Triple

T11560420
Position Surface form Disambiguated ID Type / Status
Subject Harald Cramér E274126 entity
Predicate knownFor P22 FINISHED
Object 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.
E933485 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: Cramér’s theorem in large deviations | Statement: [Harald Cramér, knownFor, Cramér’s theorem in large deviations]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Cramér’s theorem in large deviations
Context triple: [Harald Cramér, knownFor, Cramér’s theorem in large deviations]
  • A. Lyapunov central limit theorem
    The Lyapunov central limit theorem is a version of the central limit theorem that provides sufficient moment conditions under which the normalized sum of independent (not necessarily identically distributed) random variables converges in distribution to a normal law.
  • B. 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.
  • C. Limit Laws for Sums of Independent Random Variables
    Limit Laws for Sums of Independent Random Variables is a foundational mathematical work that systematically develops the theory of probability limit theorems, including results such as the law of large numbers and central limit behavior for sums of independent random variables.
  • D. 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.
  • E. Kolmogorov zero–one law
    The Kolmogorov zero–one law is a fundamental result in probability theory stating that certain events determined by the tail behavior of independent random variables must have probability either zero or one.
  • 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: Cramér’s theorem in large deviations
Triple: [Harald Cramér, knownFor, Cramér’s theorem in large deviations]
Generated description
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.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Cramér’s theorem in large deviations
Target entity description: 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.
  • A. Lyapunov central limit theorem
    The Lyapunov central limit theorem is a version of the central limit theorem that provides sufficient moment conditions under which the normalized sum of independent (not necessarily identically distributed) random variables converges in distribution to a normal law.
  • B. 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.
  • C. Limit Laws for Sums of Independent Random Variables
    Limit Laws for Sums of Independent Random Variables is a foundational mathematical work that systematically develops the theory of probability limit theorems, including results such as the law of large numbers and central limit behavior for sums of independent random variables.
  • D. 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.
  • E. Kolmogorov zero–one law
    The Kolmogorov zero–one law is a fundamental result in probability theory stating that certain events determined by the tail behavior of independent random variables must have probability either zero or one.
  • 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_69d6aae4dfa48190a3ab0b19a159a3c5 completed April 8, 2026, 7:22 p.m.
NER Named-entity recognition batch_69d88a899d4481909a3bce3147763b51 completed April 10, 2026, 5:28 a.m.
NED1 Entity disambiguation (via context triple) batch_69e6e88b84d48190948243646bb5fd2b completed April 21, 2026, 3:01 a.m.
NEDg Description generation batch_69e6ef951eb881909810b5923385c4c6 completed April 21, 2026, 3:31 a.m.
NED2 Entity disambiguation (via description) batch_69e6f92ed97c819081576add624dcc27 completed April 21, 2026, 4:12 a.m.
Created at: April 8, 2026, 9:37 p.m.