Triple

T11560422
Position Surface form Disambiguated ID Type / Status
Subject Harald Cramér E274126 entity
Predicate knownFor P22 FINISHED
Object Cramér–Wold theorem
The Cramér–Wold theorem is a fundamental result in probability theory stating that a multivariate distribution is uniquely determined by the distributions of all its one-dimensional linear projections.
E933486 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–Wold theorem | Statement: [Harald Cramér, knownFor, Cramér–Wold theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Cramér–Wold theorem
Context triple: [Harald Cramér, knownFor, Cramér–Wold theorem]
  • A. 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.
  • B. 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.
  • C. Cameron–Martin theorem
    The Cameron–Martin theorem is a fundamental result in probability theory and functional analysis that characterizes how Gaussian measures on infinite-dimensional spaces change under shifts by elements of a special Hilbert subspace (the Cameron–Martin space).
  • D. Lindeberg–Feller central limit theorem
    The Lindeberg–Feller central limit theorem is a general form of the central limit theorem that provides conditions under which sums of independent, not necessarily identically distributed random variables converge in distribution to a normal law.
  • E. Khinchin–Kolmogorov theorem
    The Khinchin–Kolmogorov theorem is a fundamental result in probability theory that provides conditions under which series of independent random variables converge almost surely.
  • 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–Wold theorem
Triple: [Harald Cramér, knownFor, Cramér–Wold theorem]
Generated description
The Cramér–Wold theorem is a fundamental result in probability theory stating that a multivariate distribution is uniquely determined by the distributions of all its one-dimensional linear projections.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Cramér–Wold theorem
Target entity description: The Cramér–Wold theorem is a fundamental result in probability theory stating that a multivariate distribution is uniquely determined by the distributions of all its one-dimensional linear projections.
  • A. 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.
  • B. 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.
  • C. Cameron–Martin theorem
    The Cameron–Martin theorem is a fundamental result in probability theory and functional analysis that characterizes how Gaussian measures on infinite-dimensional spaces change under shifts by elements of a special Hilbert subspace (the Cameron–Martin space).
  • D. Lindeberg–Feller central limit theorem
    The Lindeberg–Feller central limit theorem is a general form of the central limit theorem that provides conditions under which sums of independent, not necessarily identically distributed random variables converge in distribution to a normal law.
  • E. Khinchin–Kolmogorov theorem
    The Khinchin–Kolmogorov theorem is a fundamental result in probability theory that provides conditions under which series of independent random variables converge almost surely.
  • 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.