Triple

T11961932
Position Surface form Disambiguated ID Type / Status
Subject Clark–Ocone formula E284688 entity
Predicate relatedTo P37 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: [Clark–Ocone formula, relatedTo, Itô’s lemma]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Itô’s lemma
Context triple: [Clark–Ocone formula, relatedTo, 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. Itô integral
    The Itô integral is a fundamental stochastic integral used in probability theory and mathematical finance to rigorously define integration with respect to Brownian motion and more general semimartingales.
  • D. Itô isometry
    Itô isometry is a fundamental result in stochastic calculus that relates the L² norm of a stochastic integral with respect to Brownian motion to the L² norm of its integrand, enabling rigorous analysis of stochastic processes.
  • E. Itô–Taylor expansion
    The Itô–Taylor expansion is a stochastic generalization of the Taylor series that expresses solutions of stochastic differential equations as series involving iterated Itô integrals, forming the basis for higher-order numerical schemes.
  • 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_69d6ab2eaeb881909f7914758f859413 completed April 8, 2026, 7:23 p.m.
NER Named-entity recognition batch_69d9037848f481908276716675464464 completed April 10, 2026, 2:04 p.m.
NED1 Entity disambiguation (via context triple) batch_69f4592fa9a48190a0450e3d0c57c4d3 completed May 1, 2026, 7:41 a.m.
Created at: April 8, 2026, 9:45 p.m.