Triple
T10617373
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Alexander Beilinson |
E276155
|
entity |
| Predicate | influenced |
P9
|
FINISHED |
| Object | geometric Langlands theory |
E753154
|
NE FINISHED |
How this triple was built (2 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: geometric Langlands theory | Statement: [Alexander Beilinson, influenced, geometric Langlands theory]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: geometric Langlands theory Context triple: [Alexander Beilinson, influenced, geometric Langlands theory]
-
A.
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.
-
B.
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.
-
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.
Kazhdan–Lusztig theory
Kazhdan–Lusztig theory is a framework in representation theory and algebraic geometry that studies Hecke algebras and their bases via Kazhdan–Lusztig polynomials, with deep connections to the representation theory of Lie algebras and geometry of Schubert varieties.
-
E.
Langlands dual group
The Langlands dual group is an algebraic group constructed from a given reductive group by interchanging its root and coroot data, playing a central role in the Langlands program’s connections between number theory and representation theory.
- F. None of above.
- G. Unsure - the case is ambiguous/there is not enough information to decide.
Provenance (3 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_69d6aaf948d88190806cc3a8c47a3fb2 |
completed | April 8, 2026, 7:22 p.m. |
| NER | Named-entity recognition | batch_69d6df6e2df4819099a19b59d90d0dd1 |
completed | April 8, 2026, 11:06 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69d96b7bb7108190b0f1cbe4117abec0 |
completed | April 10, 2026, 9:28 p.m. |
Created at: April 8, 2026, 7:33 p.m.