Triple
T11576271
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Joseph Bernstein |
E274511
|
entity |
| Predicate | influenced |
P9
|
FINISHED |
| Object |
theory of D-modules
The theory of D-modules is a branch of algebraic analysis and algebraic geometry that studies modules over rings of differential operators, providing a powerful framework for understanding systems of linear differential equations and their geometric and representation-theoretic properties.
|
E934439
|
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: theory of D-modules | Statement: [Joseph Bernstein, influenced, theory of D-modules]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: theory of D-modules Context triple: [Joseph Bernstein, influenced, theory of D-modules]
-
A.
Beilinson–Bernstein localization theorem
The Beilinson–Bernstein localization theorem is a fundamental result in geometric representation theory that realizes representations of semisimple Lie algebras as sheaves of differential operators on flag varieties, establishing an equivalence between algebraic and geometric categories.
-
B.
Picard–Vessiot theory
Picard–Vessiot theory is a branch of differential Galois theory that studies linear differential equations via the symmetries of their solution fields, analogous to classical Galois theory for polynomial equations.
-
C.
Weyl algebra
The Weyl algebra is a fundamental noncommutative algebra generated by position and momentum operators satisfying canonical commutation relations, central in quantum mechanics and representation theory.
-
D.
Hodge theory
Hodge theory is a branch of mathematics that studies the relationship between differential forms, cohomology, and complex geometry, particularly on complex manifolds.
-
E.
Hilbert scheme theory
Hilbert scheme theory is a branch of algebraic geometry that studies parameter spaces representing families of subschemes of projective space, capturing how such geometric objects vary in moduli.
- 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: theory of D-modules Triple: [Joseph Bernstein, influenced, theory of D-modules]
Generated description
The theory of D-modules is a branch of algebraic analysis and algebraic geometry that studies modules over rings of differential operators, providing a powerful framework for understanding systems of linear differential equations and their geometric and representation-theoretic properties.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: theory of D-modules Target entity description: The theory of D-modules is a branch of algebraic analysis and algebraic geometry that studies modules over rings of differential operators, providing a powerful framework for understanding systems of linear differential equations and their geometric and representation-theoretic properties.
-
A.
Beilinson–Bernstein localization theorem
The Beilinson–Bernstein localization theorem is a fundamental result in geometric representation theory that realizes representations of semisimple Lie algebras as sheaves of differential operators on flag varieties, establishing an equivalence between algebraic and geometric categories.
-
B.
Picard–Vessiot theory
Picard–Vessiot theory is a branch of differential Galois theory that studies linear differential equations via the symmetries of their solution fields, analogous to classical Galois theory for polynomial equations.
-
C.
Weyl algebra
The Weyl algebra is a fundamental noncommutative algebra generated by position and momentum operators satisfying canonical commutation relations, central in quantum mechanics and representation theory.
-
D.
Hodge theory
Hodge theory is a branch of mathematics that studies the relationship between differential forms, cohomology, and complex geometry, particularly on complex manifolds.
-
E.
Hilbert scheme theory
Hilbert scheme theory is a branch of algebraic geometry that studies parameter spaces representing families of subschemes of projective space, capturing how such geometric objects vary in moduli.
- 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_69d6aae5ac3c81908d2b0a3a665665b2 |
completed | April 8, 2026, 7:22 p.m. |
| NER | Named-entity recognition | batch_69d89049721081909278adfada668ef9 |
completed | April 10, 2026, 5:53 a.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69e713f7ca4c81908f29143df420fd71 |
completed | April 21, 2026, 6:06 a.m. |
| NEDg | Description generation | batch_69e720f9a8588190aa766d2e1628207a |
completed | April 21, 2026, 7:02 a.m. |
| NED2 | Entity disambiguation (via description) | batch_69e72315dda08190996aa84587c5fc80 |
completed | April 21, 2026, 7:11 a.m. |
Created at: April 8, 2026, 9:38 p.m.