Triple

T3365581
Position Surface form Disambiguated ID Type / Status
Subject Kiyoshi Itô E70827 entity
Predicate knownFor P22 FINISHED
Object Itô’s lemma E59984 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’s lemma | Statement: [Kiyoshi Itô, knownFor, Itô’s lemma]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Itô’s lemma
Context triple: [Kiyoshi Itô, knownFor, Itô’s lemma]
  • A. Itô’s lemma chosen
    Itô’s lemma is a fundamental result in stochastic calculus that generalizes the chain rule to functions of stochastic processes, especially Brownian motion.
  • 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. 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.
  • D. 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.
  • E. Itô processes
    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.
  • 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_69ad85a729d48190afd789cd8417f289 completed March 8, 2026, 2:20 p.m.
NER Named-entity recognition batch_69adb28643f48190b78b0222f8323344 completed March 8, 2026, 5:31 p.m.
NED1 Entity disambiguation (via context triple) batch_69b3254daf8c8190b2141682503c111e completed March 12, 2026, 8:42 p.m.
Created at: March 8, 2026, 3:13 p.m.