Triple
T11440064
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Martin Hairer |
E271120
|
entity |
| Predicate | notableWork |
P4
|
FINISHED |
| Object |
theory of regularity structures
The theory of regularity structures is a mathematical framework developed by Martin Hairer to rigorously analyze and solve a broad class of singular stochastic partial differential equations.
|
E926684
|
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 regularity structures | Statement: [Martin Hairer, notableWork, theory of regularity structures]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: theory of regularity structures Context triple: [Martin Hairer, notableWork, theory of regularity structures]
-
A.
Three regularity results in harmonic analysis
"Three regularity results in harmonic analysis" is the doctoral thesis of mathematician Terence Tao, focusing on advanced problems in harmonic analysis and the study of regularity properties of functions and operators.
-
B.
Malliavin calculus
Malliavin calculus is a branch of stochastic analysis that extends differential calculus to functionals of stochastic processes, particularly Brownian motion, enabling probabilistic proofs of regularity and smoothness for solutions to stochastic differential equations.
-
C.
Bourgain spaces
Bourgain spaces are function spaces introduced by Jean Bourgain that are tailored to study the well-posedness and regularity of nonlinear dispersive partial differential equations.
-
D.
Freidlin–Wentzell theory
Freidlin–Wentzell theory is a mathematical framework in probability that analyzes the behavior of stochastic dynamical systems under small random perturbations using large deviation principles.
-
E.
Kolmogorov continuity theorem
The Kolmogorov continuity theorem is a fundamental result in probability theory that provides conditions under which a stochastic process admits a modification with continuous (or Hölder-continuous) sample paths.
- 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 regularity structures Triple: [Martin Hairer, notableWork, theory of regularity structures]
Generated description
The theory of regularity structures is a mathematical framework developed by Martin Hairer to rigorously analyze and solve a broad class of singular stochastic partial differential equations.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: theory of regularity structures Target entity description: The theory of regularity structures is a mathematical framework developed by Martin Hairer to rigorously analyze and solve a broad class of singular stochastic partial differential equations.
-
A.
Three regularity results in harmonic analysis
"Three regularity results in harmonic analysis" is the doctoral thesis of mathematician Terence Tao, focusing on advanced problems in harmonic analysis and the study of regularity properties of functions and operators.
-
B.
Malliavin calculus
Malliavin calculus is a branch of stochastic analysis that extends differential calculus to functionals of stochastic processes, particularly Brownian motion, enabling probabilistic proofs of regularity and smoothness for solutions to stochastic differential equations.
-
C.
Bourgain spaces
Bourgain spaces are function spaces introduced by Jean Bourgain that are tailored to study the well-posedness and regularity of nonlinear dispersive partial differential equations.
-
D.
Freidlin–Wentzell theory
Freidlin–Wentzell theory is a mathematical framework in probability that analyzes the behavior of stochastic dynamical systems under small random perturbations using large deviation principles.
-
E.
Kolmogorov continuity theorem
The Kolmogorov continuity theorem is a fundamental result in probability theory that provides conditions under which a stochastic process admits a modification with continuous (or Hölder-continuous) sample paths.
- 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_69d6aadeef688190874bcecd88b3dd9b |
completed | April 8, 2026, 7:22 p.m. |
| NER | Named-entity recognition | batch_69d80888190c8190b6365550ffe4931c |
completed | April 9, 2026, 8:14 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69e5d39554c48190969cc0ebd4dbc368 |
completed | April 20, 2026, 7:19 a.m. |
| NEDg | Description generation | batch_69e5d91b047c81909ea4c7f114bfbba5 |
completed | April 20, 2026, 7:43 a.m. |
| NED2 | Entity disambiguation (via description) | batch_69e5e2de4cd081908d30c44853565029 |
completed | April 20, 2026, 8:25 a.m. |
Created at: April 8, 2026, 9:35 p.m.