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.