Triple

T21783463
Position Surface form Disambiguated ID Type / Status
Subject Fefferman–Phong inequality E537775 entity
Predicate relatedTo P37 FINISHED
Object Hardy inequality — 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: Hardy inequality | Statement: [Fefferman–Phong inequality, relatedTo, Hardy inequality]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Hardy inequality
Context triple: [Fefferman–Phong inequality, relatedTo, Hardy inequality]
  • 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. Sobolev inequality
    The Sobolev inequality is a fundamental result in functional analysis and partial differential equations that bounds the size of a function in certain Lebesgue spaces by the size of its derivatives, enabling key embedding and regularity properties.
  • C. 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.
  • 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. Poincaré inequality
    The Poincaré inequality is a fundamental result in functional analysis and partial differential equations that bounds the average oscillation of a function by the size of its gradient, playing a key role in Sobolev space theory and the study of elliptic problems.
  • 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_69e0c47198f881908cb0d237266c10e9 completed April 16, 2026, 11:13 a.m.
NER Named-entity recognition batch_69f0462ed0ec81908833e18c164e8b5c completed April 28, 2026, 5:31 a.m.
Created at: April 16, 2026, 6:52 p.m.