a key role in the theory of automorphic forms and L-functions.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Shimura lift Target entity description: The Shimura lift is a fundamental construction in number theory that associates modular forms of half-integral weight to modular forms of integral weight, playing a key role in the theory of automorphic forms and L-functions.
-
A.
Siegel modular form
A Siegel modular form is a type of complex analytic function defined on the Siegel upper half-space that generalizes classical modular forms to higher dimensions and plays a central role in number theory and algebraic geometry.
-
B.
Shimura varieties
Shimura varieties are higher-dimensional algebraic varieties that generalize modular curves and play a central role in the Langlands program by connecting number theory, automorphic forms, and arithmetic geometry.
-
C.
Eisenstein series
Eisenstein series are special types of complex analytic functions on the upper half-plane (or more general symmetric spaces) that play a central role in the theory of modular and automorphic forms, connecting number theory, representation theory, and harmonic analysis.
-
D.
Hecke eigenforms
Hecke eigenforms are special modular forms that are simultaneous eigenfunctions of all Hecke operators, playing a central role in modern number theory and the theory of automorphic forms.
-
E.
Hecke operators
Hecke operators are algebraic operators acting on modular forms that play a central role in number theory, particularly in understanding congruences, L-functions, and the arithmetic of modular forms.
- 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_69d8b9e87e18819087104a44dc4dc5b1 |
completed | April 10, 2026, 8:50 a.m. |
| NER | Named-entity recognition | batch_69e46f69b11c8190b09add33f81776b3 |
completed | April 19, 2026, 6 a.m. |
| NED1 | Entity disambiguation (via context triple) | batch_6a02166234f0819099c452808234e3e4 |
completed | May 11, 2026, 5:48 p.m. |
| NEDg | Description generation | batch_6a0217ca2ec881908573b0423c3610f7 |
completed | May 11, 2026, 5:54 p.m. |
| NED2 | Entity disambiguation (via description) | batch_6a0218636e048190a48bc7f066c7bee1 |
completed | May 11, 2026, 5:56 p.m. |
Created at: April 10, 2026, 9:59 a.m.