Triple
T18479169
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Chebyshev inequalities |
E451512
|
entity |
| Predicate | alsoKnownAs |
P39
|
FINISHED |
| Object | Chebyshev–Cantelli inequalities |
—
|
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: Chebyshev–Cantelli inequalities | Statement: [Chebyshev inequalities, alsoKnownAs, Chebyshev–Cantelli inequalities]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Chebyshev–Cantelli inequalities Context triple: [Chebyshev inequalities, alsoKnownAs, Chebyshev–Cantelli inequalities]
-
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.
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.
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.
-
E.
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.
- 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.