Triple

T2716820
Position Surface form Disambiguated ID Type / Status
Subject Itô’s lemma E59984 entity
Predicate appliesTo P1129 FINISHED
Object Itô processes E60316 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: Itô processes | Statement: [Itô’s lemma, appliesTo, Itô processes]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Itô processes
Context triple: [Itô’s lemma, appliesTo, Itô processes]
  • A. Itô processes chosen
    Itô processes are a class of stochastic processes, typically modeled as solutions to stochastic differential equations, that form the fundamental objects of study in Itô calculus and modern stochastic analysis.
  • B. Itô calculus
    Itô calculus is a branch of stochastic analysis that extends classical calculus to functions of stochastic processes, particularly Brownian motion, enabling rigorous treatment of stochastic differential equations.
  • C. Ornstein–Uhlenbeck process
    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.
  • D. Itô’s lemma
    Itô’s lemma is a fundamental result in stochastic calculus that generalizes the chain rule to functions of stochastic processes, especially Brownian motion.
  • E. 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.
  • 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_69ab4ac92a088190bc74bca14038e3de completed March 6, 2026, 9:44 p.m.
NER Named-entity recognition batch_69abda964d4881908179b2a1b16411e4 completed March 7, 2026, 7:58 a.m.
NED1 Entity disambiguation (via context triple) batch_69afb68c3ccc81909995d17651af27ed completed March 10, 2026, 6:13 a.m.
Created at: March 6, 2026, 9:55 p.m.