Triple

T20471096
Position Surface form Disambiguated ID Type / Status
Subject Hermite constant E502193 entity
Predicate usedFor P98 FINISHED
Object Minkowski-type 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: Minkowski-type inequalities | Statement: [Hermite constant, usedFor, Minkowski-type inequalities]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Minkowski-type inequalities
Context triple: [Hermite constant, usedFor, Minkowski-type inequalities]
  • A. Minkowski inequality chosen
    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.
  • B. Meyer inequalities
    Meyer inequalities are fundamental estimates in Malliavin calculus that relate Sobolev-type norms of random variables to norms involving iterated Malliavin derivatives, playing a key role in regularity and integrability results on Wiener space.
  • C. Hardy–Littlewood–Pólya inequality
    The Hardy–Littlewood–Pólya inequality is a fundamental result in majorization theory and inequalities that characterizes how convex functions behave under rearrangements of sequences or vectors.
  • D. Maclaurin’s inequality in symmetric means
    Maclaurin’s inequality in symmetric means is a classical result in mathematical analysis that relates and bounds the sequence of elementary symmetric means of a set of nonnegative real numbers, showing they form a decreasing sequence.
  • E. Korn inequality
    Korn inequality is a fundamental result in functional analysis and the mathematical theory of elasticity that provides bounds relating the full gradient of a vector field to its symmetric part, ensuring control of deformations by their strains.
  • 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_69e0b4ae5f1081908768b0c9a3a0bf38 completed April 16, 2026, 10:06 a.m.
NER Named-entity recognition batch_69e699608d7c8190910217817e789915 completed April 20, 2026, 9:23 p.m.
Created at: April 16, 2026, 11:33 a.m.