Triple

T12597190
Position Surface form Disambiguated ID Type / Status
Subject Mertens’ theorems E300762 entity
Predicate relatedTo P37 FINISHED
Object Chebyshev’s theorems E451512 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: Chebyshev’s theorems | Statement: [Mertens’ theorems, relatedTo, Chebyshev’s theorems]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Chebyshev’s theorems
Context triple: [Mertens’ theorems, relatedTo, Chebyshev’s theorems]
  • 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. 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. Chebyshev’s sum inequality
    Chebyshev’s sum inequality is a mathematical inequality that provides bounds on the sum of products of similarly ordered sequences, widely used in analysis and probability theory.
  • 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. Turán–Kubilius inequality
    The Turán–Kubilius inequality is a fundamental result in probabilistic number theory that provides bounds on the distribution of additive arithmetic functions.
  • 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_69d7bdea2ca881908f379526c13b1145 completed April 9, 2026, 2:55 p.m.
NER Named-entity recognition batch_69d954cf33b88190bff339fcd3142cc8 completed April 10, 2026, 7:51 p.m.
NED1 Entity disambiguation (via context triple) batch_69f65ec75fc08190aa13cbb0161eb35c completed May 2, 2026, 8:29 p.m.
Created at: April 9, 2026, 5:08 p.m.