Triple

T18495192
Position Surface form Disambiguated ID Type / Status
Subject Hardy inequality E451926 entity
Predicate hasVariant P455 FINISHED
Object Hardy inequality with remainder term E451926 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: Hardy inequality with remainder term | Statement: [Hardy inequality, hasVariant, Hardy inequality with remainder term]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Hardy inequality with remainder term
Context triple: [Hardy inequality, hasVariant, Hardy inequality with remainder term]
  • A. Hardy inequality chosen
    The Hardy inequality is a fundamental result in mathematical analysis that provides bounds on integrals or sums involving a function and its distance from a point, with important applications in functional analysis and partial differential equations.
  • B. Lieb–Thirring inequality
    The Lieb–Thirring inequality is a fundamental result in mathematical physics and analysis that provides bounds on sums of negative eigenvalues of Schrödinger operators, with deep applications to quantum mechanics and stability of matter.
  • C. Morawetz inequalities
    Morawetz inequalities are fundamental energy and decay estimates in the study of partial differential equations, especially wave and dispersive equations, that provide control over the long-time behavior of solutions.
  • D. 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.
  • E. Caffarelli–Kohn–Nirenberg inequalities
    The Caffarelli–Kohn–Nirenberg inequalities are a family of weighted interpolation inequalities in analysis that generalize classical Sobolev and Hardy inequalities and play a key role in the study of partial differential equations and regularity theory.
  • 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_69d8d3855d50819097fc8561b0299dd9 completed April 10, 2026, 10:40 a.m.
NER Named-entity recognition batch_69e532bfeef4819096b2fa28abb662b9 completed April 19, 2026, 7:53 p.m.
NED1 Entity disambiguation (via context triple) batch_6a049acadbf48190b71688c715f36c77 completed May 13, 2026, 3:37 p.m.
Created at: April 10, 2026, 11:35 a.m.