Triple

T18479174
Position Surface form Disambiguated ID Type / Status
Subject Chebyshev inequalities E451512 entity
Predicate isSpecialCaseOf P2372 FINISHED
Object Markov inequality — NE NERFINISHED

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: Markov inequality | Statement: [Chebyshev inequalities, isSpecialCaseOf, Markov inequality]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Markov inequality
Context triple: [Chebyshev inequalities, isSpecialCaseOf, Markov inequality]
  • A. Chebyshev inequalities chosen
    Chebyshev inequalities are probabilistic bounds that limit how much a random variable’s values can deviate from its mean in terms of its variance.
  • B. Azuma–Hoeffding inequality
    The Azuma–Hoeffding inequality is a concentration inequality that bounds the probability of large deviations for martingales with bounded differences, generalizing Hoeffding’s inequality to dependent sequences.
  • C. Bennett inequality
    Bennett inequality is a probabilistic bound that provides exponential tail estimates for sums of independent random variables, refining classical concentration inequalities like Bernstein’s.
  • D. 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.
  • E. Karamata's inequality
    Karamata's inequality is a fundamental result in majorization theory that generalizes several classical inequalities by comparing sums of convex (or concave) functions over majorized sequences.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.

Provenance (2 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_69d8d38465a0819099b9b42d2a662ac1 completed April 10, 2026, 10:40 a.m.
NER Named-entity recognition batch_69e53065e8388190bb216dae89f8cf75 completed April 19, 2026, 7:43 p.m.
Created at: April 10, 2026, 11:35 a.m.