Triple
T100578
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Feynman–Kac formula |
E2031
|
entity |
| Predicate | uses |
P98
|
FINISHED |
| Object |
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.
|
E9112
|
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: Itô calculus | Statement: [Feynman–Kac formula, uses, Itô calculus]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Itô calculus Context triple: [Feynman–Kac formula, uses, Itô calculus]
-
A.
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.
-
B.
Fokker–Planck equation
The Fokker–Planck equation is a partial differential equation that describes the time evolution of the probability density function of a stochastic (random) process, such as Brownian motion.
-
C.
Brownian motion
Brownian motion is the random, jittery movement of microscopic particles suspended in a fluid, whose explanation provided key evidence for the existence of atoms and the molecular nature of matter.
-
D.
Langevin dynamics
Langevin dynamics is a stochastic approach to modeling the motion of particles in a fluid by combining deterministic forces with random thermal fluctuations, often used to simulate Brownian motion and other nonequilibrium processes.
-
E.
Einstein–Smoluchowski relation
The Einstein–Smoluchowski relation is a fundamental equation in statistical physics that links the diffusion coefficient of particles undergoing Brownian motion to their mobility and thermal energy.
- 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: Itô calculus Triple: [Feynman–Kac formula, uses, Itô calculus]
Generated description
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.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Itô calculus Target entity description: 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.
-
A.
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.
-
B.
Fokker–Planck equation
The Fokker–Planck equation is a partial differential equation that describes the time evolution of the probability density function of a stochastic (random) process, such as Brownian motion.
-
C.
Brownian motion
Brownian motion is the random, jittery movement of microscopic particles suspended in a fluid, whose explanation provided key evidence for the existence of atoms and the molecular nature of matter.
-
D.
Langevin dynamics
Langevin dynamics is a stochastic approach to modeling the motion of particles in a fluid by combining deterministic forces with random thermal fluctuations, often used to simulate Brownian motion and other nonequilibrium processes.
-
E.
Einstein–Smoluchowski relation
The Einstein–Smoluchowski relation is a fundamental equation in statistical physics that links the diffusion coefficient of particles undergoing Brownian motion to their mobility and thermal energy.
- 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_69a24d4862f881908cc8b89d3a78031d |
completed | Feb. 28, 2026, 2:04 a.m. |
| NER | Named-entity recognition | batch_69a24ff1a8cc8190843d4c6807cebd09 |
completed | Feb. 28, 2026, 2:16 a.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69a266ee56548190a781e2d0ea7fac2b |
completed | Feb. 28, 2026, 3:54 a.m. |
| NEDg | Description generation | batch_69a2678d1b808190aa9e6451d7945f58 |
completed | Feb. 28, 2026, 3:57 a.m. |
| NED2 | Entity disambiguation (via description) | batch_69a26853ed9881909e55192266bfd0b4 |
completed | Feb. 28, 2026, 4 a.m. |
Created at: Feb. 28, 2026, 2:09 a.m.