Triple

T736586
Position Surface form Disambiguated ID Type / Status
Subject Minkowski inequality E14946 entity
Predicate dependsOn P100 FINISHED
Object Hölder inequality E87726 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: Hölder inequality | Statement: [Minkowski inequality, dependsOn, Hölder inequality]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Hölder inequality
Context triple: [Minkowski inequality, dependsOn, Hölder inequality]
  • A. Hölder inequality chosen
    Hölder inequality is a fundamental result in mathematical analysis that generalizes the Cauchy–Schwarz inequality and provides bounds for integrals or sums of products in Lᵖ spaces.
  • B. Minkowski inequality
    The Minkowski inequality is a fundamental result in functional analysis and measure theory that generalizes the triangle inequality to L^p spaces, providing a key tool for studying norms and integrable functions.
  • C. Jensen inequality
    Jensen's inequality is a fundamental result in convex analysis and probability theory that relates the value of a convex (or concave) function of an expectation to the expectation of the function, providing bounds that underlie many other inequalities and convergence results.
  • D. 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.
  • E. 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.
  • 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_69a4934d9930819099eed80096b0597d completed March 1, 2026, 7:28 p.m.
NER Named-entity recognition batch_69a4a5da30b88190afbd12ae6109cc1b completed March 1, 2026, 8:47 p.m.
NED1 Entity disambiguation (via context triple) batch_69a65e3df8e48190905f89acbf7f3667 completed March 3, 2026, 4:06 a.m.
Created at: March 1, 2026, 7:37 p.m.