Triple

T14314169
Position Surface form Disambiguated ID Type / Status
Subject Bernstein inequalities E354909 entity
Predicate hasVariant P455 FINISHED
Object Bernstein-type concentration inequality E354909 NE FINISHED

How this triple was built (2 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: Bernstein-type concentration inequality | Statement: [Bernstein inequalities, hasVariant, Bernstein-type concentration inequality]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Bernstein-type concentration inequality
Context triple: [Bernstein inequalities, hasVariant, Bernstein-type concentration inequality]
  • A. Chernoff bound
    The Chernoff bound is a probabilistic inequality that gives exponentially decreasing upper bounds on the tail probabilities of sums of independent random variables.
  • B. Chebyshev inequalities
    Chebyshev inequalities are probabilistic bounds that limit how much a random variable’s values can deviate from its mean in terms of its variance.
  • C. 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.
  • D. Bernstein inequalities chosen
    Bernstein inequalities are fundamental results in approximation theory and probability that provide bounds on the derivatives or deviations of functions and random variables under certain smoothness or moment conditions.
  • E. Khinchin–Kahane type inequalities
    Khinchin–Kahane type inequalities are fundamental results in probability and functional analysis that bound moments or norms of random series (often with Rademacher or Gaussian coefficients) in terms of each other, providing powerful tools for studying the geometry of Banach spaces and random processes.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.

Provenance (3 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_69d8278ed42c8190b9f882dcce611347 completed April 9, 2026, 10:26 p.m.
NER Named-entity recognition batch_69de85b49e5481909b9ffab2d922e284 completed April 14, 2026, 6:21 p.m.
NED1 Entity disambiguation (via context triple) batch_69fd4687c6bc819088452892128c420e completed May 8, 2026, 2:12 a.m.
Created at: April 10, 2026, 1:12 a.m.