Triple

T6801459
Position Surface form Disambiguated ID Type / Status
Subject Poincaré inequality E156195 entity
Predicate hasVariant P455 FINISHED
Object Poincaré–Wirtinger inequality E156195 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: Poincaré–Wirtinger inequality | Statement: [Poincaré inequality, hasVariant, Poincaré–Wirtinger inequality]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Poincaré–Wirtinger inequality
Context triple: [Poincaré inequality, hasVariant, Poincaré–Wirtinger inequality]
  • A. Poincaré inequality chosen
    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.
  • B. Gagliardo–Nirenberg interpolation inequalities
    The Gagliardo–Nirenberg interpolation inequalities are fundamental results in functional analysis and partial differential equations that bound intermediate norms of functions by combinations of lower and higher order norms, playing a key role in regularity theory and nonlinear analysis.
  • C. Fefferman–Phong inequality
    The Fefferman–Phong inequality is a fundamental result in harmonic analysis and partial differential equations that provides weighted \(L^2\) estimates controlling functions by their gradients and associated potentials.
  • D. Hardy inequality
    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.
  • E. Lyapunov inequality
    The Lyapunov inequality is a fundamental result in stability theory and analysis that provides bounds relating norms or moments of functions or solutions to differential equations, widely used in studying the stability of dynamical systems.
  • 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_69c68826e6a48190a3d220b541e639de completed March 27, 2026, 1:37 p.m.
NER Named-entity recognition batch_69c6d2e595188190a0bb4b595df3adb2 completed March 27, 2026, 6:56 p.m.
NED1 Entity disambiguation (via context triple) batch_69c71a9b0cc48190819380aeaf0228e7 completed March 28, 2026, 12:02 a.m.
Created at: March 27, 2026, 2:16 p.m.