Triple

T12282711
Position Surface form Disambiguated ID Type / Status
Subject Malliavin calculus E292751 entity
Predicate hasOperator P179 FINISHED
Object Ornstein–Uhlenbeck operator E48273 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: Ornstein–Uhlenbeck operator | Statement: [Malliavin calculus, hasOperator, Ornstein–Uhlenbeck operator]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Ornstein–Uhlenbeck operator
Context triple: [Malliavin calculus, hasOperator, Ornstein–Uhlenbeck operator]
  • A. Ornstein–Uhlenbeck process chosen
    The Ornstein–Uhlenbeck process is a continuous-time stochastic process that models mean-reverting random motion, widely used in physics and quantitative finance to describe systems fluctuating around a long-term equilibrium.
  • B. Feynman–Kac formula
    The Feynman–Kac formula is a fundamental result connecting solutions of certain partial differential equations with expectations over stochastic processes, forming a bridge between quantum mechanics, probability theory, and mathematical finance.
  • C. Hilbert–Schmidt operators
    Hilbert–Schmidt operators are a class of compact operators on Hilbert spaces characterized by having finite Hilbert–Schmidt norm, playing a central role in functional analysis and operator theory.
  • D. Steklov operator
    The Steklov operator is a boundary integral operator arising in the study of elliptic partial differential equations and spectral problems, particularly in the context of Steklov eigenvalue problems.
  • E. Clark–Ocone formula
    The Clark–Ocone formula is a key result in stochastic calculus and Malliavin calculus that provides an explicit integral representation of square-integrable random variables with respect to Brownian motion.
  • 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_69d6ab690ad081908c0ed3870ec82d53 completed April 8, 2026, 7:24 p.m.
NER Named-entity recognition batch_69d91cf2b09c81908a11581d33f65be0 completed April 10, 2026, 3:53 p.m.
NED1 Entity disambiguation (via context triple) batch_69f61e70dec8819098199fbb54d888c1 completed May 2, 2026, 3:55 p.m.
Created at: April 8, 2026, 9:52 p.m.