Triple
T13070790
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Paul Lévy |
E329449
|
entity |
| Predicate | knownFor |
P22
|
FINISHED |
| Object |
Lévy–Khintchine formula
The Lévy–Khintchine formula is a fundamental result in probability theory that characterizes the characteristic functions of infinitely divisible distributions via a canonical decomposition involving a drift term, a Gaussian component, and a Lévy measure.
|
E613407
|
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: Lévy–Khintchine formula | Statement: [Paul Lévy, knownFor, Lévy–Khintchine formula]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Lévy–Khintchine formula Context triple: [Paul Lévy, knownFor, Lévy–Khintchine formula]
-
A.
Khinchin–Pollaczek formula
The Khinchin–Pollaczek formula is a result in probability theory and queueing theory that provides an explicit expression for the stationary waiting-time distribution in certain single-server queues.
-
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.
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.
-
D.
Bochner theorem on characteristic functions
The Bochner theorem on characteristic functions is a fundamental result in probability theory and harmonic analysis that characterizes which functions are Fourier transforms of probability measures by requiring them to be positive-definite, continuous, and normalized at zero.
-
E.
Dynkin formula
Dynkin formula is a fundamental result in the theory of Markov processes that expresses the expected value of a function of the process at a stopping time in terms of its generator and an integral over time.
- 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: Lévy–Khintchine formula Triple: [Paul Lévy, knownFor, Lévy–Khintchine formula]
Generated description
The Lévy–Khintchine formula is a fundamental result in probability theory that characterizes the characteristic functions of infinitely divisible distributions via a canonical decomposition involving a drift term, a Gaussian component, and a Lévy measure.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Lévy–Khintchine formula Target entity description: The Lévy–Khintchine formula is a fundamental result in probability theory that characterizes the characteristic functions of infinitely divisible distributions via a canonical decomposition involving a drift term, a Gaussian component, and a Lévy measure.
-
A.
Khinchin–Pollaczek formula
The Khinchin–Pollaczek formula is a result in probability theory and queueing theory that provides an explicit expression for the stationary waiting-time distribution in certain single-server queues.
-
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.
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.
-
D.
Bochner theorem on characteristic functions
chosen
The Bochner theorem on characteristic functions is a fundamental result in probability theory and harmonic analysis that characterizes which functions are Fourier transforms of probability measures by requiring them to be positive-definite, continuous, and normalized at zero.
-
E.
Dynkin formula
Dynkin formula is a fundamental result in the theory of Markov processes that expresses the expected value of a function of the process at a stopping time in terms of its generator and an integral over time.
- F. None of above.
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_69d80771749c81909a6d9197b9504872 |
completed | April 9, 2026, 8:09 p.m. |
| NER | Named-entity recognition | batch_69d980ee6130819095d835e7ff6a8c5b |
completed | April 10, 2026, 10:59 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69f6d60510dc81909e0cba8b63a50d9c |
completed | May 3, 2026, 4:58 a.m. |
| NEDg | Description generation | batch_69f6dbb4b8848190825102be81ff693a |
completed | May 3, 2026, 5:23 a.m. |
| NED2 | Entity disambiguation (via description) | batch_69f6dc705f28819087e5d374f83d3acc |
completed | May 3, 2026, 5:26 a.m. |
Created at: April 9, 2026, 9 p.m.