Triple

T21972875
Position Surface form Disambiguated ID Type / Status
Subject Daniel Stroock E542634 entity
Predicate notableWork P4 FINISHED
Object An Introduction to the Theory of Large Deviations
"An Introduction to the Theory of Large Deviations" is a mathematical monograph that systematically develops the probabilistic theory of large deviations, focusing on rigorous asymptotic analysis of rare events.
E1511328 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: An Introduction to the Theory of Large Deviations | Statement: [Daniel Stroock, notableWork, An Introduction to the Theory of Large Deviations]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: An Introduction to the Theory of Large Deviations
Context triple: [Daniel Stroock, notableWork, An Introduction to the Theory of Large Deviations]
  • A. Cramér’s theorem in large deviations
    Cramér’s theorem in large deviations is a fundamental result in probability theory that characterizes the exponential decay rate of tail probabilities for sums of independent, identically distributed random variables via a convex rate function.
  • B. Freidlin–Wentzell theory
    Freidlin–Wentzell theory is a mathematical framework in probability that analyzes the behavior of stochastic dynamical systems under small random perturbations using large deviation principles.
  • C. Modern Probability Theory and Its Applications
    "Modern Probability Theory and Its Applications" is a foundational textbook by Emanuel Parzen that systematically develops modern probability theory and demonstrates its use in a wide range of statistical and applied contexts.
  • D. Introduction to Stochastic Control Theory
    Introduction to Stochastic Control Theory is a foundational textbook that systematically develops the theory and methods for controlling dynamical systems under uncertainty using probabilistic and stochastic-process tools.
  • E. Kolmogorov's law of the iterated logarithm
    Kolmogorov's law of the iterated logarithm is a fundamental result in probability theory that precisely characterizes the almost-sure fluctuations of partial sums of independent random variables between the law of large numbers and the central limit theorem.
  • 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: An Introduction to the Theory of Large Deviations
Triple: [Daniel Stroock, notableWork, An Introduction to the Theory of Large Deviations]
Generated description
"An Introduction to the Theory of Large Deviations" is a mathematical monograph that systematically develops the probabilistic theory of large deviations, focusing on rigorous asymptotic analysis of rare events.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: An Introduction to the Theory of Large Deviations
Target entity description: "An Introduction to the Theory of Large Deviations" is a mathematical monograph that systematically develops the probabilistic theory of large deviations, focusing on rigorous asymptotic analysis of rare events.
  • A. Cramér’s theorem in large deviations
    Cramér’s theorem in large deviations is a fundamental result in probability theory that characterizes the exponential decay rate of tail probabilities for sums of independent, identically distributed random variables via a convex rate function.
  • B. Freidlin–Wentzell theory
    Freidlin–Wentzell theory is a mathematical framework in probability that analyzes the behavior of stochastic dynamical systems under small random perturbations using large deviation principles.
  • C. Modern Probability Theory and Its Applications
    "Modern Probability Theory and Its Applications" is a foundational textbook by Emanuel Parzen that systematically develops modern probability theory and demonstrates its use in a wide range of statistical and applied contexts.
  • D. Introduction to Stochastic Control Theory
    Introduction to Stochastic Control Theory is a foundational textbook that systematically develops the theory and methods for controlling dynamical systems under uncertainty using probabilistic and stochastic-process tools.
  • E. Kolmogorov's law of the iterated logarithm
    Kolmogorov's law of the iterated logarithm is a fundamental result in probability theory that precisely characterizes the almost-sure fluctuations of partial sums of independent random variables between the law of large numbers and the central limit theorem.
  • 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_69e0c48070988190909db97667b9a0ac completed April 16, 2026, 11:14 a.m.
NER Named-entity recognition batch_69f124857dcc8190ab474cd8ab9c130a completed April 28, 2026, 9:20 p.m.
NED1 Entity disambiguation (via context triple) batch_6a0a6718c3fc8190bd74e5085e4d3b8b completed May 18, 2026, 1:10 a.m.
NEDg Description generation batch_6a0a67910f0081908d3d4771be0fb167 completed May 18, 2026, 1:12 a.m.
NED2 Entity disambiguation (via description) batch_6a0a68038d148190a9b2811f23fa802e completed May 18, 2026, 1:14 a.m.
Created at: April 16, 2026, 8:02 p.m.