Triple

T14168723
Position Surface form Disambiguated ID Type / Status
Subject Itô isometry E351146 entity
Predicate foundationFor P1450 FINISHED
Object stochastic Fubini theorems E284675 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: stochastic Fubini theorems | Statement: [Itô isometry, foundationFor, stochastic Fubini theorems]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: stochastic Fubini theorems
Context triple: [Itô isometry, foundationFor, stochastic Fubini theorems]
  • A. Fubini's theorem chosen
    Fubini's theorem is a fundamental result in measure theory that allows the evaluation of double integrals as iterated integrals under suitable integrability conditions.
  • 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. Skorokhod integral
    The Skorokhod integral is a stochastic integral extending the Itô integral to non-adapted processes, playing a central role in Malliavin calculus and anticipating stochastic analysis.
  • D. Itô–Stratonovich conversion formula
    The Itô–Stratonovich conversion formula is a key result in stochastic calculus that provides the explicit relationship for transforming stochastic integrals between the Itô and Stratonovich interpretations.
  • E. 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.
  • 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_69d8278775fc8190b0802d22ca2f495d completed April 9, 2026, 10:26 p.m.
NER Named-entity recognition batch_69de61b472288190b4a271daa54aa6cd completed April 14, 2026, 3:48 p.m.
NED1 Entity disambiguation (via context triple) batch_69fcf7f779248190921c85f99f587296 completed May 7, 2026, 8:37 p.m.
Created at: April 10, 2026, 1 a.m.