Triple
T6716262
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Salomon Bochner |
E153275
|
entity |
| Predicate | notableFor |
P22
|
FINISHED |
| Object |
Bochner integral
The Bochner integral is a generalization of the Lebesgue integral to functions taking values in Banach spaces, widely used in functional analysis and probability theory.
|
E613404
|
NE FINISHED |
How this triple was built (4 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: Bochner integral | Statement: [Salomon Bochner, notableFor, Bochner integral]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Bochner integral Context triple: [Salomon Bochner, notableFor, Bochner integral]
-
A.
Henstock–Kurzweil integral
The Henstock–Kurzweil integral is a highly general integration theory that extends and refines the Riemann integral, capable of integrating a broader class of functions while retaining many of the intuitive properties of Riemann integration.
-
B.
Lebesgue integration
Lebesgue integration is a foundational measure-theoretic framework for defining and analyzing integrals, particularly suited to handling limits, convergence, and more general functions than those allowed by Riemann integration.
-
C.
Riemann–Stieltjes integral
The Riemann–Stieltjes integral is a generalization of the Riemann integral in which integration is taken with respect to a function of bounded variation rather than just the identity function, allowing more flexible treatment of sums and distributions.
-
D.
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.
-
E.
Riemann–Liouville integral
The Riemann–Liouville integral is a fundamental operator in fractional calculus that generalizes the concept of an n-fold repeated integral to non-integer (fractional) orders.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NEDg
Description generation
gpt-5.1
Instruction
Generate a one-sentence description of the target entity. You are given a context triple in the form (subject, predicate, object), where the object is the target entity. # Instructions Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. Avoid repeating the information from the triple, unless really essential. # Response Format Return only the sentence: "Description: [one-sentence description of the target entity]"
Input
Entity: Bochner integral Triple: [Salomon Bochner, notableFor, Bochner integral]
Generated description
The Bochner integral is a generalization of the Lebesgue integral to functions taking values in Banach spaces, widely used in functional analysis and probability theory.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Bochner integral Target entity description: The Bochner integral is a generalization of the Lebesgue integral to functions taking values in Banach spaces, widely used in functional analysis and probability theory.
-
A.
Henstock–Kurzweil integral
The Henstock–Kurzweil integral is a highly general integration theory that extends and refines the Riemann integral, capable of integrating a broader class of functions while retaining many of the intuitive properties of Riemann integration.
-
B.
Lebesgue integration
Lebesgue integration is a foundational measure-theoretic framework for defining and analyzing integrals, particularly suited to handling limits, convergence, and more general functions than those allowed by Riemann integration.
-
C.
Riemann–Stieltjes integral
The Riemann–Stieltjes integral is a generalization of the Riemann integral in which integration is taken with respect to a function of bounded variation rather than just the identity function, allowing more flexible treatment of sums and distributions.
-
D.
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.
-
E.
Riemann–Liouville integral
The Riemann–Liouville integral is a fundamental operator in fractional calculus that generalizes the concept of an n-fold repeated integral to non-integer (fractional) orders.
- F. None of above. chosen
Provenance (5 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_69c68809b4608190a2509ddb5ab87f05 |
completed | March 27, 2026, 1:37 p.m. |
| NER | Named-entity recognition | batch_69c6d125db3c8190aad28919226a16da |
completed | March 27, 2026, 6:49 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69c700993128819081614ccfa68d7320 |
completed | March 27, 2026, 10:11 p.m. |
| NEDg | Description generation | batch_69c70262f3e48190b544be536ee0b674 |
completed | March 27, 2026, 10:19 p.m. |
| NED2 | Entity disambiguation (via description) | batch_69c70311418c8190a902cf21187fdc51 |
completed | March 27, 2026, 10:22 p.m. |
Created at: March 27, 2026, 2:07 p.m.