Triple

T3677826
Position Surface form Disambiguated ID Type / Status
Subject Aleksandr Khinchin E78037 entity
Predicate notableWork P4 FINISHED
Object 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.
E378997 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: Khinchin–Pollaczek formula | Statement: [Aleksandr Khinchin, notableWork, Khinchin–Pollaczek formula]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Khinchin–Pollaczek formula
Context triple: [Aleksandr Khinchin, notableWork, Khinchin–Pollaczek formula]
  • 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. 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.
  • C. Chapman–Kolmogorov equation
    The Chapman–Kolmogorov equation is a fundamental relation in the theory of stochastic processes that expresses how transition probabilities of a Markov process over longer time intervals can be obtained by integrating over intermediate states.
  • D. Berry–Esseen theorem
    The Berry–Esseen theorem is a quantitative refinement of the central limit theorem that provides explicit bounds on the rate of convergence of normalized sums of independent random variables to the normal distribution.
  • E. Isserlis’ theorem in probability theory
    Isserlis’ theorem in probability theory is a result that expresses higher-order moments of jointly Gaussian random variables in terms of sums of products of their pairwise covariances.
  • 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: Khinchin–Pollaczek formula
Triple: [Aleksandr Khinchin, notableWork, Khinchin–Pollaczek formula]
Generated description
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.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Khinchin–Pollaczek formula
Target entity description: 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.
  • 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. 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.
  • C. Chapman–Kolmogorov equation
    The Chapman–Kolmogorov equation is a fundamental relation in the theory of stochastic processes that expresses how transition probabilities of a Markov process over longer time intervals can be obtained by integrating over intermediate states.
  • D. Berry–Esseen theorem
    The Berry–Esseen theorem is a quantitative refinement of the central limit theorem that provides explicit bounds on the rate of convergence of normalized sums of independent random variables to the normal distribution.
  • E. Isserlis’ theorem in probability theory
    Isserlis’ theorem in probability theory is a result that expresses higher-order moments of jointly Gaussian random variables in terms of sums of products of their pairwise covariances.
  • 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_69ad85e18c1c8190be8aafb227f39f48 completed March 8, 2026, 2:21 p.m.
NER Named-entity recognition batch_69adc4643cf08190b2d10ddf4aac7407 completed March 8, 2026, 6:48 p.m.
NED1 Entity disambiguation (via context triple) batch_69b4c3a50d40819081aad0c72bcaee9d completed March 14, 2026, 2:10 a.m.
NEDg Description generation batch_69b4c451a5048190bfd4675cd17de655 completed March 14, 2026, 2:13 a.m.
NED2 Entity disambiguation (via description) batch_69b4c494ad80819084d6aa10fe62a63b completed March 14, 2026, 2:14 a.m.
Created at: March 8, 2026, 3:25 p.m.